Publikationsliste
Institut für Analysis und Numerik
Publikationen
Veröffentlicht
- Maggiorelli, Eleonora, Riva, Filippo, und Tolotti, Giovanni Edoardo. . „A free boundary approach to the quasistatic evolution of debonding models.“ Mathematical Models and Methods in Applied Sciences Online. doi: 10.1142/S0218202526500363.
- Seis, Christian, und Winkler, Dominik. . „Stability of traveling waves for doubly nonlinear equations.“ Tunisian Journal of Mathematics 8 (1): 157–170. doi: 10.2140/tunis.2026.8.157.
- Seis, Christian, Wiedemann, Emil, und Woźnicki, Jakub. . „Strong convergence of vorticities in the 2D viscosity limit on a bounded domain.“ Preprint. Journal of Nonlinear Science 36 (22). doi: 10.1007/s00332-026-10239-x.
- Navarro-Fernández, Víctor, und Seis, Christian. . „Exponential mixing by random cellular flows.“ Journal of Functional Analysis 290 (2). doi: 10.1016/j.jfa.2025.111227.
- Klein, Benedikt, und Ohlberger, Mario. . „Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization.“ Advances in Computational Mathematics 52 (19): 1–36. doi: 10.1007/s10444-026-10296-6.
- Seis, Christian. . „Infinite Prandtl number convection with Navier-slip boundary conditions.“ Preprint. Communications in Mathematical Physics 407 (125). doi: 10.1007/s00220-026-05637-x.
- Scheel, Arnd, und Stevens, Angela. . „Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing.“ SIAM Journal on Applied Dynamical Systems 25 (3): 2022–2043. doi: 10.1137/25M177744X.
- Wirth, Benedikt. . „Convergence of spectral discretization for the flow of diffeomorphisms.“ Preprint. Numerische Mathematik tba. doi: 10.1007/s00211-026-01538-2.
- Chandra, A., de, Lima Feltes G., und Weber, H. . „A priori bounds for the generalised parabolic Anderson model.“ Communications on Pure and Applied Mathematics 79 (5): 1315–1394. doi: 10.1002/cpa.70025.
accepted / in Press (not yet published)
- Gander, Martin J, Ohlberger, Mario, und Rave, Stephan. im Druck. „A Parareal algorithm without Coarse Propagator?“ Preprint. In Domain Decomposition Methods in Science and Engineering XXVIII, Bd. 155 aus Lecture Notes in Computational Science and Engineering, herausgegeben von Petter Bjørstad, Xiao-Chuan Cai, Victorita Dolean, David E. Keyes, Ralf Kornhuber, Jinchao Xu und Xiao-Chuan Cai. Cham: Springer Publishing. doi: 10.48550/arXiv.2409.02673.
Eingereicht / In Begutachtung
- Klein, Benedikt, Ohlberger, Mario, und Schuster, Thomas. . „Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials.“ Preprint. arXiv doi: 10.48550/arXiv.2605.19896.
- Kotowski, Dawid, und Ohlberger, Mario. . „A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications.“ Preprint. arXiv doi: 10.48550/arXiv.2604.22512.
- Kabanov, Dmitry I., Rave, Stephan, und Ohlberger, Mario. . „MaRDI Open Interfaces for Interoperable Nonlinear Optimization.“ Preprint. arXiv doi: 10.48550/arXiv.2606.20410.
- Kabanov, Dmitry I., Rave, Stephan, und Ohlberger, Mario. . „Software package MaRDI Open Interfaces for improved interoperability in numerical optimization.“ Preprint. arXiv doi: 10.48550/arXiv.2606.20490.
Veröffentlicht
- Kartmann, Michael, Klein, Benedikt, Ohlberger, Mario, Schuster, Thomas, und Volkwein, Stefan. . „Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems.“ Inverse Problems 41 (12): 1–36. doi: 10.1088/1361-6420/ae2a66.
- Marquardt, N, Hengsbach, T, Mauritz, M, Wirth, B, und Schäfers, K. . „Motion simulation of radio-labeled cells in whole-body positron emission tomography.“ IEEE Transactions on Medical Imaging 45 (3): 919–930. doi: 10.1109/TMI.2025.3614767.
- Kleikamp, Hendrik, und Renelt, Lukas. . „Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems.“ Journal of Scientific Computing 104 (78). doi: 10.1007/s10915-025-02988-w.
- Mori, Y., Perthame, B., und Stevens, A., Hrsg. . Lecture Notes on Mathematical Modelling in the Life Sciences, Bd. 1, Dynamics of Physiological Control. Contributions in Honor of Michael C. Mackey Cham, Switzerland: Springer. doi: 10.1007/978-3-031-82396-1.
- Budde, Ilka, Schlichting, André, Ing, David, Schimmelpfennig, Sandra, Kuntze, Anna, Fels, Benedikt, Romac, Joelle M.-J., Swain, Sandip M., Liddle, Rodger A., Stevens, Angela, Schwab, Albrecht, und Pethő, Zoltán. . „Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels.“ Journal of Cell Science online first. doi: 10.1242/jcs.263846.
- Kleikamp, Hendrik, Lazar, Martin, und Molinari, Cesare. . „Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems.“ Preprint. ESAIM: Mathematical Modelling and Numerical Analysis 59 (1): 291–330. doi: 10.1051/m2an/2024074.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Schmidt, Burkhard, Shehu, Aurela, Reidelbach, Marco, Biedinger, Christine, Fiedler, Jochen, Koprucki, Thomas, Iglezakis, Dorothea, und Göddeke, Dominik. . „Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics.“ In Proceedings of the 18th International Conference on Metadata and Semantics Research 2024, Communications in Computer and Information Science, herausgegeben von Michalis Sfakakis, Emmanouel Garoufallou, Matthew Damigos, Athena Salaba und Christos Papatheodorou. Cham: Springer. doi: 10.1007/978-3-031-81974-2_8.
- Kleikamp, Hendrik, und Ohlberger, Mario. . „Adaptive Model Hierarchies for Multi-Query Scenarios.“ Preprint. In MATHMOD 2025 - Discussion Contribution Volume, herausgegeben von Andreas Körner, Andreas Kugi, Wolfgang Kemmetmüller, Andreas Deutschmann-Olek, Andreas Steinböck, Christian Hartl-Nesic und Lukasz Piotr Jadachowski. Wien: ARGESIM Verlag. doi: 10.34726/9007.
- Song, Chunqiu, Weber, Hendrik, und Wulkenhaar, Raimar. . „Stochastic quantization of λϕ^4_2-theory in 2-d Moyal space.“ Preprint. arXiv doi: 10.48550/arXiv.2502.02355.
- Lazzaroni, Giuliano; Wozniak, Piotr; Zeppieri, Caterina Ida. . „Strong approximation of special functions of bounded variation functions with prescribed jump direction.“ Mathematical News / Mathematische Nachrichten 298 (1): 312–327. doi: 10.1002/mana.202300346.
- Mauritz, Marco, und Wirth, Benedikt. . „Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction.“ Inverse Problems 41 035002. doi: 10.1088/1361-6420/ada97a.
- Meyer, David, Niebel, Lukas, und Seis, Christian. . „Steady bubbles and drops in inviscid fluids.“ Calculus of Variations and Partial Differential Equations 64 (299). doi: 10.1007/s00526-025-03144-w.
- Klein, Benedikt, und Ohlberger, Mario. . „A Trust Region RB-ML-ROM Approach for Parabolic PDE Constrained Optimization.“ Preprint. In MATHMOD 2025 - Discussion Contribution Volume, herausgegeben von Andreas Körner, Andreas Kugi, Wolfgang Kemmetmüller, Andreas Deutschmann-Olek, Andreas Steinböck, Christian Hartl-Nesic und Lukasz Piotr Jadachowski. Wien: ARGESIM Verlag. doi: 10.34726/9000.
- Kabanov, Dmitry I., Rave, Stephan, und Ohlberger, Mario. . „Improving Interoperability in Scientific Computing via MaRDI Open Interfaces.“ Journal of Open Research Software 13 (1) 29. doi: 10.5334/jors.569.
- Dzikonski, Dustin, Bekker, Elena, Zamboni, Riccardo, Ciechanska, Dominika, Schwab, Albrecht, Denz, Cornelia, und Imbrock, Jörg. . „Hybrid Microfluidic Chip Design with Two-Photon Polymerized Protein-Based Hydrogel Microstructures for Single Cell Experiments.“ Advanced Materials Technologies 10 2401571 . doi: 10.1002/admt.202401571.
- Huang, Ruojun, Matetski, Konstantin, und Weber, Hendrik. . „Scaling limit of a weakly asymmetric simple exclusion process in the framework of regularity structures.“ Preprint. arXiv doi: 10.48550/arXiv.2505.00621.
- Stevens, A. . „Laudatio zur Verleihung der Georg-Cantor-Medaille an Felix Otto.“ Mitteilungen der Deutschen Mathematiker-Vereinigung 33 (1): 7–9. doi: 10.1515/dmvm-2025-0006.
- Bauerschmidt, Roland, Dagallier, Benoit, und Weber, Hendrik. . „Holley--Stroock uniqueness method for the φ42 dynamics.“ Preprint. arXiv doi: 10.48550/arXiv.2504.08606.
- Tempelmayr, Markus, und Weber, Hendrik. . „A priori bounds for stochastic porous media equations via regularity structures.“ Preprint. arXiv doi: 10.48550/arXiv.2507.03575.
- Bourne, David, Schmitzer, Bernhard, und Wirth, Benedikt. . „Semi-discrete unbalanced optimal transport and quantization.“ Preprint. European Journal of Applied Mathematics FirstView: 1–43. doi: 10.1017/S0956792525100144.
- Kunisch, Manuel, Beutler, Sascha, Pilger, Christian, Kiefer, Friedemann, Huser, Thomas, und Wirth, Benedikt. . „Active Axial Motion Compensation in Multiphoton-Excited Fluorescence Microscopy.“ Optics Express 33 (2): 3620–3636. doi: 10.1364/OE.547244.
- Lohmann, Julius, Schmitzer, Bernhard, und Wirth, Benedikt. . „Formulas for the h-mass on 1-currents with coefficients in R^m.“ Calculus of Variations and Partial Differential Equations 64 288. doi: 10.1007/s00526-025-03151-x.
- Tolotti, Giovanni Edoardo. . „On the Hierarchy of Plate Models for a Singularly Perturbed Multi-Well Nonlinear Elastic Energy.“ Preprint. Journal of Nonlinear Science 35 77. doi: 10.1007/s00332-025-10174-3.
- Tolotti, Giovanni Edoardo. . „Stability of the Von Kármán regime for thin plates under Neumann boundary conditions.“ Preprint. ESAIM: Control, Optimisation and Calculus of Variations 31 61. doi: 10.1051/cocv/2025050.
Eingereicht / In Begutachtung
- Engwer, Christian, Ohlberger, Mario, und Renelt, Lukas. . „Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems.“ Preprint. arXiv doi: 10.48550/arXiv.2507.00678.
- Gander, Martin J, Ohlberger, Mario, und Rave, Stephan. . „A Parareal Algorithm with Spectral Coarse Solver.“ Preprint. arXiv doi: 10.48550/arXiv.2508.08873.
Veröffentlicht
- Otto, Felix, Sauer, Jonas, Smith, Scott, und Weber, Hendrik. . „A priori bounds for quasi-linear SPDEs in the full sub-critical regime.“ Journal of the European Mathematical Society 27: 71–118. doi: 10.4171/jems/1574.
- Esquivel Calzada, Salvador Cesar, und Weber, Hendrik. . „A priori bounds for the dynamic fractional Φ4 model on T3 in the full subcritical regime.“ Preprint. arXiv e-prints
- Engwer, Christian, Ohlberger, Mario, und Renelt, Lukas. . „Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems.“ SIAM Journal on Scientific Computing 46 (5): A3205–A3229. doi: 10.1137/23M1613402.
- Kartmann, Michael, Keil, Tim, Ohlberger, Mario, Volkwein, Stephan, und Kaltenbacher, Barbara. . „Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems.“ Computational Science and Engineering 1 (3): 1–30. doi: 10.1007/s44207-024-00002-z.
- Engwer, Christian, Ohlberger, Mario, und Renelt, Lukas. . „Construction of local reduced spaces for Friedrichs' systems via randomized training.“ Beitrag präsentiert auf der Central-European Conference on Scientific Computing, ALGORITMY, Podbanské
- Budde, Ilka, Schlichting, André, Ing, David, Schimmelpfennig, Sandra, Kuntze, Anna, Fels, Benedikt, Romac, Joelle M.-J., Swain, Sandip M., Liddle, Rodger A., Stevens, Angela, Schwab, Albrecht, und Pethő, Zoltán. . „Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels.“ Preprint. bioRxiv Cold Spring Harbor Laboratory. doi: 10.1101/2023.12.22.572956.
- Kleikamp, Hendrik. . „Application of an adaptive model hierarchy to parametrized optimal control problems.“ Preprint. In Proceedings of the Conference Algoritmy 2024, herausgegeben von P. Frolkovič und K.Mikula and D. Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
- de Lima Feltes, Guilherme, und Weber, Hendrik. . „Brownian particle in the curl of 2-d stochastic heat equations.“ Preprint. Journal of Statistical Physics 191 16. doi: 10.1007/s10955-023-03224-1.
- Keil, Tim, und Ohlberger, Mario. . „A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems.“ ESAIM: Mathematical Modelling and Numerical Analysis 58: 79–105. doi: 10.1051/m2an/2023089.
- Meyer, David, und Seis, Christian. . „Propagation of regularity for transport equations. A Littlewood-Paley approach.“ Preprint. Indiana University Mathematics Journal 73 (2): 445–473.
- Ceci, Stefano, und Seis, Christian. . „On the dynamics of vortices in viscous 2D flows.“ Preprint. Mathematische Annalen 388: 1937–1967. doi: 10.1007/s00208-023-02568-z.
- Seis, Christian, und Winkler, Dominik. . „Invariant Manifolds for the Thin Film Equation.“ Preprint. Archive for Rational Mechanics and Analysis 248 (2). doi: 10.1007/s00205-024-01968-y.
- Wenzel, Tizian, Haasdonk, Bernard, Kleikamp, Hendrik, Ohlberger, Mario, und Schindler, Felix. . „Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.“ Preprint. In Large-Scale Scientific Computations, Bd. 13952 aus Lecture Notes in Computer Science, herausgegeben von I. Lirkov und S. Margenov. Cham: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- Keil, Tim, Ohlberger, Mario, und Schindler, Felix. . „Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.“ Preprint. In Large-Scale Scientific Computations, Bd. 13952 aus Lecture Notes in Computer Science, herausgegeben von I Lirkov und S Margenov. Cham: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
- Baumann, Lena, und Pirner, Marlies. . „Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions.“ In Hyperbolic Problems: Theory, Numerics, Applications. Volume II : HYP2022, Málaga, Spain, June 20-24, 2022, Bd. 35 aus SEMA SIMAI Springer Series, herausgegeben von Carlos Parés, Manuel Castro, Tomas Morales de Luna und Maria Luz Muñoz-Ruiz. Cham: Springer Nature. doi: 10.1007/978-3-031-55264-9_22.
- Choi, Beomjun, und Seis, Christian. . „Finite-dimensional leading order dynamics for the fast diffusion equation near extinction.“ Preprint. Discrete and Continuous Dynamical Systems - Series A 44 (9): 2697–2712. doi: 10.3934/dcds.2024043.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Biedinger, Christine, Fiedler, Jochen, Reidelbach, Marco, Shehu, Aurela, Schmidt, Burkhard, Koprucki, Thomas, Iglezakis, Dorothea, und Göddeke, Dominik. . „Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines.“ In Metadata and Semantic Research - 17th Research Conference, MTSR 2023, Milan, Italy, October 25–27, 2023, Revised Selected Papers, Bd. 2048 aus Communications in Computer and Information Science, herausgegeben von Emmanouel Garoufallou und Fabio Sartori. Cham: Springer. doi: 10.1007/978-3-031-65990-4_14.
- Seis, Christian, und Winkler, Dominik. . „Fine large-time asymptotics for the axisymmetric Navier-Stokes equations.“ Preprint. Journal of Evolution Equations 24 72. doi: 10.1007/s00028-024-01001-5.
- Holler, Martin, und Wirth, Benedikt. . „Exact reconstruction and reconstruction from noisy data with anisotropic total variation.“ SIAM Journal on Mathematical Analysis 56 (3): 2938–2967. doi: 10.1137/22M1508571.
- Braunsmann, Juliane, Rajković, Marko, Rumpf, Martin, und Wirth, Benedikt. . „Convergent Autoencoder Approximation of Low Bending and Low Distortion Manifold Embeddings.“ ESAIM: Mathematical Modelling and Numerical Analysis 58 (1): 335–361. doi: 10.1051/m2an/2023088.
- Chevyrev, I., Gerasimovičs, A., und Weber, H. . „Feature Engineering with Regularity Structures.“ Journal of Scientific Computing 98 (13). doi: 10.1007/s10915-023-02401-4.
- Esposito, A, Patacchini, FS, und Schlichting, A. . „On a Class of Nonlocal Continuity Equations on Graphs.“ European Journal of Applied Mathematics 35 (1): 109–126. doi: 10.1017/S0956792523000128.
- Holler, Martin, Schlüter, Alexander, und Wirth, Benedikt. . „Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space.“ Applied and Computational Harmonic Analysis 70 101631. doi: 10.1016/j.acha.2024.101631.
- Chandra, Ajay, de Lima Feltes, Guilherme, und Weber, Hendrik. . „A priori bounds for 2-d generalised Parabolic Anderson Model.“ Preprint. arXiv doi: 10.48550/arXiv.2402.05544.
- de Nitti, Nicola, Meyer, David, und Seis, Christian. . „Optimal Regularity for the 2D Euler Equations in the Yudovich class.“ Preprint. Journal de Mathématiques Pures et Appliquées 191. doi: 10.1016/j.matpur.2024.103631.
- Pirner, Marlies. . „A consistent kinetic Fokker-Planck model for gas mixtures.“ Journal of Statistical Physics 191 (11) 143. doi: 10.1007/s10955-024-03361-1.
- Singh, A, Thale, S, Leibner, T, Lamparter, L, Ricker, A, Nüsse, H, Klingauf, J, Galic, M, Ohlberger, M, und Matis, M. . „Dynamic interplay of microtubule and actomyosin forces drive tissue extension.“ Nature Communications 15 (1): 3198–3198. doi: 10.1038/s41467-024-47596-8.
- Tim, Keil, Mario, Ohlberger, Felix, Schindler, und Julia, Schleuß. . „Local training and enrichment based on a residual localization strategy.“ Preprint. In Proceedings of the Conference Algoritmy 2024, Bd. 8 aus Proceedings of the Conference Algoritmy, herausgegeben von P Frolkovič, K Mikula und D Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
- Mauritz, Marco, Schmitzer, Bernhard, und Wirth, Benedikt. . „A Bayesian model for dynamic mass reconstruction from PET listmode data.“ SIAM Journal on Mathematical Analysis 56 (5): 5840–5880. doi: 10.1137/23M161923X.
- Grazieschi, Paolo, Matetski, Konstantin, und Weber, Hendrik. . „The dynamical Ising-Kac model in 3D converges to Φ4/3.“ Probability Theory and Related Fields 190 (1-2). doi: 10.1007/s00440-024-01316-x.
- Grazieschi, Paolo, Matetski, Konstantin, und Weber, Hendrik. . „Martingale-driven integrals and singular SPDEs.“ Preprint. Probability Theory and Related Fields 190: 1063–1120. doi: 10.1007/s00440-024-01311-2.
- Balduf, P, und Thürigen, J. . „Primitive asymptotics in $\phi^4$ vector theory.“ Preprint. arXiv.org doi: 10.48550/arXiv.2412.08617.
- Ben Achour, J, Benedetti, D, Bojowald, M, Brandenberger, R, Butera, S, Ferrero, R, Giacomini, F, Giesel, K, Goeller, C, Haas, T, Höhn, P, Kirklin, J, Marchetti, L, Oriti, D, Percacci, R, Pereira, A, Pithis, A, Sakellariadou, M, Steinhaus, S, und Thürigen, J. . „Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives.“ General Relativity and Gravitation 57 2. doi: 10.1007/s10714-024-03335-4.
Eingereicht / In Begutachtung
- Kleikamp, Hendrik, und Wenzel, Tizian. . „Kernel Methods in the Deep Ritz framework: Theory and practice.“ Preprint. arXiv doi: 10.48550/arXiv.2410.03503.
- Fischer, J, Hensel, S, Laux, T, und Simon, T.M. . „A weak-strong uniqueness principle for the Mullins-Sekerka equation.“ Preprint. arXiv doi: 10.48550/arXiv.2404.02682.
- Muratov, C.B., Simon, T.M., und Slastikov, V.V. . „Existence of higher degree minimizers in the magnetic skyrmion problem.“ Preprint. arXiv doi: 10.48550/arXiv.2409.07205.
Veröffentlicht
- Boussange, V., Becker, S., Jentzen, A., Kuckuck, B., und Pellissier, L. . „Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions.“ Preprint. SN Partial Differential Equations and Applications 4 51. doi: 10.1007/s42985-023-00244-0.
- Renelt, Lukas, Ohlberger, Mario, und Engwer, Christian. . „An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.“ Preprint. In Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, Springer Proceedings in Mathematics & Statistics, herausgegeben von Emmanuel Franck, Jürgen Fuhrmann, Michel-Dansac Victor und Laurent Navoret. Cham: Springer. doi: 10.1007/978-3-031-40860-1_30.
- Friedrich, Manuel, und Machill, Lennart. . „One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.“ Preprint. Calculus of Variations and Partial Differential Equations 62 (7) 190. doi: 10.1007/s00526-023-02525-3.
- Haasdonk, B, Kleikamp, H, Ohlberger, M, Schindler, F, und Wenzel, T. . „A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.“ SIAM Journal on Scientific Computing 45 (3): A1039–1065. doi: 10.1137/22M1493318.
- Chandra, Ajay, Moinat, Augustin, und Weber, Hendrik. . „A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime.“ Archive for Rational Mechanics and Analysis 247 (3) 48. doi: 10.1007/s00205-023-01876-7.
- Eberle, Simon, Jentzen, Arnulf, Riekert, Adrian, und Weiss, Georg S. . „Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation.“ Electronic Research Archive 31 (5): 2519–2554. doi: 10.3934/era.2023128.
- Hahn, Tim, Jamalabadi, Hamidreza, Nozari, Erfan, Winter, Nils R., Ernsting, Jan, Gruber, Marius, Mauritz, Marco J., Grumbach, Pascal, Fisch, Lukas, Leenings, Ramona, Sarink, Kelvin, Blanke, Julian, Vennekate, Leon Kleine, Emden, Daniel, Opel, Nils, Grotegerd, Dominik, Enneking, Verena, Meinert, Susanne, Borgers, Tiana, Klug, Melissa, Leehr, Elisabeth J., Dohm, Katharina, Heindel, Walter, Gross, Joachim, Dannlowski, Udo, Redlich, Ronny, und Repple, Jonathan. . „Towards a network control theory of electroconvulsive therapy response.“ PNAS Nexus 2 (2). doi: 10.1093/pnasnexus/pgad032.
- Beck, C, Hutzenthaler, M, Jentzen, A, und Kuckuck, B. . „An overview on deep learning-based approximation methods for partial differential equations.“ Discrete and Continuous Dynamical Systems - Series B 28 (6): 3697–3746. doi: 10.3934/dcdsb.2022238.
- Choi, Beomjun, McCann, Robert J., und Seis, Christian. . „Asymptotics near extinction for nonlinear fast diffusion on a bounded domain.“ Preprint. Archive for Rational Mechanics and Analysis 247 16. doi: 10.1007/s00205-023-01850-3.
- Navarro-Fernández, V, und Schlichting, A. . „Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients.“ ESAIM: Mathematical Modelling and Numerical Analysis 57 (4): 2131–2158. doi: 10.1051/m2an/2023035.
- Jentzen, A, und Riekert, A. . „Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation.“ Journal of Mathematical Analysis and Applications 517 (2) 126601. doi: 10.1016/j.jmaa.2022.126601.
- Hutzenthaler, M, Jentzen, A, Kruse, T, und Nguyen, TA. . „Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations.“ Journal of Numerical Mathematics 31 (2): 1–28. doi: 10.1515/jnma-2021-0111.
- Grohs, P, Hornung, F, Jentzen, A, und Zimmermann, P. . „Space-time error estimates for deep neural network approximations for differential equations.“ Advances in Computational Mathematics 49 (1) 4. doi: 10.1007/s10444-022-09970-2.
- Becker, S, Gess, B, Jentzen, A, und Kloeden, PE. . „Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen--Cahn equations.“ Stochastics and Partial Differential Equations: Analysis and Computations 11 (1): 211–268. doi: 10.1007/s40072-021-00226-6.
- Keil, Tim, und Rave, Stephan. . „An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition.“ SIAM Journal on Scientific Computing 45 (4). doi: 10.1137/21M1460016.
- Landstorfer, M, Ohlberger, M, Rave, S, und Tacke, M. . „A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells.“ European Journal of Applied Mathematics 34 (3): 554–591. doi: 10.1017/S0956792522000353.
- Herzing, Tobias, Klingenberg, Christian, und Pirner, Marlies. . „Hypocoercivity of the linearized BGK equation with stochastic coefficients.“ Methods and Applications of Analysis 30(3): 113–128. doi: 10.4310/MAA.2023.v30.n3.a2.
- Bae, Gi-Chan, Klingenberg, Christian, Pirner, Marlies, und Yun, Seok-Bae. . „BGK model for two-component gases near a global Maxwellian.“ SIAM Journal on Mathematical Analysis 55 (2). doi: 10.1137/22M1469535.
- Favre, Gianluca, Pirner, Marlies, und Schmeiser, Christian. . „Hypocoercivity and reaction-diffusion limit for a non-linear generation-recombination model.“ Archive for Rational Mechanics and Analysis 247 (4) 72. doi: 10.1007/s00205-023-01902-8.
- Monteil, A, Muratov, C.B., Simon, T.M., und Slastikov, V.V. . „Magnetic skyrmions under confinement.“ Preprint. Communications in Mathematical Physics 404: 1571–1605. doi: 10.1007/s00220-023-04864-w.
- Rüland, A., und Simon, T.M. . „On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation.“ Preprint. Journal of Elasticity 153: 455–475. doi: 10.1007/s10659-023-10011-2.
- Medani, Takfarinas, Garcia-Prieto, Juan, Tadel, Francois, Antonakakis, Marios, Erdbrügger, Tim, Höltershinken, Malte, Mead, Wayne, Schrader, Sophie, Joshi, Anand, Engwer, Christian, Wolters, Carsten H., Mosher, John C., und Leahy, Richard M. . „Brainstorm-DUNEuro: An integrated and user-friendly Finite Element Method for modeling electromagnetic brain activity.“ NeuroImage 267 119851. doi: 10.1016/j.neuroimage.2022.119851.
- Ohlberger, M., Banholzer, S., Haasdonk, B., Keil, T.Kleikamp H., Mechelli, L., Oguntola, M, Schindler F., Volkwein, S., und Wenzel, T. . „Model Reduction and Learning for PDE Constrained Optimization.“ Beitrag präsentiert auf der Oberwolfach Workshop on Optimization Problems for PDEs in Weak Space-Time Form, Oberwolfach doi: 10.4171/OWR/2023/13.
- Guastini, Mara, Rajković, Marko, Rumpf, Martin, und Wirth, Benedikt. . „The variational approach to the flow of Sobolev-diffeomorphisms model.“ In Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, herausgegeben von Luca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato und Matteo Santacesaria. Cham: Springer. doi: 10.1007/978-3-031-31975-4_42.
- Sassen, Josua, Hildebrandt, Klaus, Rumpf, Martin, und Wirth, Benedikt. . „Parametrizing product shape manifolds by composite networks.“ Beitrag präsentiert auf der International Conference on Learning Representations (ICLR 2023), Kigali
- Beck, Lisa, Cinti, Eleonora, und Seis, Christian. . „Optimal regularity of isoperimetric sets with Hölder densities.“ Preprint. Calculus of Variations and Partial Differential Equations 62 (214). doi: 10.1007/s00526-023-02542-2.
- Schleuß, Julia, Smetana, Kathrin, und ter Maat, Lukas. . „Randomized quasi-optimal local approximation spaces in time.“ SIAM Journal on Scientific Computing 45 (3). doi: 10.1137/22M1481002.
- Himpe, Christian, und Grundel, sara. . „System Order Reduction for Gas and Energy Networks.“ Beitrag präsentiert auf der 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Aachen doi: 10.1002/pamm.202200201.
- Hahn, Bernadette, und Wirth, Benedikt. . „Convex reconstruction of moving particles with inexact motion model.“ Proceedings in Applied Mathematics and Mechanics n/a e202300054. doi: 10.1002/pamm.202300054.
- Bernand-Mantel, A., Fondet, A, Barnova, S., Simon, T.M., und Muratov, C.B. . „Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets.“ Physical Review B 2023 L161405. doi: 10.1103/PhysRevB.108.L161405.
- Tolomeo, Leonardo, und Weber, Hendrik. . „Phase transition for invariant measures of the focusing Schrödinger equation.“ Preprint. arXiv doi: 10.48550/arXiv.2306.07697.
- Luckhaus, Stephan, und Stevens, Angela. . „A free boundary problem-in time-for the spread of Covid-19.“ Journal of Mathematical Biology 86 (45). doi: 10.1007/s00285-023-01881-0.
- Erdbrügger, T., Westhoff, A., Höltershinken, M., Radecke, J.-O., Buschermöhle, Y., Buyx, A., Wallois, F., Pursiainen, S., Gross, J., Lencer, R., Engwer, C., und Wolters, C.H. . „CutFEM forward modeling for EEG source analysis.“ Frontiers in Human Neuroscience 17 1216758. doi: 10.3389/fnhum.2023.1216758.
- Luckhaus, Stephan, und Stevens, Angela. . „A two level contagion process and its deterministic McKendrick limit with relevance for the Covid epidemic.“ Ensaios Matemáticos 38: 343–358. doi: 10.21711/217504322023/em3813.
- Bach, A.; Marziani, R.; Zeppieri, C.I.. . „Γ-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals.“ Calculus of Variations and Partial Differential Equations 62 (199).
- Bach, A.; Esposito, T.; Marziani, R; Zeppieri, C.I.. . „Gradient Damage Models for Heterogeneous Materials.“ SIAM Journal on Mathematical Analysis 55 (4). doi: 10.1137/22M1499145.
- Ruf, Matthias; Zeppieri, Caterina Ida. . „Stochastic homogenization of degenerate integral functionals with linear growth.“ Calculus of Variations and Partial Differential Equations 62 (138) 138. doi: 10.1007/s00526-023-02476-9.
- D'Onofrio, C.; Zeppieri, C.I.. . „Gamma-convergence and stochastic homogenisation of degenerate integral functionals in weighted Sobolev spaces.“ Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2).
- Pellet, X.; Scardia, L.; Zeppieri, C.I.. . „Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains.“ Advances in Calculus of Variations 17 (3). doi: 10.1515/acv-2022-0052.
accepted / in Press (not yet published)
- Jentzen, A, und Riekert, A. im Druck. „Strong overall error analysis for the training of artificial neural networks via random initializations.“ Communications in Mathematics and Statistics. doi: 10.1007/s40304-022-00292-9.
- Grohs, P, Ibragimov, S, Jentzen, A, und Koppensteiner, S. im Druck. „Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality.“ Journal of Complexity 101746. doi: 10.1016/j.jco.2023.101746.
Eingereicht / In Begutachtung
- Gonon, L., Graeber, R., und Jentzen, A. . „The necessity of depth for artificial neural networks to approximate certain classes of smooth bounded functions without the curse of dimensionality.“ Preprint. arXiv.org
- Jentzen, A., Riekert, A., und von Wurstemberger, P. . „Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations.“ Preprint. arXiv.org
- Dereich, S., Jentzen, A., und Kassing, S. . „On the existence of minimizers in shallow residual ReLU neural network optimization landscapes.“ Preprint. arXiv.org
- Beck, C., Jentzen, A., Kleinberg, K., und Kruse, T. . „Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems.“ Preprint. arXiv.org
- Julia, Schleuß, und Kathrin, Smetana. . „DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions.“ Preprint. arXiv doi: 10.48550/arXiv.2302.00348.
Veröffentlicht
- Keil, T, Kleikamp, H, Lorentzen, R, Oguntola, M, und Ohlberger, M. . „Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery.“ Advances in Computational Mathematics 2022 (48) 73. doi: 10.1007/s10444-022-09981-z.
- Peletier, Mark A., und Schlichting, André. . „Cosh gradient systems and tilting.“ Nonlinear Analysis: Theory, Methods and Applications 2203 113094. doi: 10.1016/j.na.2022.113094.
- Leibner, Tobias. . „Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition.“ Dissertationsschrift, Universität Münster.
- Friedrich, Manuel, und Machill, Lennart. . „Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons.“ Nonlinear Differential Equations and Applications 29 (2): 1–42. doi: 10.1007/s00030-021-00745-0.
- Schlichting, André, und Seis, Christian. . „The Scharfetter-Gummel scheme for aggregation-diffusion equations.“ IMA Journal of Numerical Analysis 42 (3). doi: 10.1093/imanum/drab039.
- Seis, C. . „Bounds on the rate of enhanced dissipation.“ Communications in Mathematical Physics Online first. doi: 10.1007/s00220-022-04588-3.
- Nobili, Camilla, und Seis, Christian. . „Renormalization and energy conservation for axisymmetry fluid flows.“ Mathematische Annalen 382: 1–36. doi: 10.1007/s00208-020-02050-0.
- Menz, G, Schlichting, A, Tang, W, und Wu, T. . „Ergodicity of the infinite swapping algorithm at low temperature.“ Stochastic Processes and their Applications 151: 519–552. doi: 10.1016/j.spa.2022.06.015.
- Dirks, C, und Wirth, B. . „An adaptive finite element approach for lifted branched transport problems.“ In Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization, herausgegeben von Herzog Roland, Heinkenschloss Matthias, Kalise Dante, Stadler Georg und Trélat Emmanuel. Berlin, Boston: De Gruyter.
- Gavrilenko, Pavel, Haasdonk, Bernard, Iliev, Oleg, Ohlberger, Mario, Schindler, Felix, Toktaliev, Pavel, Wenzel, Tizian, und Youssef, Maha. . „A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows.“ In Large-Scale Scientific Computing, Bd. 13127 aus Lecture Notes in Computer Science (LNCS), herausgegeben von Ivan Lirkov und Svetozar Margenov. Cham: Springer VDI Verlag. doi: 10.1007/978-3-030-97549-4_43.
- Keil, Tim, und Ohlberger, Mario. . „Model Reduction for Large Scale Systems.“ In Large-Scale Scientific Computing, Bd. 13127 aus Lecture Notes in Computer Science (LNCS), herausgegeben von Ivan Lirkov und Svetozar Margenov. Cham: Springer International Publishing. doi: 10.1007/978-3-030-97549-4_2.
- Gander, Martin Rave Stephan. . „Localized Reduced Basis Additive Schwarz Methods.“ In Domain Decomposition Methods in Science and Engineering XXVI, herausgegeben von Susanne C. Brenner Brenner, Eric Chung, Axel Klawonn, Felix Kwok, Jinchao Xu und Jun Zou. Cham: Springer International Publishing. doi: 10.1007/978-3-030-95025-5_52.
- Niethammer, Barbara, Pego, Robert L., Schlichting, André, und Velázquez, Juan J. L. . „Oscillations in a Becker-Döring model with injection and depletion.“ SIAM Journal on Applied Mathematics 82 (4): 1194–1219. doi: 10.1137/20M1398664.
- Navarro-Fernández, V, Schlichting, A, und Seis, C. . „Optimal stability estimates and a new uniqueness result for advection-diffusion equations.“ Pure and Applied Analysis 4 (3): 571–596. doi: 10.2140/paa.2022.4.571.
- Gonon, Lukas, Grohs, Philipp, Jentzen, Arnulf, Kofler, Dvid, und Šiška, David. . „Uniform error estimates for artificial neural network approximations for heat equations.“ IMA Journal of Numerical Analysis 42 (3): 1991–2054. doi: 10.1093/imanum/drab027.
- Hutzenthaler, M, Jentzen, A, und Kruse, T. . „Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities.“ Foundations of Computational Mathematics 22 (4): 905–966. doi: 10.1007/s10208-021-09514-y.
- Cheridito, P, Jentzen, A, und Rossmannek, F. . „Efficient approximation of high-dimensional functions with neural networks.“ IEEE Transactions on Neural Networks and Learning Systems 33 (7): 3079–3093. doi: 10.1109/TNNLS.2021.3049719.
- Jentzen, A, Kuckuck, B, Müller-Gronbach, T, und Yaroslavtseva, L. . „Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives.“ Discrete and Continuous Dynamical Systems - Series B 27 (7): 3707–3724. doi: 10.3934/dcdsb.2021203.
- E, W., Han, J., und Jentzen, A. . „Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning.“ Nonlinearity 35 (1): 278–310. doi: 10.1088/1361-6544/ac337f.
- Effland, A, Heeren, B, Rumpf, M, und Wirth, B. . „Consistent Curvature Approximation on Riemannian Shape Spaces.“ IMA Journal of Numerical Analysis 42 (1): 78–106.
- Banholzer, S, Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, und Volkwein, S. . „An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization.“ Pure and Applied Functional Analysis 7 (5): 1561–1596.
- Potthoff, Jonas, und Wirth, Benedikt. . „Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions.“ ESAIM: Control, Optimisation and Calculus of Variations 28 27.
- Striewski, Paul, und Wirth, Benedikt. . „Elastic 3D-2D Image Registration.“ Journal of Mathematical Imaging and Vision 64: 443–462.
- Kleikamp, Hendrik, Ohlberger, Mario, und Rave, Stephan. . „Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain.“ In MATHMOD 2022 - Discussion Contribution Volume, Bd. 17 aus ARGESIM Report, herausgegeben von Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi und Inge Troch. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17129.
- Brecher, C, Buchmeiser, MR, Burkert, A, Busemeyer, MR, Conermann, S, Ertl, T, Friedrich, M, Helmig, R, Hohmann, V, Johnston, AJ, Kollmeier, B, Larkum, M, Louis, J, Menges, A, Morgner, U, Müller, J, Niessen, C, Ohlberger, M, Schäffner, W, Schmidt, P, Schmitz, D, Seeger, W, Stammer, D, Thomas, A, Traninger, A, Wegener, M, Colomb, J, Hermann, S, Kopsch-Xhema, J, Range, J, und Flemisch, B. . „Commitment zu aktivem Daten- und -softwaremanagement in großen Forschungsverbünden: Commitment to active data and software management in large research alliances.“ Bausteine Forschungsdatenmanagement 1: 121–123.. doi: 10.17192/bfdm.2022.1.8412.
- Himpe, C, Grundel, S, und Benner, P. . „Efficient Gas Network Simulations.“ In German Success Stories in Industrial Mathematics, Bd. 35 aus Mathematics in Industry, herausgegeben von HG Bock, KH Küfer, P Maass, A Milde und V Schulz. doi: 10.1007/978-3-030-81455-7_4.
- Jentzen, A, und Riekert, A. . „On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks.“ Journal of Machine Learning 1 (2): 141–246. doi: 10.4208/jml.220114a.
- Jentzen, Arnulf, und Riekert, Adrian. . „A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions.“ Journal of Machine Learning Research 23 (260): 1–50.
- Jentzen, Arnulf, und Riekert, Adrian. . „A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions.“ Zeitschrift für Angewandte Mathematik und Physik 73 (5) 188. doi: 10.1007/s00033-022-01716-w.
- Cheridito, P, Jentzen, A, und Rossmannek, F. . „Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions.“ Journal of Nonlinear Science 32 (5) 64. doi: 10.1007/s00332-022-09823-8.
- Cheridito, Patrick, Jentzen, Arnulf, Riekert, Adrian, und Rossmannek, Florian. . „A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions.“ Journal of Complexity 72 101646. doi: 10.1016/j.jco.2022.101646.
- Beck, C, Jentzen, A, und Kuckuck, B. . „Full error analysis for the training of deep neural networks.“ Infinite Dimensional Analysis, Quantum Probability and Related Topics 25 (2) 2150020. doi: 10.1142/S021902572150020X.
- Grohs, P, Jentzen, A, und Salimova, D. . „Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms.“ SN Partial Differential Equations and Applications 3 (4) 45. doi: 10.1007/s42985-021-00100-z.
- Elbrächter, D., Grohs, P., Jentzen, A., und Schwab, C. . „DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing.“ Constructive Approximation 55 (1): 3–71. doi: 10.1007/s00365-021-09541-6.
- Abgrall, R, Öffner, P, und Ranocha, H. . „Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization.“ Journal of Computational Physics 2022: 110955.. doi: 10.1016/j.jcp.2022.110955.
- Ranocha, H, Schlottke-Lakemper, M, Winters, AR, Faulhaber, E, Chan, J, und Gassner, G. . „Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing.“ Proceedings of the JuliaCon Conferences 1 (1): 77.. doi: 10.21105/jcon.00077.
- Lohmann, Julius, Schmitzer, Bernhard, und Wirth, Benedikt. . „Formulation of branched transport as geometry optimization.“ Journal de Mathématiques Pures et Appliquées 163: 739–779. doi: 10.1016/j.matpur.2022.05.021.
- Haasdonk, B, Ohlberger, M, und Schindler, F. . „An adaptive model hierarchy for data-augmented training of kernel models for reactive flow.“ In MATHMOD 2022 Discussion Contribution Volume, herausgegeben von Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi und Inge Troch. Vienna: ARGESIM Verlag. doi: 10.11128/arep.17.a17155.
- Ceci, S, und Seis, C. . „On the dynamics of point vortices for the 2D Euler equation with Lp vorticity.“ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380 (2226). doi: 10.1098/rsta.2021.0046.
- Benner, P., Burger, M., Göddeke, D., Himpe, C., Hintermüller, M., Heiland, J., Koprucki, T., Ohlberger, M., Rave, S., Reidelbach, M., Saak, J., Schöbel, A., und Tabelow, K. . „Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative).“ GAMM Rundbrief 1/2022: 40–43.
- Pirner, Marlies, und Warnecke, Sandra. . „A review on a general multi-species BGK model: modelling, theory and numerics.“ In From Kinetik Theory to Turbulence Modeling : The Legacy of Carlo Cercignani, Springer INdAM Series, herausgegeben von Paolo Barbante, Francesco Belgiorno, Silvia Lorenzani und Lorenzo Valdettaro. Singapur: Springer. doi: 10.1007/978-981-19-6462-6_17.
- Favre, Gianluca, Pirner, Marlies, und Schmeiser, Christian. . „Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit.“ Kinetic and Related Models 15 (5): 823–841. doi: 10.3934/krm.2022015.
- Haack, Jeff, Hauck, Cory, Klingenberg, Christian, Pirner, Marlies, und Warnecke, Sandra. . „Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency.“ Journal of Computational Physics 473 111729. doi: 10.1016/j.jcp.2022.111729.
- Keil, Tim. . „Adaptive Reduced Basis Methods for Multiscale Problems and Large-scale PDE-constrained Optimization.“ Dissertationsschrift, WWU Münster. doi: 10.48550/arXiv.2211.09607.
- Lohmann, Julius, Schmitzer, Bernhard, und Wirth, Benedikt. . „Duality in branched transport and urban planning.“ Applied Mathematics and Optimization 86 45. doi: 10.1007/s00245-022-09927-3.
- Bruno, Stefano, Gess, Benjamin, und Weber, Hendrik. . „Optimal regularity in time and space for stochastic porous medium equations.“ Annals of Probability 50 (6): 2288–2343. doi: 10.1214/22-AOP1583.
- Gunaratnam, Trishen, Oh, Tadahiro, Tzvetkov, Nikolay, und Weber, Hendrik. . „Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions.“ Probability and Mathematical Physics 3 (2): 343–379. doi: 10.2140/pmp.2022.3.343.
- Chandra, Ajay, Gunaratnam, Trishen S., und Weber, Hendrik. . „Phase Transitions for ϕ^4_3.“ Communications in Mathematical Physics 392: 691–782. doi: 10.1007/s00220-022-04353-6.
- Bonnefoi, Timothée, Chandra, Ajay, Moinat, Augustin, und Weber, Hendrik. . „A priori bounds for rough differential equations with a non-linear damping term.“ Journal of Differential Equations 318: 58–93. doi: 10.1016/j.jde.2022.02.006.
- Julia, Schleuß, und Kathrin, Smetana. . „Optimal local approximation spaces for parabolic problems.“ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 20 (1). doi: 10.1137/20M1384294.
- Fritze, René, und Rave, Stephan. . „Specification and Validation of Numerical Algorithms with the Gradual Contracts Pattern.“ In Testing Software and Systems, Lecture Notes in Computer Science, herausgegeben von David Clark, Hector Menendez und Ana Rosa Cavalli. Cham: Springer International Publishing.
- Himpe, Christian, Grundel, Sara, und Benner, Peter. . „Next-Gen Gas Network Simulation.“ In Progress in Industrial Mathematics at ECMI 2021, Bd. 39 aus Mathematics in Industry, herausgegeben von Matthias Ehrhardt und Michael Günther. Cham: Springer. doi: 10.1007/978-3-031-11818-0_15.
- Muratov, C.B., und Simon, T.M. . Correction to: A Nonlocal Isoperimetric Problem with Dipolar Repulsion doi: 10.1007/s00220-022-04426-6.
- Stevens, Angela, und Winkler, Michael. . „Taxis-driven persistent localization in a degenerate Keller-Segel system.“ Communications in Partial Differential Equations 47 (12): 2341–2362. doi: 10.1080/03605302.2022.2122836.
- Luckhaus, Stephan, und Stevens, Angela. . „Kermack and McKendrick Models on a Two-Scale Network and Connections to the Boltzmann Equations.“ In Mathematics Going Forward. Lecture Notes in Mathematics, vol 2313, Lecture Notes in Mathematics, herausgegeben von Jean Michel Morel und Bernard Teissier. Cham: Springer. doi: 10.1007/978-3-031-12244-6_29.
- Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia, und Zeppieri, Caterina Ida. . „A global method for deterministic and stochastic homogenisation in BV.“ Annals of PDE 8 (1): 8–8. doi: 10.1007/s40818-022-00119-4.
Eingereicht / In Begutachtung
- Fokina, D, Iliev, O, Toktaliev, P, Oseledets, I, und Schindler, F. . „On the Performance of Machine Learning Methods for Breakthrough Curve Prediction.“ arXiv [physics.flu-dyn] 2204.11719. doi: 10.48550/arXiv.2204.11719.
- Ranocha, H. . A Note on Numerical Fluxes Conserving Harten's Entropies for the Compressible Euler Equations
- Singh, A, Thale, S, Leibner, T, Ricker, A, Nüsse, H, Klingauf, J, Ohlberger, M, und Matis, M. . „Dynamic interplay of protrusive microtubule and contractile actomyosin forces drives tissue extension.“ eLife 2022. doi: 10.1101/2022.06.21.496930.
- Ibragimov, Shokhrukh, Jentzen, Arnulf, Kröger, Timo, und Riekert, Adrian. . „On the existence of infinitely many realization functions of non-global local minima in the training of artificial neural networks with ReLU activation.“ Preprint. ArXiv doi: 10.48550/arXiv.2202.11481.
- Eberle, Simon, Jentzen, Arnulf, Riekert, Adrian, und Weiss, Georg. . „Normalized gradient flow optimization in the training of ReLU artificial neural networks.“ Preprint. ArXiv doi: 10.48550/arXiv.2207.06246.
- Freese, P, Hauck, M, Keil, T, und Peterseim, D. . „A Super-Localized Generalized Finite Element Method.“ Preprint. arXiv 2022 doi: 10.48550/arXiv.2211.09461.
- Fischer, J, Hensel, S, Laux, T, und Simon, T.M. . „Local minimizers of the interface length functional based on a concept of local paired calibrations.“ Preprint. arXiv doi: 10.48550/arXiv.2212.11840.
- Becker, S., Jentzen, A., und Müller, M. S.von Wurstemberger P. . „Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing.“ Preprint. arXiv.org
- Jentzen, A., Kröger, und T.. . „On bounds for norms of reparameterized ReLU artificial neural network parameters: sums of fractional powers of the Lipschitz norm control the network parameter vector.“ Preprint. arXiv.org
- Cheridito, P., Jentzen, A., und Rossmannek, F. . „Gradient descent provably escapes saddle points in the training of shallow ReLU networks.“ Preprint. arXiv.org
- Beck, C., Becker, S., Cheridito, P., Jentzen, A., und Neufeld, A. . „An efficient Monte Carlo scheme for Zakai equations.“ Preprint. arXiv.org
- Gallon, D., Jentzen, A., und Lindner, F. . „Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks.“ Preprint. arXiv.org
- Ibragimov, S., Jentzen, A., und Riekert, A. . „Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability.“ Preprint. arXiv.org
Veröffentlicht
- Schlichting, André, und Seis, Christian. . „The Scharfetter–Gummel scheme for aggregation–diffusion equations.“ IMA Journal of Numerical Analysis 42 (3): 2361–2402. doi: 10.1093/imanum/drab039.
- Eichenberg, C, und Schlichting, A. . „Self-similar behavior of the exchange-driven growth model with product kernel.“ Commun. Partial. Differ. Equ. 46 (3): 498–546. doi: 10.1080/03605302.2020.1845205.
- Esposito, A, Patacchini, F, Schlichting, A, und Slepčev, D. . „Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit.“ Arch. Ration. Mech. Anal. 2021. doi: 10.1007/s00205-021-01631-w.
- Seis, Christian. . „A note on the vanishing viscosity limit in the Yudovich class.“ Canadian Mathematical Bulletin 64 (1): 112–122. doi: 10.4153/S0008439520000296.
- Bastian, P, Blatt, M, Dedner, A, Dreier, N, Engwer, C, Fritze, R, Gräser, C, Kempf, D, Klöfkorn, R, Ohlberger, M, und Sander, O. . „The DUNE Framework: Basic Concepts and Recent Developments.“ Computers & Mathematics with Applications 81: 75–112. doi: 10.1016/j.camwa.2020.06.007.
- Ceci, Stefano, und Seis, Christian. . „Vortex dynamics for 2D Euler flows with unbounded vorticity.“ Revista Matematica Iberoamericana 37 (5): 1969–1990. doi: 10.4171/rmi/1255.
- Buhr, Andreas, Iapichino, Laura, Ohlberger, Mario, Rave, Stephan, Schindler, Felix, und Smetana, Kathrin. . „Localized model reduction for parameterized problems.“ In Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, herausgegeben von P Benner, S Grivet-Talocia, A Quarteroni, G Rozza, W Schilders und L Sileira. doi: 10.1515/9783110671490-006.
- Streitbürger, Florian Engwer Christian, und May, Sandra Nüßing Andreas. . „Monotonicity considerations for stabilized DG cut cell schemes for the unsteady advection equation.“ Beitrag präsentiert auf der ENUMATH2019, Egmond aan Zee, The Netherlands
- Fehr, J, Himpe, C, Rave, S, und Saak, J. . „Sustainable Research Software Hand-Over.“ Journal of Open Research Software 9 (1). doi: 10.5334/jors.307/.
- Leibner, T, und Ohlberger, M. . „A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations.“ ESAIM: Mathematical Modelling and Numerical Analysis 55: 2567–2608.. doi: 10.1051/m2an/2021065.
- Nussenzveig, Lopes H. J., Seis, C, und Wiedemann, E. . „On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity.“ Nonlinearity 34 (5): 3112–3121.. doi: 10.1088/1361-6544/abe51f.
- Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, und Volkwein, S. . „A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization.“ ESAIM: Mathematical Modelling and Numerical Analysis 55: 1239–1269.. doi: 10.1051/m2an/2021019.
- Dreier, Nils-Arne, und Engwer, Christian. . „Strategies for the vectorized Block Conjugate Gradients method.“ Beitrag präsentiert auf der ENUMATH2019, Egmond aan Zee, The Netherlands
- Schlottke-Lakemper, M, Winters, AR, Ranocha, H, und Gassner, GJ. . „A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.“ Journal of Computational Physics 2021: 110467.. doi: 10.1016/j.jcp.2021.110467.
- Schrader, S, Westhoff, A, Piastra, MC, Miinalainen, T, Pursiainen, S, Vorwerk, J, Brinck, H, Wolters, CH, und Engwer, C. . „DUNEuro- A software toolbox for forward modeling in bioelectromagnetism.“ PloS one 2021. doi: 10.1371/journal.pone.0252431.
- Braunsmann, J, Rajkovic, M, Rumpf, M, und Wirth, B. . „Learning low bending and low distortion manifold embeddings.“ In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), herausgegeben von The Computer Vision Foundation. -: Wiley-IEEE Press.
- Dirks, C, Striewski, P, Wirth, B, Aalto, A, und Olguin-Olguin, A. . „A mathematical model for cell polarization in zebrafish primordial germ cells.“ IMA Mathematical Medicine and Biology 38 (2): 218–254.
- Mitsotakis, Dimitrios, Ranocha, Hendrik, Ketcheson, David I, und Süli, Endre. . „A conservative fully-discrete numerical method for the regularized shallow water wave equations.“ SIAM Journal on Scientific Computing 42. doi: 10.1137/20M1364606.
- LeFloch, PG, und Ranocha, H. . „Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts.“ Journal of Scientific Computing 87. doi: 10.1007/s10915-021-01463-6.
- Dreier, Nils-Arne. . „Hardware-Oriented Krylov Methods for High-Performance Computing.“ Dissertationsschrift, WWU Münster. doi: 10.48550/arXiv.2104.02494.
- Ranocha, H, und Nordström, J. . „A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions.“ Journal of Scientific Computing 87. doi: 10.1007/s10915-021-01454-7.
- Ranocha, H, Mitsotakis, D, und Ketcheson, DI. . „A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations.“ Communications in Computational Physics 29 (4): 979–1029. doi: 10.4208/cicp.OA-2020-0119.
- Ranocha, H. . „On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators.“ IMA Journal of Numerical Analysis 41 (1): 654–682. doi: 10.1093/imanum/drz070.
- Rojas, D, Boukharfane, R, Dalcin, L, Fernández, DCDR, Ranocha, H, Keyes, DE, und Parsani, M. . „On the robustness and performance of entropy stable discontinuous collocation methods.“ Journal of Computational Physics 426: 109891.. doi: 10.1016/j.jcp.2020.109891.
- Beck, C, Hutzenthaler, M, und Jentzen, A. . „On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations.“ Stochastics and Dynamics 21 (8): Paper No. 2150048, 68 pp... doi: 10.1142/S0219493721500489.
- Cheridito, P, Jentzen, A, und Rossmannek, F. . „Non-convergence of stochastic gradient descent in the training of deep neural networks.“ Journal of Complexity 64: Paper No. 101540, 10 pp...
- Andersson, A, Jentzen, A, und Kurniawan, R. . „Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values.“ Journal of Mathematical Analysis and Applications 495 (1): 124558, 33.. doi: 10.1016/j.jmaa.2020.124558.
- Jentzen, AKuckuck B, und Neufeld, Avon Wurstemberger P. . „Strong error analysis for stochastic gradient descent optimization algorithms.“ IMA Journal of Numerical Analysis 41 (1): 455–492. doi: 10.1093/imanum/drz055.
- Cox, S, Hutzenthaler, M, Jentzen, A, Neerven, J, und Welti, T. . „Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions.“ IMA Journal of Numerical Analysis 41 (1): 493–548. doi: 10.1093/imanum/drz063.
- Clason, C, Lorenz, D, Mahler, H, und Wirth, B. . „Entropic regularization of continuous optimal transport problems.“ Journal of Mathematical Analysis and Applications 494 (1): 124432..
- Seis, Christian, und Winkler, Dominik. . „A well-posedness result for a system of cross-diffusion equations.“ Journal of Evolution Equations 21 (2): 2471–2489.. doi: 10.1007/s00028-021-00690-6.
- Jentzen, A, Salimova, D, und Welti, T. . „A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients.“ Communications in Mathematical Sciences 19 (5): 1167–1205. doi: 10.4310/CMS.2021.v19.n5.a1.
- Jentzen, A, Lindner, F, und Pušnik, P. . „Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise.“ Nonlinear Analysis: Theory, Methods and Applications 210: Paper No. 112310.. doi: 10.1016/j.na.2021.112310.
- Jentzen, A, und Kurniawan, R. . „Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients.“ Foundations of Computational Mathematics 21 (2): 445–536. doi: 10.1007/s10208-020-09448-x.
- Jentzen, A, Kuckuck, B, Müller-Gronbach, T, und Yaroslavtseva, L. . „On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values.“ Journal of Mathematical Analysis and Applications 502 (2): Paper No. 125240.. doi: 10.1016/j.jmaa.2021.125240.
- Jacobe de Naurois, Ladislas, Jentzen, Arnulf, und Welti, Timo. . „Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise.“ Applied Mathematics and Optimization 84 (suppl. 2): 1187–1217. doi: 10.1007/s00245-020-09744-6.
- E, W, Hutzenthaler, M, Jentzen, A, und Kruse, T. . „Multilevel Picard iterations for solving smooth semilinear parabolic heat equations.“ SN Partial Differential Equations and Applications 2 (6): Paper No. 80.. doi: 10.1007/s42985-021-00089-5.
- Becker, S, Cheridito, P, Jentzen, A, und Welti, T. . „Solving high-dimensional optimal stopping problems using deep learning.“ European Journal of Applied Mathematics 32 (3): 470–514. doi: 10.1017/S0956792521000073.
- Beck, C, Gonon, L, Hutzenthaler, M, und Jentzen, A. . „On existence and uniqueness properties for solutions of stochastic fixed point equations.“ Discrete and Continuous Dynamical Systems - Series B 26 (9): 4927–4962. doi: 10.3934/dcdsb.2020320.
- Beck, C, Becker, S, Grohs, P, Jaafari, N, und Jentzen, A. . „Solving the Kolmogorov PDE by means of deep learning.“ Journal of Scientific Computing 88 (3): Paper No. 73.. doi: 10.1007/s10915-021-01590-0.
- Beck, C, Becker, S, Cheridito, P, Jentzen, A, und Neufeld, A. . „Deep splitting method for parabolic PDEs.“ SIAM Journal on Scientific Computing 43 (5): A3135–A3154.. doi: 10.1137/19M1297919.
- Clason, C, Tameling, C, und Wirth, B. . „Convex relaxation of discrete vector-valued optimization problems.“ SIAM Review 63 (4): 783–821.
- Hardering, H, und Wirth, B. . „Quartic Lp-convergence of cubic Riemannian splines.“ IMA Journal of Numerical Analysis 42 (4): 3360–3385. doi: 10.1093/imanum/drab077.
- Ranocha, H, Dalcin, L, Parsani, M, und Ketcheson, DI. . „Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.“ Communications on Applied Mathematics and Computation 2021. doi: 10.1007/s42967-021-00159-w.
- Himpe, C. . „Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms.“ In Model Reduction of Complex Dynamical Systems, Bd. 171 aus International Series of Numerical Mathematics, herausgegeben von P Benner, T Breiten, H Faßbender, M Hinze, T Stykel und R Zimmermann. doi: 10.1007/978-3-030-72983-7_7.
- Himpe, C, Grundel, S, und Benner, P. . „Model Order Reduction for Gas and Energy Networks.“ Journal of Mathematics in Industry 11: 13.. doi: 10.1186/s13362-021-00109-4.
- Clees, T, Baldin, A, Benner, P, Grundel, S, Himpe, C, Klaassen, B, Küsters, F, Marheineke, N, Nikitina, L, Nikitin, I, Pade, J, Stahl, N, Strohm, C, Tischendorf, C, und Wirsen, A. . „MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.“ In Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, Bd. 34 aus Mathematics in Industry, herausgegeben von S Göttlich, M Herty und A Milde. doi: 10.1007/978-3-030-62732-4_11.
- Nüßlein, S, Ranocha, H, und Ketcheson, DI. . „Positivity-Preserving Adaptive Runge-Kutta Methods.“ Communications in Applied Mathematics and Computational Science 16 (2): 155–179. doi: 10.2140/camcos.2021.16.155.
- Ranocha, H, Luna, M, und Ketcheson, DI. . „On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations.“ Partial Differential Equations and Applications 2 (6): 76.. doi: 10.1007/s42985-021-00126-3.
- Simon, und T.M.. . „Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures.“ SIAM Journal on Mathematical Analysis 53 (4). doi: 10.1137/18M1220017.
- Simon, und T.M.. . „Rigidity of branching microstructures in shape memory alloys.“ Archive for Rational Mechanics and Analysis 241: 1707–1783. doi: 10.1007/s00205-021-01679-8.
- Bernand-Mantel, A., Muratov, C.B., und Simon, T.M. . „A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree ±1 harmonic maps from from R² to S².“ Archive for Rational Mechanics and Analysis 239: 219–299. doi: 10.1007/s00205-020-01575-7.
- Ranocha, H. . „SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties.“ Journal of Open Source Software 6 (64): 3454.. doi: 10.21105/joss.03454.
- Ranocha, H, und Gassner, GJ. . „Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes.“ Communications on Applied Mathematics and Computation 2021. doi: 10.1007/s42967-021-00148-z.
- Ostaszewski, K, Glassmeier, K, Goetz, C, Heinisch, P, Henri, P, Park, SA, Ranocha, H, Richter, I, Rubin, M, und Tsurutani, B. . „Steepening of magnetosonic waves in the inner coma of comet 67P/Churyumov-Gerasimenko.“ Annales Geophysicae 39 (4): 721–742. doi: 10.5194/angeo-39-721-2021.
- Brunken, Julia. . „Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations.“ Dissertationsschrift, Universität Münster.
- Pirner, Marlies. . „On multi-species BGK models with velocity dependent collision frequencies.“ In Small Collaboration: Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations (hybridmeeting), Bd. 19 aus Oberwolfach Report, herausgegeben von Christian Klingenberg, Qin Li und Marlies Pirner. Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. doi: 10.4171/OWR/2021/19.
- Bae, Gi-Chan, Klingenberg, Christian, Pirner, Marlies, und Yun, Seok-Bae. . „BGK model of the multi-species Uehling Uhlenbeck equation.“ Kinetic and Related Models 14 (1): 25–44. doi: 10.3934/krm.2020047.
- Haack, Jeff, Hauck, Cory, Klingenberg, Christian, Pirner, Marlies, und Warnecke, Sandra. . „A consistent BGK model with velocity-dependent collision frequency for gas mixtures.“ Journal of Statistical Physics 184 (3) 31. doi: 10.1007/s10955-021-02821-2.
- Pirner, Marlies. . „A review on BGK models for gas mixtures of mono and polyatomic molecules.“ Fluids 6 (11) 393. doi: 10.3390/fluids6110393.
- Scheel, Arnd, Stevens, Angela, und Tenbrock, Christoph. . „Signaling gradients in surface dynamics as basis for planarian regeneration.“ Journal of Mathematical Biology 83 (6). doi: 10.1007/s00285-021-01627-w.
- Scheel, Arnd, und Stevens, Angela. . „Regeneration of Tissue: Lessons Learned from Flatworms.“ SIAM News Blog
- Cicalese, M; Focardi, M.; Zeppieri, C.I.. . „Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps.“ Journal of Nonlinear Science 31 (78).
accepted / in Press (not yet published)
- Beneventano, P, Cheridito, P, Graeber, R, Jentzen, A, und Kuckuck, B. im Druck. „Deep neural network approximation theory for high-dimensional functions.“ Sampling Theory in Signal and Image Processing.
- Cox, S, Hutzenthaler, M, und Jentzen, A. im Druck. „Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations.“ Memoirs of the American Mathematical Society.
Eingereicht / In Begutachtung
- Jentzen, A, und Kröger, T. . „Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases.“ arXiv.
- Hutzenthaler, M, Jentzen, A, Pohl, K, Riekert, A, und Scarpa, L. . „Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions.“ arXiv.
- Hutzenthaler, M, Jentzen, A, Kuckuck, B, und Padgett, JL. . „Strong $L^p$-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations.“ arXiv.
- Beck, C, Hutzenthaler, M, Jentzen, A, und Magnani, E. . „Full history recursive multilevel Picard approximations for ordinary differential equations with expectations.“ arXiv.
- Esposito, A, Gvalani, RS, Schlichting, A, und Schmidtchen, M. . „On a novel gradient flow structure for the aggregation equation.“ Preprint. arXiv doi: 10.48550/arXiv.2112.08317.
- Ranocha, H, Schlottke-Lakemper, M, Chan, J, Rueda-Ramírez, AM, Winters, AR, Hindenlang, F, und Gassner, GJ. . Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
- Ketcheson, DI, und Ranocha, H. . Computing with B-series
- Torlo, D, Öffner, P, und Ranocha, H. . A New Stability Approach for Positivity-Preserving Patankar-type Schemes
- Leibner, T, Matis, M, Ohlberger, M, und Rave, S. . „Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD.“ arXiv [math.NA] 2111.00129.
Veröffentlicht
- Hellman, Fredrik, Keil, Tim, und Målqvist, Axel. . „Numerical Upscaling of Perturbed Diffusion Problems.“ SIAM Journal on Scientific Computing 2020 (Volume 42, Issue 4): A2014–A2036.. doi: 10.1137/19M1278211.
- Bach, A, und Sommer, L. . „A Gamma-convergence result for fluid-filled fracture propagationDO - 10.1051/m2an/2020016.“ ESAIM: Mathematical Modelling and Numerical Analysis 54 (3). doi: 10.1051/m2an/2020016.
- Friedrich, M, und Stefanelli, U. . „Ripples in graphene: A variational approach.“ Comm. Math. Phys. 379.
- Friedrich, M, und Stefanelli, U. . „Crystallization in a one-dimensional periodic landscape.“ J. Stat.Phys. 179.
- Crismale, V, und Friedrich, M. . „Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity.“ Arch. Ration. Mech. Anal. 237.
- Heeren, B, Rumpf, M, Wardetzky, M, und Wirth, B. . „Discrete Riemannian calculus on shell space.“ In Geometric Partial Differential Equations - Part I, Bd. 21 aus Handbook of Numerical Analysis, herausgegeben von A Bonito und RH Nochetto. Elsevier. doi: 10.1016/bs.hna.2019.06.005.
- Böttcher, U, und Wirth, B. . „Convex Lifting-Type Methods for Curvature Regularization.“ In Handbook of Variational Methods for Nonlinear Geometric Data, herausgegeben von P Grohs, M Holler und A Weinmann. Cham: Springer International Publishing. doi: 10.1007/978-3-030-31351-7_7.
- Schmitzer, B, Schäfers, KP, und Wirth, B. . „Dynamic Cell Imaging in PET With Optimal Transport Regularization.“ IEEE Transactions on Medical Imaging 39 (5): 1626–1635. doi: 10.1109/TMI.2019.2953773.
- Ferrari, L, Dirks, C, und Wirth, B. . „Phase field approximations of branched transportation problems.“ Calculus of Variations and Partial Differential Equations 59 (1): Paper No. 37, 34.. doi: 10.1007/s00526-019-1680-3.
- Wirth, B. . „Green's function for the Neumann-Poisson problem on n-dimensional balls.“ American Mathematical Monthly 127 (8): 737–743.
- Jentzen, Avon Wurstemberger P. . „Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates.“ Journal of Complexity 57: 101438.. doi: 10.1016/j.jco.2019.101438.
- Bastian, P, Altenbernd, M, Dreier, N, Engwer, C, Fahlke, J, Fritze, R, Geveler, M, Göddeke, D, Iliev, O, Ippisch, O, Mohring, J, Müthing, S, Ohlberger, M, Ribbrock, D, Shegunov, N, und Turek, S. . „Exa-Dune -- Flexible PDE Solvers, Numerical Methods and Applications.“ In Software for Exascale Computing - SPPEXA 2016-2019, Bd. 136 aus LNCSE, herausgegeben von Hans-Joachim Bungartz, Severin. Uekermann Benjamin Reiz, Philipp Neumann und Wolfgang E Nagel. Cham: Springer International Publishing. doi: 10.1007/978-3-030-47956-5_9.
- Davoli, E, und Friedrich, M. . „Two-well rigidity and multidimensional sharp-interface limits for Solid-Solid phase transitions.“ Calc. Var. PDE 59.
- Friedrich, M, und Kreutz, L. . „Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice.“ Nonlinearity 33.
- Friedrich, M, und F., Solombrino F. . „Functionals defined on piecewise rigid functions: Integral representation and Gamma-convergence.“ Arch. Ration. Mech. Anal. 236.
- Seis, Christian. . „On the Littlewood-Paley spectrum for passive scalar transport equations.“ Journal of Nonlinear Science 30 (2): 645–656. doi: 10.1007/s00332-019-09585-w.
- Ohlberger, Mario, Schweizer, Ben, Urban, Maik, und Verfürth, Barbara. . „Mathematical analysis of transmission properties of electromagnetic meta-materials.“ Networks and Heterogeneous Media 15 (1): 29–56. doi: 10.3934/nhm.2020002.
- Buchfink, P, Haasdonk, B, und Rave, S. . „PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems.“ Beitrag präsentiert auf der ALGORITMY 2020, Vysoké Tatry
- Schlichting, André. . „The exchange-driven growth model: basic properties and longtime behavior.“ Journal of Nonlinear Science 30 (3): 793–830. doi: 10.1007/s00332-019-09592-x.
- Gvalani, RS, und Schlichting, A. . „Barriers of the McKean–Vlasov energy via a mountain pass theorem in the space of probability measures.“ Journal of Functional Analysis 279 (11): 108720.. doi: 10.1016/j.jfa.2020.108720.
- Erbar, Matthias, Fathi, Max, und Schlichting, André. . „Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces.“ Latin American Journal of Probability and Mathematical Statistics 17 (1): 445–471. doi: 10.30757/alea.v17-18.
- Anzt, H, Bach, F, Druskat, S, Löffler, F, Loewe, A, Renard, B, Seemann, G, Struck, A, Achhammer, E, Aggarwal, P, Appel, F, Bader, M, Brusch, L, Busse, C, Chourdakis, G, Dabrowski, P, Ebert, P, Flemisch, B, Friedl, S, Fritzsch, B, Funk, M, Gast, V, Goth, F, Grad, J, Hermann, S, Hohmann, F, Janosch, S, Kutra, D, Linxweiler, J, Muth, T, Peters-Kottig, W, Rack, F, Raters, F, Rave, S, Reina, G, Reißig, M, Ropinski, T, Schaarschmidt, J, Seibold, H, Thiele, J, Uekermann, B, Unger, S, und Weeber, R. . „An environment for sustainable research software in Germany and beyond: current state, open challenges, and call for action.“ F1000Research 9 (295). doi: 10.12688/f1000research.23224.1.
- Schneider, Florian Leibner Tobias. . „First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory.“ Journal of Computational Physics 416: 109547.. doi: 10.1016/j.jcp.2020.109547.
- Heeren, B, Paulus, S, Goldbach, H, Kuhlmann, H, Mahlein, A-K, Rumpf, M, und Wirth, B. . „Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets.“ BMC Bioinformatics 21 (335).
- Abgrall, R, Mélédo, El, Öffner, P, und Ranocha, H. . „Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes.“ In Hyperbolic Problems: Theory, Numerics, Applications, Bd. 10 aus AIMS on Applied Mathematics, herausgegeben von A Bressan, M Lewicka, D Wang und Y Zheng. Springfield: Springer.
- Heinisch, P, Ostaszewski, K, und Ranocha, H. . „Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL.“ In Proceedings of the International Workshop on OpenCL, IWOCL '20, April 2020, Munich (Germany) New York, NY, USA: ACM Press. doi: 10.1145/3388333.3403035.
- Ranocha, H. . „Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators.“ In Spectral and High Order Methods for Partial Differential Equations {ICOSAHOM} 2018, Bd. 134 aus Lecture Notes in Computational Science and Engineering, herausgegeben von SJ Sherwin, D Moxey, J Peiró, PE Vincent und C Schwab. Cham: Springer. doi: 10.1007/978-3-030-39647-3_42.
- Ranocha, H, Ostaszewski, K, und Heinisch, P. . „Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators.“ Communications on Applied Mathematics and Computation 2: 581–611. doi: 10.1007/s42967-019-00057-2.
- Ranocha, H, Sayyari, M, Dalcin, L, Parsani, M, und Ketcheson, DI. . „Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.“ SIAM Journal on Scientific Computing 42 (2): A612–A638.. doi: 10.1137/19M1263480.
- Öffner, P, Glaubitz, J, und Ranocha, H. . „Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods.“ International Journal of Numerical Analysis and Modeling 17 (3): 332–349.
- Ranocha, H, und Ketcheson, DI. . „Relaxation Runge-Kutta Methods for Hamiltonian Problems.“ Journal of Scientific Computing 84 (1). doi: 10.1007/s10915-020-01277-y.
- Ranocha, H, Dalcin, L, und Parsani, M. . „Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.“ Computers and Mathematics with Applications 80 (5): 1343–1359. doi: 10.1016/j.camwa.2020.06.016.
- Ranocha, H, Lóczi, L, und Ketcheson, DI. . „General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes.“ Numerische Mathematik 146. doi: 10.1007/s00211-020-01158-4.
- Ketcheson, DI, Parsani, M, Grant, ZJ, Ahmadia, A, und Ranocha, H. . „RK-Opt: A package for the design of numerical ODE solvers.“ Journal of Open Source Software 5 (54): 2514.. doi: 10.21105/joss.02514.
- Ranocha, H, und Ketcheson, DI. . „Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems.“ SIAM Journal on Numerical Analysis 58 (6): 3382–3405. doi: 10.1137/19M1290346.
- Ketcheson, DI, Ranocha, H, Parsani, M, Waheed, U, und Hadjimichael, Y. . „NodePy: A package for the analysis of numerical ODE solvers.“ Journal of Open Source Software 5 (55): 2515.. doi: 10.21105/joss.02515.
- Hutzenthaler, M, Jentzen, A, Kruse, T, und Nguyen, TA. . „A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations.“ SN Partial Differential Equations and Applications 1 (2) 10. doi: 10.1007/s42985-019-0006-9.
- Becker, S, Cheridito, P, und Jentzen, A. . „Pricing and Hedging American-Style Options with Deep Learning.“ Journal of Risk and Financial Management 13 (7) 158. doi: 10.3390/jrfm13070158.
- Fehrman, B, Gess, B, und Jentzen, A. . „Convergence rates for the stochastic gradient descent method for non-convex objective functions.“ Journal of Machine Learning Research 21: Paper No. 136, 48..
- Jentzen, A, und Pušnik, P. . „Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities.“ IMA Journal of Numerical Analysis 40 (2): 1005–1050. doi: 10.1093/imanum/drz009.
- Berner, J, Grohs, P, und Jentzen, A. . „Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.“ SIAM Journal on Mathematics of Data Science 2 (3): 631–657. doi: 10.1137/19M125649X.
- Hutzenthaler, M., Jentzen, A., und von Wurstemberger, P. . „Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.“ Electronic Journal of Probability 25: Paper No. 101, 73.. doi: 10.1214/20-EJP423.
- Becker, S, Gess, B, Jentzen, A, und Kloeden, PE. . „Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations.“ BIT Numerical Mathematics 60 (4): 1057–1073. doi: 10.1007/s10543-020-00807-2.
- Becker, S, Braunwarth, R, Hutzenthaler, M, Jentzen, A, und von, Wurstemberger P. . „Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations.“ Communications in Computational Physics 28 (5): 2109–2138. doi: 10.4208/cicp.oa-2020-0130.
- Jentzen, A, Lindner, F, und Pušnik, P. . „Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions.“ Numerical Algorithms 85 (4): 1447–1473. doi: 10.1007/s11075-019-00871-y.
- Beck, C, Hornung, F, Hutzenthaler, M, Jentzen, A, und Kruse, T. . „Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations.“ Journal of Numerical Mathematics 28 (4): 197–222. doi: 10.1515/jnma-2019-0074.
- Hutzenthaler, M, Jentzen, A, Kruse, T, Nguyen, TA, und von, Wurstemberger P. . „Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations.“ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2244): 630–654. doi: 10.1098/rspa.2019.0630.
- Hutzenthaler, M, und Jentzen, A. . „On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients.“ Annals of Probability 48 (1): 53–93. doi: 10.1214/19-AOP1345.
- Repple, J, Mauritz, M, Meinert, S, de, Lange SC, Grotegerd, D, Opel, N, Redlich, R, Hahn, T, Förster, K, Leehr, EJ, Winter, N, Goltermann, J, Enneking, V, Fingas, SM, Lemke, H, Waltemate, L, Nenadic, I, Krug, A, Brosch, K, Schmitt, S, Stein, F, Meller, T, Jansen, A, Steinsträter, O, Baune, BT, Kircher, T, Dannlowski, U*, und van, den Heuvel MP* (*equal contribution). . „Severity of current depression and remission status are associated with structural connectome alterations in major depressive disorder.“ Molecular Psychiatry 25. doi: 10.1038/s41380-019-0603-1.
- Fischer, J., Laux, T., und Simon, T.M. . „Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies.“ SIAM Journal on Mathematical Analysis 52 (6): 6222–6233. doi: 10.1137/20M1322182.
- Bernand-Mantel, A., Muratov, C.B., und Simon, T.M. . „Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions.“ Physical Review B 101 (4) 045416. doi: 10.1103/PhysRevB.101.045416.
- Crestetto, Anais, Klingenberg, Christian, und Pirner, Marlies. . „Kinetic/fluid micro-macro numerical scheme for a two component gas mixture.“ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 18 (2). doi: 10.1137/17M1141023.
- Moinat, Augustin, und Weber, Hendrik. . „Space-time localisation for the dynamic Phi-4/3 model.“ Communications on Pure and Applied Mathematics 73 (12): 2519–2555. doi: 10.1002/cpa.21925.
- Tsatsoulis, Pavlos, und Weber, Hendrik. . „Exponential loss of memory for the 2-dimensional Allen–Cahn equation with small noise.“ Probability Theory and Related Fields 177: 257–322. doi: 10.1007/s00440-019-00945-x.
- Moinat, Augustin, und Weber, Hendrik. . „Local bounds for stochastic reaction diffusion equations.“ Electronic Journal of Probability 25: 1–26. doi: 10.1214/19-EJP397.
- Hilhorst, Danielle, Matano, Hiroshi, Nguyen, Thanh Nam, und Weber, Hendrik. . „Generation of Interface for Solutions of the Mass Conserved Allen--Cahn Equation.“ SIAM Journal on Mathematical Analysis 52 (3): 2624–2654. doi: 10.1137/18M1204747.
- Kaib, Gunnar, Kang, Kyungkeun, und Stevens, Angela. . „Global minimisers for anisotropic attractive-repulsive interactions.“ European Journal of Applied Mathematics 31 (5): 854–870. doi: 10.1017/S0956792519000299.
- Bach, A; Braides, A.; Zeppieri, C.I.. . „Quantitative analysis of finite-difference approximations of free-discontinuity problems.“ Interfaces and Free Boundaries 22. doi: 10.4171/IFB/443.
- Zeppieri, C.I.. . „Homogenisation of high-contrast brittle materials.“ Mathematics in Engineering 2 (1).
Online First
- Bansal, H, Rave, S, Iapichino, L, Schilders, WHA, und van, de Wouw N. . „Model order reduction framework for problems with moving discontinuities.“ Beitrag präsentiert auf der Proceedings of ENUMATH 2019, Egmond aan Zee
accepted / in Press (not yet published)
- Crismale, V, Friedrich, M, und Solombrino, F. im Druck. „Integral representation for energies in linear elasticity with surface discontinuities.“ Adv. Calc. Var. 2020.
- Friedrich, M, Kruzik, M, und Stefanelli, U. im Druck. „Equilibrium of immersed hyperelastic solids.“ DCDS-S 2020.
- Friedrich, M, Kruzik, M, und Valdman, J. im Druck. „Numerical approximation of von Kármán viscoelastic plates.“ DCDS-S 2020.
- Rave, S, und Saak, J. im Druck. „A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction.“ Beitrag präsentiert auf der ENUMATH 2019, Graz Springer.
- Mlinarić, P, Rave, S, und Saak, J. im Druck. „Parametric model order reduction using pyMOR.“ Beitrag präsentiert auf der MODRED 2019, Graz Springer.
- Altenbernd, Mirco Dreier Nils-Arne, und Engwer, Christian Göddeke Dominik. im Druck. „Towards local-failure local-recovery in PDE frameworks: the case of linear solvers.“ Beitrag präsentiert auf der HPCSE 2019, Ostrava, Czech Republic
Eingereicht / In Begutachtung
- Friedrich, M, Perugini, M, und Solombrino, F. . Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD
- Davoli, E, und Friedrich, M. . Two-well linearization for solid-solid phase transitions
- Brunken, Julia Smetana Kathrin. . „Stable and efficient Petrov-Galerkin methods for a kinetic Fokker-Planck equation.“ arXiv 2020.
- Friedrich, M, Kreutz, L, und Schmidt, B. . Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy
- Beck, C, Gonon, L, und Jentzen, A. . „Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations.“ IMA Journal of Numerical Analysis.
- Jentzen, A, und Welti, T. . „Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation.“ SIAM Journal on Numerical Analysis.
- Hornung, F, Jentzen, A, und Salimova, D. . „Space-time deep neural network approximations for high-dimensional partial differential equations.“ Journal of Nonlinear Science.
- Bercher, A, Gonon, L, Jentzen, A, und Salimova, D. . Lecture Notes in Mathematics, Weak error analysis for stochastic gradient descent optimization algorithms Springer VDI Verlag.
- Hutzenthaler, M, Jentzen, A, Kruse, T, und Nguyen, TA. . „Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities.“ Nonlinearity.
- Beck, C, Jentzen, A, und Kruse, T. . „Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations.“ Advances in Computational Mathematics.
- Beck, C, Becker, S, Cheridito, P, Jentzen, A, und Neufeld, A. . „Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems.“ arXiv.
- Beneventano, P, Cheridito, P, Jentzen, A, und von, Wurstemberger P. . „High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations.“ arXiv.
- Friedrich, M, Perugini, M, und Solombrino, F. . Gamma-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation
Veröffentlicht
- Feinauer, J, Hein, S, Rave, S, Schmidt, S, Westhoff, D, Zausch, J, Iliev, O, Latz, A, Ohlberger, M, und Schmidt, V. . „MULTIBAT: Unified workflow for fast electrochemical 3D simulations of lithium-ion cells combining virtual stochastic microstructures, electrochemical degradation models and model order reduction.“ Journal of Computational Science 31: 172–184. doi: 10.1016/j.jocs.2018.03.006.
- Schmitzer, B, und Wirth, B. . „A framework for Wasserstein-1-type metrics.“ Journal of Convex Analysis 26 (2): 353–396.
- Lehrenfeld, Christoph, und Rave, Stephan. . „Mass Conservative Reduced Order Modeling of a Free Boundary Osmotic Cell Swelling Problem.“ Advances in Computational Mathematics 45 (5): 2215–2239. doi: 10.1007/s10444-019-09691-z.
- Brunken, Julia, Smetana, Kathrin, und Urban, Karsten. . „(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods.“ SIAM Journal on Scientific Computing 41 (1). doi: 10.1137/18M1176269.
- Schmitzer, B, und Wirth, B. . „Dynamic Models of Wasserstein-1-Type Unbalanced Transport.“ ESAIM: Control, Optimisation and Calculus of Variations 25: 23..
- Friedrich, M, Mainini, E, Piovano, P, und Stefanelli, U. . „Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule.“ Arch. Ration. Mech. Anal. 231.
- Heeren, B, Rumpf, M, und Wirth, B. . „Variational time discretization of Riemannian splines.“ IMA Journal of Numerical Analysis 26 (2): 353–396. doi: 10.1093/imanum/drx077.
- Hain, S, Ohlberger, M, Radic, M, und Urban, K. . „A Hierarchical A-Posteriori Error Estimatorfor the Reduced Basis Method.“ Advances in Computational Mathematics 45: 2191–2214. doi: 10.1007/s10444-019-09675-z.
- Marchese, Andrea, und Wirth, Benedikt. . „Approximation of rectifiable 1-currents and weak-∗relaxation of the h-mass.“ Journal of Mathematical Analysis and Applications 479 (2): 2268–2283. doi: 10.1016/j.jmaa.2019.07.059.
- Wirth, B. . „Phase field models for two-dimensional branched transportation problems.“ Calculus of Variations and Partial Differential Equations 58 (5): Paper No. 164, 31.. doi: 10.1007/s00526-019-1615-z.
- Dondl, PW, Novaga, M, Wirth, B, und Wojtowytsch, S. . „A phase-field approximation of the perimeter under a connectedness constraint.“ SIAM Journal on Mathematical Analysis 51 (5): 3902–3920. doi: 10.1137/18M1225197.
- Jentzen, A, Salimova, D, und Welti, T. . „Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations.“ Journal of Mathematical Analysis and Applications 469 (2): 661–704. doi: 10.1016/j.jmaa.2018.09.032.
- Hefter, M, und Jentzen, A. . „On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes.“ Finance and Stochastics 23 (1): 139–172. doi: 10.1007/s00780-018-0375-5.
- Becker, S, und Jentzen, A. . „Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations.“ Stochastic Processes and their Applications 129 (1): 28–69. doi: 10.1016/j.spa.2018.02.008.
- Conus, D, Jentzen, A, und Kurniawan, R. . „Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients.“ Annals of Applied Probability 29 (2): 653–716. doi: 10.1214/17-AAP1352.
- Andersson, A, Hefter, M, Jentzen, A, und Kurniawan, R. . „Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces.“ Potential Analysis 50 (3): 347–379. doi: 10.1007/s11118-018-9685-7.
- E, W, Hutzenthaler, M, Jentzen, A, und Kruse, T. . „On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations.“ Journal of Scientific Computing 79 (3): 1534–1571. doi: 10.1007/s10915-018-00903-0.
- Becker, S, Cheridito, P, und Jentzen, A. . „Deep optimal stopping.“ Journal of Machine Learning Research 20: Paper No. 74, 25..
- Jentzen, A, Lindner, F, und Pušnik, P. . „On the Alekseev-Gröbner formula in Banach spaces.“ Discrete and Continuous Dynamical Systems - Series B 24 (8): 4475–4511. doi: 10.3934/dcdsb.2019128.
- Beck, C, E, W, und Jentzen, A. . „Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations.“ Journal of Nonlinear Science 29 (4): 1563–1619. doi: 10.1007/s00332-018-9525-3.
- Da, Prato G, Jentzen, A, und Röckner, M. . „A mild Itô formula for SPDEs.“ Transactions of the American Mathematical Society 372 (6): 3755–3807. doi: 10.1090/tran/7165.
- Balicki, L, Mlinarić, P, Rave, S, und Saak, J. . „System-theoretic model order reduction with pyMOR.“ PAMM 19. doi: 10.1002/pamm.201900459.
- Ohlberger, M, Buhr, A, Eikhorn, D, Engwer, C, und Rave, S. . „Advances in Model Order Reduction for Large Scale or Multi-Scale Problems.“ Oberwolfach Reports 16 (3): 2510–2512. doi: 10.4171/OWR/2019/40.
- Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia, und Zeppieri, Caterina Ida. . „Γ-convergence of free-discontinuity problems.“ Annales de l'Institut Henri Poincaré C. Analyse non linéaire 36 (4): 1035–1079. doi: 10.1016/j.anihpc.2018.11.003.
- Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia, und Zeppieri, Caterina Ida. . „Stochastic homogenisation of free-discontinuity problems.“ Archive for Rational Mechanics and Analysis 233 (2): 935–974. doi: 10.1007/s00205-019-01372-x.
- Pellet, X, Scardia, L, und Zeppieri, CI. . „Homogenization of high-contrast Mumford-Shah energies.“ SIAM J. Math. Anal. 51: 1696–1729.
- Friedrich, M. . „Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials.“ Mathematics in Engineering 2.
- Friedrich, M, und Kreutz, L. . „Crystallization in the hexagonal lattice for ionic dimers.“ Math. Models Methods Appl. Sci. 29.
- Friedrich, M. . „A compactness result in GSBV^p and applications to Gamma-convergence for free discontinuity problems.“ Calc. Var. PDE 68.
- Hellman, Fredrik, Keil, Tim, und Målqvist, Axel. . „Multiscale methods for perturbed diffusion problems.“ Oberwolfach Reports 16: 2099–2181. doi: 10.4171/OWR/2019/35.
- Schleuß, Julia. . Master's thesis, Optimal local approximation spaces for parabolic problems (Master's thesis)
- Rave, Stephan, und Schindler, Felix. . „A locally conservative reduced flux reconstruction for elliptic problems.“ In Special Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Bd. 19 , herausgegeben von J Eberhardsteiner und M Schöberl. John Wiley & Sons. doi: 10.1002/pamm.201900026.
- Conlon, JG, und Schlichting, A. . „A non-local problem for the Fokker-Planck equation related to the Becker-Döring model.“ Discrete and Continuous Dynamical Systems - Series A 39 (4): 1821–1889. doi: 10.3934/dcds.2019079.
- Schlichting, A. . „Macroscopic limit of the Becker-Döring equation via gradient flows.“ ESAIM: Control, Optimisation and Calculus of Variations 25 (22): 36.. doi: 10.1051/cocv/2018011.
- Schlichting, A. . „Poincaré and Log–Sobolev Inequalities for Mixtures.“ Entropy 21 (1): 89.. doi: 10.3390/e21010089.
- Schlichting, A, und Slowik, M. . „Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities.“ Annals of Applied Probability 29 (6): 3438–3488. doi: 10.1214/19-AAP1484.
- Carrillo, JA, Gvalani, RS, Pavliotis, GA, und Schlichting, A. . „Long-Time Behaviour and Phase Transitions for the McKean-Vlasov Equation on the Torus.“ Archive for Rational Mechanics and Analysis 235 (1): 635–690. doi: 10.1007/s00205-019-01430-4.
- Sommer, Liesel. . An unfitted discontinuous Galerkin scheme for a phase-field approximation of pressurized fractures, [Electronic ed.], herausgegeben von C Engwer.
- Taha, M, Aldirawi, M, März, S, Seebach, J, Odenthal-Schnittler, M, Bondareva, O, Bojovic, V, Schmandra, T, Wirth, B, Mietkowska, M, Rottner, K, und Schnittler, H. . „EPLIN-α and -β isoforms modulate endothelial cell dynamics through a spatio-temporally differentiated interaction with actin.“ Cell Reports 29 (4): P1010–1026.E6..
- Ranocha, H. . „Mimetic Properties of Difference Operators: Product and Chain Rules as for Functions of Bounded Variation and Entropy Stability of Second Derivatives.“ BIT Numerical Mathematics 59 (2): 547–563. doi: 10.1007/s10543-018-0736-7.
- Öffner, P, und Ranocha, H. . „Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients.“ Journal of Scientific Computing 79 (3): 1572–1607. doi: 10.1007/s10915-018-00902-1.
- Öffner, P, Glaubitz, J, und Ranocha, H. . „Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach.“ ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN) 52 (6): 2215–2245. doi: 10.1051/m2an/2018072.
- Ranocha, H. . „Some Notes on Summation by Parts Time Integration Methods.“ Results in Applied Mathematics 1: 100004.. doi: 10.1016/j.rinam.2019.100004.
- Benner, P, und Himpe, C. . „Cross-Gramian-Based Dominant Subspaces.“ Advances in Computational Mathematics 45 (5): 2533–2553. doi: 10.1007/s10444-019-09724-7.
- Grundel, S, Himpe, C, und Saak, J. . „On Empirical System Gramians.“ In Bd. 19 aus Proceedings in Applied Mathematics and Mechanics (PAMM) doi: 10.1002/pamm.201900006.
- Muratov, C.B., und Simon, T.M. . „A nonlocal isoperimetric problem with dipolar repulsion.“ Communications in Mathematical Physics 372: 1059–1115. doi: 10.1007/s00220-019-03455-y.
- Klingenberg, Christian, Pirner, Marlies, und Puppo, Gabriella. . „A consistent kinetic model for a two-component mixture of polyatomic molecules.“ Communications in Mathematical Sciences 17 (1): 149–173. doi: 10.4310/CMS.2019.v17.n1.a6.
- Liu, Liu, und Pirner, Marlies. . „Hypocoercivity for a BGK model for gas mixtures.“ Journal of Differential Equations 267 (1): 119–149. doi: 10.1016/j.jde.2019.01.006.
- Otto, Felix, und Weber, Hendrik. . „Quasi-linear SPDEs in divergence form.“ Stochastics and Partial Differential Equations: Analysis and Computations 7 (1): 64–85. doi: 10.1007/s40072-018-0122-0.
- Otto, Felix, und Weber, Hendrik. . „Quasilinear SPDEs via Rough Paths.“ Archive for Rational Mechanics and Analysis 232 (2): 873–950. doi: 10.1007/s00205-018-01335-8.
- Kang, Kyungkeun, Scheel, Arnd, und Stevens, Angela. . „Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup.“ Nonlinearity 32 (6). doi: 10.1088/1361-6544/ab046d.
Online First
- Riesselmann, Johannes Ketteler Jonas Wilhelm, und Schedensack, Mira Balzani Daniel. . „Three‐field mixed finite element formulations for gradient elasticity at finite strains.“ GAMM-Mitteilungen xxx. doi: 10.1002/gamm.202000002.
Eingereicht / In Begutachtung
- Friedrich, M., und M, Kruzik. . Derivation of von Kármán plate theory in the framework of threedimensional viscoelasticity
- Schneider, Florian Leibner Tobias. . „First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis.“ arXiv 2019.
- Hutzenthaler, M, Jentzen, A, Lindner, F, und Pušnik, P. . „Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations.“ arXiv.
- Giles, MB, Jentzen, A, und Welti, T. . „Generalised multilevel Picard approximations.“ IMA J. Numer. Anal..
- Cox, S, Jentzen, A, und Lindner, F. . „Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise.“ arXiv.
- Beccari, M, Hutzenthaler, M, Jentzen, A, Kurniawan, R, Lindner, F, und Salimova, D. . „Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities.“ arXiv.
Veröffentlicht
- Gallistl, D, Henning, P, und Verfürth, B. . „Numerical homogenization of H(curl)-problems.“ SIAM J. Numer. Anal. 56 (3): 1570–1596. doi: 10.1137/17M1133932.
- Burger, Martin, DiFrancesco, Marco, Fagioli, Simone, und Stevens, Angela. . „Sorting phenomena in a mathematical model for two mutually attracting/repelling species.“ SIAM Journal on Mathematical Analysis 50 (3): 3210–3250. doi: 10.1137/17M1125716.
- Ohlberger, M, und Verfürth, B. . „A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast.“ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 16 (1): 385–411. doi: 10.1137/16M1108820.
- Verfürth, B. . „Numerical multiscale methods for Maxwell's equations in heterogeneous media.“ Dissertationsschrift, Universität Münster.
- Dreier, Nils-Arne, Engwer, Christian, und Hartmann, Dirk. . „Galerkin local maximum entropy method.“ International Journal for Numerical Methods in Fluids. doi: 10.1002/fld.4513.
- Engwer, Christian Altenbernd Mirco, und Dreier, Nils-Arne Dominik Göddeke. . „A high-level C++ approach to manage local errors, asynchrony and faults in an MPI application.“ Beitrag präsentiert auf der 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing, Cambridge, Vereinigtes Königreich doi: 10.1109/PDP2018.2018.00117.
- Friedrich, M, und Stefanelli, U. . „Graphene ground states.“ Z. Angew. Math. Phys. 69.
- Friedrich, M, und Kruzik, M. . „On the passage from nonlinear to linearized viscoelasticity.“ SIAM J. Math. Anal. 50.
- Friedrich, M. . A piecewise Korn inequality in SBD and applications to embedding and density results
- Friedrich, M, und Solombrino, F. . „Quasistatic crack growth in 2d-linearized elasticity.“ Ann. Inst. H. Poincaré Anal. Non Linéaire 35: 27–64. doi: 10.1016/j.anihpc.2017.03.002.
- Friedrich, M. . „On a decomposition of regular domains into John domains with uniform constants.“ ESAIM Control Optim. Calc. Var. 24. doi: 10.1051/cocv/2017029.
- Clason, C, Tameling, C, und Wirth, B. . „Vector-valued multibang control of differential equations.“ SIAM Journal on Control and Optimization 56 (3): 2295–2326.
- Brancolini, Alessio, und Rossmanith, Carolin Wirth Benedikt. . „Optimal micropatterns in 2D transport networks and their relation to image inpainting.“ Archive for Rational Mechanics and Analysis 228 (1): 279–308. doi: 10.1007/s00205-017-1192-2.
- Brancolini, A, und Wirth, B. . „General transport problems with branched minimizers as functionals of 1-currents with prescribed boundary.“ Calculus of Variations and Partial Differential Equations 57 (3): Paper No. 82, 39.. doi: 10.1007/s00526-018-1364-4.
- Hutzenthaler, M, Jentzen, A, und Wang, X. . „Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations.“ Mathematics of Computation 87 (311): 1353–1413. doi: 10.1090/mcom/3146.
- Naurois, L, Jentzen, A, und Welti, T. . „Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations.“ In Stochastic partial differential equations and related fields, Bd. 229 aus Springer Proc. Math. Stat., herausgegeben von A. Eberle, M. Grothaus, W. Hoh, M. Kassmann, W. Stannat und G. Trutnau. Springer VDI Verlag. doi: 10.1007/978-3-319-74929-7_13.
- Han, J, Jentzen, A, und E, W. . „Solving high-dimensional partial differential equations using deep learning.“ Proceedings of the National Academy of Sciences of the United States of America 115 (34): 8505–8510. doi: 10.1073/pnas.1718942115.
- Jentzen, A, und Pušnik, P. . „Exponential moments for numerical approximations of stochastic partial differential equations.“ Stochastics and Partial Differential Equations: Analysis and Computations 6 (4): 565–617. doi: 10.1007/s40072-018-0116-y.
- Cox, S, Jentzen, A, Kurniawan, R, und Pušnik, P. . „On the mild Itô formula in Banach spaces.“ Discrete and Continuous Dynamical Systems - Series B 23 (6): 2217–2243. doi: 10.3934/dcdsb.2018232.
- Hutzenthaler, M, Jentzen, A, und Salimova, D. . „Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations.“ Communications in Mathematical Sciences 16 (6): 1489–1529. doi: 10.4310/CMS.2018.v16.n6.a2.
- Eickhorn, Dennis. . Randomisierte lokalisierte Modellreduktion mit Robin-Transferoperator (Masterarbeit)
- Ohlberger, Mario, Rave, Stephan, Schindler, Felix, und Wedemeier, Tobias. . „Model reduction for parameterized systems and inverse problems.“ Oberwolfach Reports 2018 (39): 2454–2457. doi: 10.4171/OWR/2018/39.
- Duong, MH, Lamacz, A, Peletier, MA, Schlichting, A, und Sharma, U. . „Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics.“ Nonlinearity 31 (10): 4517–4566. doi: 10.1088/1361-6544/aaced5.
- Conlon, JG, und Schlichting, A. . „A non-local Fokker-Planck equation related to nucleation and coarsening.“ In Oberwolfach Reports Interplay Anal. Probab. Appl. Math., herausgegeben von V Betz, N Dirr, W König und F Theil. European Mathematical Society Publishing House. doi: 10.4171/OWR/2018/6.
- Böhm, C, und Wirth, B. . „Mathematik Münster: Dynamik, Geometrie, Struktur. Beispiele einer geometrischen Sichtweise.“ Mitteilungen der Deutschen Mathematiker-Vereinigung 26 (4).
- Ranocha, H. . „Generalised Summation-by-Parts Operators and Entropy Stability of Numerical Methods for Hyperbolic Balance Laws.“ Dissertationsschrift, TU Braunschweig.
- Glaubitz, J, Öffner, P, Ranocha, H, und Sonar, T. . „Artificial Viscosity for Correction Procedure via Reconstruction Using Summation-by-Parts Operators.“ In Theory, Numerics and Applications of Hyperbolic Problems II, Bd. 237 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von C Klingenberg und M Westdickenberg. Cham: Springer International Publishing. doi: 10.1007/978-3-319-91548-7_28.
- Öffner, P, Ranocha, H, und Sonar, T. . „Correction Procedure via Reconstruction Using Summation-by-Parts Operators.“ In Theory, Numerics and Applications of Hyperbolic Problems II, Bd. 237 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von C Klingenberg und M Westdickenberg. Cham: Springer International Publishing. doi: 10.1007/978-3-319-91548-7_37.
- Ostaszewski, K, Heinisch, P, und Ranocha, H. . „Advantages and Pitfalls of OpenCL in Computational Physics.“ In Proceedings of the International Workshop on OpenCL, IWOCL '18, May 2018, Oxford (United Kingdom) New York, NY, USA: ACM Press. doi: 10.1145/3204919.3204929.
- Ranocha, H, Glaubitz, J, Öffner, P, und Sonar, T. . „Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators.“ Applied Numerical Mathematics 128: 1–23. doi: 10.1016/j.apnum.2018.01.019.
- Ranocha, H. . „Generalised Summation-by-Parts Operators and Variable Coefficients.“ Journal of Computational Physics 362: 20–48. doi: 10.1016/j.jcp.2018.02.021.
- Ranocha, H, und Öffner, P. . „L_2 Stability of Explicit Runge-Kutta Schemes.“ Journal of Scientific Computing 75 (2): 1040–1056. doi: 10.1007/s10915-017-0595-4.
- Ranocha, H. . „Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations.“ Journal of Scientific Computing 76 (1): 216–242. doi: 10.1007/s10915-017-0618-1.
- Benner, P, Himpe, C, und Mitchell, T. . „On Reduced Input-Output Dynamic Mode Decomposition.“ Advances in Computational Mathematics 44 (6): 1751–1768. doi: 10.1007/s10444-018-9592-x.
- Benner, P, Grundel, S, Himpe, C, Huck, C, Streubel, T, und Tischendorf, C. . „Gas Network Benchmark Models.“ In Applications of Differential-Algebraic Equations: Examples and Benchmarks, Differential-Algebraic Equations Forum, herausgegeben von S Campbell, A Ilchmann, V Mehrmann und T Reis. doi: 10.1007/11221_2018_5.
- Himpe, C. . „emgr - The Empirical Gramian Framework.“ Algorithms 11 (7): 91.. doi: 10.3390/a11070091.
- Benner, P, Grundel, S, und Himpe, C. . „Parametric Model Order Reduction for Gas Flow Models.“ In Bd. MoRePaS 4 aus ScienceOpen Posters ScienceOpen. doi: 10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1.
- Himpe, C, Leibner, T, und Rave, S. . „HAPOD - Fast, Simple and Reliable Distributed POD Computation.“ In Bd. 55 aus ARGESIM Report doi: 10.11128/arep.55.a55283.
- Simon, und T.M.. . „Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow.“ Dissertationsschrift, Universität Leipzig.
- Laux, T, und Simon, T.M. . „Convergence of the Allen-Cahn equation to multi-phase mean curvature flow.“ Communications on Pure and Applied Mathematics 71 (8): 1597–1647. doi: 10.1002/cpa.21747.
- Ayala, D, Doering, C.R., und Simon, T.M. . „Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations.“ Journal of Fluid Mechanics 837: 839–857. doi: 10.1017/jfm.2017.874.
- Pirner, Marlies. . „On kinetic modelling of gas mixtures.“ Dissertationsschrift, Universität Würzburg. doi: 10.25972/WUP-978-3-95826-081-8.
- Klingenberg, Christian, Pirner, Marlies, und Puppo, Gabriella. . „Kinetic ES-BGK models for a multi-component gas mixture.“ In Theory, Numerics and Applications of Hyperbolic Problems II : Aachen, Germany, August 2016, Bd. 237 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von Christian Klingenberg und Michael Westdickenberg. Cham: Springer. doi: 10.1007/978-3-319-91548-7_15.
- Li, Qin, Klingenberg, Christian, und Pirner, Marlies. . „On quantifying uncertainties for the linearized BGK kinetic equation.“ In Theory, Numerics and Applications of Hyperbolic Problems II : Aachen, Germany, August 2016, Bd. 237 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von Christian Klingenberg und Michael Westdickenberg. Cham: Springer. doi: 10.1007/978-3-319-91548-7_14.
- Klingenberg, Christian, und Pirner, Marlies. . „Existence, Uniqueness and Positivity of solutions for BGK models for mixtures.“ Journal of Differential Equations 265 (2): 702–727. doi: 10.1016/j.jde.2017.09.019.
- Pirner, Marlies. . „A BGK model for gas mixtures of polyatomic molecules allowing for slow and fast relaxation of the temperatures.“ Journal of Statistical Physics 173 (6): 1660–1687. doi: 10.1007/s10955-018-2158-y.
- Kottke, Kathrin, Deninger, Christopher, und Ohlberger, Mario. . „Mathematik Münster: Dynamik – Geometrie – Struktur.“ Mitteilungen der Deutschen Mathematiker-Vereinigung 26 (4): 189–193. doi: 10.1515/dmvm-2018-0058.
- Shen, Hao, und Weber, Hendrik. . „Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits.“ Journal of Functional Analysis 275 (6): 1321–1367. doi: 10.1016/j.jfa.2017.12.014.
- Tsatsoulis, Pavlos, und Weber, Hendrik. . „Spectral gap for the stochastic quantization equation on the 2-dimensional torus.“ Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 54 (3): 1204–1249. doi: 10.1214/17-AIHP837.
- Debussche, Arnaud, und Weber, Hendrik. . „The Schrodinger equation with spatial white noise potential.“ Electronic Journal of Probability 23: 1–16. doi: 10.1214/18-EJP143.
- Otto, Felix, Sauer, Jonas, Smith, Scott, und Weber, Hendrik. . „Parabolic equations with rough coefficients and singular forcing.“ Preprint. arXiv doi: 10.48550/arXiv.1803.07884.
- Ambrosi, Davide, Liu, Chun, Röger, Matthias, und Stevens, Angela, Hrsg. . Oberwolfach Reports, Bd. 15, The Mathematics of Mechanobiology and Cell Signaling Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. doi: 10.14760/OWR-2018-8.
- Himpe, C, Leibner, T, und Rave, S. . „Hierarchical Approximate Proper Orthogonal Decomposition.“ SIAM Journal on Scientific Computing 40 (5): A3267–A3292.
- Ohlberger, Mario, Schaefer, Michael, und Schindler, Felix. . „Localized Model Reduction in PDE Constrained Optimization.“ In Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 , Bd. 169 aus International Series of Numerical Mathematics, herausgegeben von V Schulz und D Seck. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-90469-6_8.
- Li, G., Peterseim, D., und Schedensack, M. . „Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions.“ IMA Journal of Numerical Analysis 38 (3): 1229–1253. doi: 10.1093/imanum/drx027.
- Hu, Jun, und Schedensack, Mira. . „Two low-order nonconforming finite element methods for the Stokes flow in 3D.“ IMA Journal of Numerical Analysis xxx. doi: 10.1093/imanum/dry021.
- Seis, Christian. . „Optimal stability estimates for continuity equations.“ Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148 (A): 1279–1296.. doi: 10.1017/S0308210518000173.
- Seis, Christian. . „The thin film equation close to self-similarity.“ Analysis and PDE 11 (5): 1303–1342.. doi: 10.2140/apde.2018.11.1303.
- Schlichting, A., und Seis, C. . „Analysis of the implicit upwind finite volume scheme with rough coefficients.“ Numerische Mathematik 139 (1): 155–186. doi: 10.1007/s00211-017-0935-1.
accepted / in Press (not yet published)
- Hudde, A, Hutzenthaler, M, Jentzen, A, und Mazzonetto, S. im Druck. „On the Itô--Alekseev--Gröbner formula for stochastic differential equations.“ Ann. Inst. Henri Poincaré Probab. Stat..
- Grohs, P, Hornung, F, Jentzen, A, und von, Wurstemberger P. im Druck. „A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black--Scholes partial differential equations.“ Memoirs of the American Mathematical Society.
- Verfürth, B. im Druck. „Heterogeneous Multiscale Method for the Maxwell equations with high contrast.“ ESAIM Math. Model. Numer. Anal. xx.
Veröffentlicht
- Ohlberger, M, und Verfürth, B. . „Localized Orthogonal Decomposition for two-scale Helmholtz-type problems.“ AIMS Mathematics 2 (3): 458–478. doi: 10.3934/Math.2017.2.458.
- Smetana, K, und Ohlberger, M. . „Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniques.“ M2AN Math. Model. Numer. Anal. 51 (2): 641–677. doi: 10.1051/m2an/2016031.
- Haidl, M, Steuwer, M, Dirks, H, Humernbrum, T, und Gorlatch, S. . „Towards Composable GPU Programming: Programming GPUs with Eager Actions and Lazy Views.“ In Proceedings of the 8th International Workshop on Programming Models and Applications for Multicores and Manycores, herausgegeben von Q Chen und Z Huang. New York, NY: ACM Press. doi: 10.1145/3026937.3026942.
- Song, J, Buscher, K, Wang, Y, Wang, H, Li, L, Di, Russo J, Zhang, X, Lütke-Enking, S, Zarbock, A, Striewski, P, Wirth, B, Kuzmanov, I, Wiendl, H, und Sorokin, L. . „Endothelial Basement Membrane Laminin 511 Contributes to Endothelial Junctional Tightness and thereby Inhibits Leukocyte Transmigration.“ Cell Reports 18 (5): 1256–1269.
- Baur, U, Benner, P, Haasdonk, B, Himpe, C, Martini, I, und Ohlberger, M. . „Comparison of methods for parametric model order reduction of instationary problems.“ In Model Reduction and Approximation: Theory and Algorithms., Bd. 15 aus CS, herausgegeben von P Benner, A Cohen, M Ohlberger und K Willcox. Philadelphia, PA: SIAM Publications. doi: 10.1137/1.9781611974829.ch9.
- Ohlberger, Mario. . „Book review of: A. Quarteroni et al., Reduced basis methods for partial differential equations. An introduction.“ SIAM Rev. 59 (3): 690–692.
- Benner, P, Ohlberger, M, Patera, A, Rozza, G, und Urban, K, Hrsg. . MS&A, Bd. 17, Model Reduction of Parametrized Systems Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8.
- Barth, T, Herbin, R, und Ohlberger, M. . „Finite Volume Methods: Foundation and Analysis.“ In Encyclopedia of Computational Mechanics, herausgegeben von E Stein, Borst R de und T Hughes. John Wiley & Sons. doi: 10.1002/9781119176817.ecm2010.
- Ohlberger, M, und Schindler, F. . „Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization.“ In Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, herausgegeben von C Cancès und P Omnes. Cham: Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- Benner, P, Cohen, A, Ohlberger, M, und Willcox, K. . Computational Science and Engineering, Bd. 15, Model Reduction and Approximation: Theory and Algorithms Philadelphia, PA: SIAM Publications. doi: 10.1137/1.9781611974829.
- Dedner, Andreas, Girke, Stefan, Klöfkorn, Robert, und Malkmus, Tobias. . „The DUNE-FEM-DG module.“ Archive of Numerical Software 5 (1): 21–61. doi: 10.11588/ans.2017.1.28602.
- Vorwerk, J, Engwer, C, Pursiainen, S, und Wolters, CH. . „A Mixed Finite Element Method to Solve the EEG Forward Problem.“ IEEE Transactions on Medical Imaging 36 (4): 930–941. doi: 10.1109/TMI.2016.2624634.
- Leibner, T, Milk, R, und Schindler, F. . „Extending DUNE: The dune-xt modules.“ Archive of Numerical Software 5 (1): 193–216. doi: 10.11588/ans.2017.1.27720.
- Burger, M., Lorz, A., und Wolfram, M. . „Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth.“ Kinetic and Related Models 10 (1): 117–140. doi: 10.3934/krm.2017005.
- Berkels, B, und Wirth, B. . „Joint denoising and distortion correction of atomic scale scanning transmission electron microscopy images.“ Inverse Problems 33 (9): 095002..
- Verfürth, B. . „Heterogeneous Multiscale Method for a Helmholtz problem with high contrast.“ Beitrag präsentiert auf der Winter school on Numerical Analysis of Multiscale Problems, HIM Bonn, Germany
- Ohlberger, M, Rave, S, und Schindler, F. . „True Error Control for the Localized Reduced Basis Method for Parabolic Problems.“ In Model Reduction of Parametrized Systems, Bd. 17 aus MS&A (Modeling, Simulation and Applications), herausgegeben von P. Benner, M. Ohlberger, A. Patera, G. Rozza und K. Urban. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- Ohlberger, M, und Rave, S. . „Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry.“ In Model Reduction of Parametrized Systems, Bd. 17 aus MS&A (Modeling, Simulation and Applications), herausgegeben von P. Benner, M. Ohlberger, A. Patera, G. Rozza und K. Urban. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_13.
- Himpe, C, und Ohlberger, M. . „Cross-Gramian-Based Model Reduction: A Comparison.“ In Model Reduction of Parametrized Systems, Bd. 17 aus MS&A (Modeling, Simulation and Applications), herausgegeben von P Benner, M Ohlberger, A Patera, G Rozza und K Urban. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_17.
- Buhr, A, Engwer, C, Ohlberger, M, und Rave, S. . „ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics.“ In Model Reduction of Parametrized Systems, Bd. 17 aus MS&A (Modeling, Simulation and Applications), herausgegeben von P. Benner, M. Ohlberger, A. Patera, G. Rozza und K. Urban. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_9.
- Engwer, C, Vorwerk, J, Ludewig, J, und Wolters, CH. . „A Discontinuous Galerkin Method for the EEG Forward Problem.“ SIAM Journal on Scientific Computing 39 (1): B138–B164. doi: 10.1137/15M1048392.
- Buhr, A, Engwer, C, Ohlberger, M, und Rave, S. . „ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications.“ SIAM Journal on Scientific Computing 39 (4): A1435–A1465.. doi: 10.1137/15M1054213.
- Engwer, C, und Nüßing, A. . „Geometric Reconstruction of Implicitly Defined Surfaces and Domains with Topological Guarantees.“ ACM Transactions on Mathematical Software 44 (2). doi: 10.1145/3104989.
- Stevens, Angela. . „Mathematics in the Life-Sciences: A personal point of view.“ Jahresbericht der deutschen Mathematiker-Vereinigung 119: 143–168. doi: 10.1365/s13291-017-0165-6.
- Grosskinsky, Stefan, Marahrens, Daniel, und Stevens, Angela. . „A Hydrodynamic Limit for Chemotaxis in a given Heterogeneous Environment.“ Vietnam Journal of Mathematics 45 (1-2): 127–152. doi: 10.1007/s10013-016-0209-8.
- Neugebauer, F, Möddel, G, Rampp, S, Burger, M, und Wolters, C. . „The effect of head model simplification on beamformer source localization.“ Frontiers in Neuroscience 11 (625). doi: 10.3389/fnins.2017.00625.
- Himpe, C, Leibner, T, Rave, S, und Saak, J. . „Fast Low-Rank Empirical Cross Gramians.“ PAMM 17 (1): 841–842. doi: 10.1002/pamm.201710388.
- Berendsen, J., Burger, M., und Pietschmann, J.-F. . „On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion.“ Nonlinear Analysis 159.
- Egger, H., Pietschmann, J.-F., und Schlottbom, M. . „On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms.“ Inverse Problems 33. doi: 10.1088/1361-6420/aa8cae.
- Friedrich, M. . „A Korn-type inequality in SBD for functions with small jump sets.“ Math. Models Methods Appl. Sci. (M3AS) 27: 2461–2484. doi: 10.1142/S021820251750049X.
- Friedrich, M. . „A derivation of linearized Griffith energies from nonlinear models.“ Arch. Ration. Mech. Anal. 225: 425–467. doi: 10.1007/s00205-017-1108-1.
- Bauer, C, Clason, C, Lorenz, D, und Wirth, B. . „A Sinkhorn-Newton method for entropic optimal transport.“ Beitrag präsentiert auf der Neural Information Processing Systems Conference, Long Beach, USA
- Zhang, C, Berkels, B, Wirth, B, und Voyles, PM. . „Joint Denoising and Distortion Correction for Atomic Column Detection in Scanning Transmission Electron Microscopy Images.“ Microscopy and Microanalysis 23(S1): 164–165.
- Andersson, A, Jentzen, A, Kurniawan, R, und Welti, T. . „On the differentiability of solutions of stochastic evolution equations with respect to their initial values.“ Nonlinear Analysis: Theory, Methods and Applications 162: 128–161. doi: 10.1016/j.na.2017.03.003.
- E, W, Han, J, und Jentzen, A. . „Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations.“ Communications in Mathematics and Statistics 5 (4): 349–380. doi: 10.1007/s40304-017-0117-6.
- Gerencsér, M, Jentzen, A, und Salimova, D. . „On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions.“ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2207): 20170104, 16.. doi: 10.1098/rspa.2017.0104.
- Keil, Tim. . Variational crimes in the Localized orthogonal decomposition method (master's thesis)
- Eberle, S, Niethammer, B, und Schlichting, A. . „Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation.“ Nonlinear Analysis: Theory, Methods and Applications 158: 142–167. doi: 10.1016/j.na.2017.04.009.
- Ranocha, H, Öffner, P, und Sonar, T. . „Summation-by-Parts and Correction Procedure via Reconstruction.“ In Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Bd. 119 aus Lecture Notes in Computational Science and Engineering, herausgegeben von ML Bittencourt, NA Dumont und JS Hesthaven. Cham: Springer. doi: 10.1007/978-3-319-65870-4_45.
- Ranocha, H. . „Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods.“ GEM - International Journal on Geomathematics 8 (1): 85–133. doi: 10.1007/s13137-016-0089-9.
- Ranocha, H, Öffner, P, und Sonar, T. . „Extended skew-symmetric form for summation-by-parts operators and varying Jacobians.“ Journal of Computational Physics 342: 13–28. doi: 10.1016/j.jcp.2017.04.044.
- Klingenberg, Christian, Pirner, Marlies, und Puppo, Gabriella. . „A consistent kinetic model for a two-component mixture with an application to plasma.“ Kinetic and Related Models 10 (2): 445–465. doi: 10.3934/krm.2017017.
- Berglund, Nils, Di Gesu, Giacomo, und Weber, Hendrik. . „An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two.“ Electronic Journal of Probability 22: 1–27. doi: 10.1214/17-EJP60.
- Mourrat, Jean-Christophe, und Weber, Hendrik. . „Convergence of the Two-Dimensional Dynamic Ising-Kac Model to Φ24.“ Communications on Pure and Applied Mathematics 70 (4): 717–812. doi: 10.1002/cpa.21655.
- Lu, Yulong, Stuart, Andrew, und Weber, Hendrik. . „Gaussian Approximations for Probability Measures on R<i>d</i>.“ SIAM/ASA Journal on Uncertainty Quantification 5 (1). doi: 10.1137/16M1105384.
- Lu, Yulong, Stuart, Andrew, und Weber, Hendrik. . „Gaussian Approximations for Transition Paths in Brownian Dynamics.“ SIAM Journal on Mathematical Analysis 49 (4). doi: 10.1137/16M1071845.
- Mourrat, Jean-Christophe, und Weber, Hendrik. . „Global well-posedness of the dynamic Φ4 model in the plane.“ Annals of Probability 45 (4): 2398–2476. doi: 10.1214/16-AOP1116.
- Mourrat, Jean-Christophe, und Weber, Hendrik. . „The Dynamic Phi-4/3 Model Comes Down from Infinity.“ Communications in Mathematical Physics 356 (3): 673–753. doi: 10.1007/s00220-017-2997-4.
- Chandra, Ajay, und Weber, Hendrik. . „Stochastic PDEs, Regularity structures, and interacting particle systems.“ Annales de la Faculté des sciences de Toulouse: Mathématiques 6 / 26 (4): 847–909. doi: 10.5802/afst.1555.
- Scheel, Arnd, und Stevens, Angela. . „Wavenumber selection in coupled transport equations.“ Journal of Mathematical Biology 75 (5): 1047–1073. doi: 10.1007/s00285-017-1107-8.
- Schedensack, M. . „Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition.“ ESAIM: Mathematical Modelling and Numerical Analysis 51 (2): 399–425. doi: 10.1051/m2an/2016024.
- Peterseim, D., und Schedensack, M. . „Relaxing the CFL Condition for the Wave Equation on Adaptive Meshes.“ Journal of Scientific Computing 72 (3): 1196–1213. doi: 10.1007/s10915-017-0394-y.
- Schedensack, M. . „A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees.“ Computational Methods in Applied Mathematics 17 (1): 161–185. doi: 10.1515/cmam-2016-0031.
- Alaeian, Hadiseh, Schedensack, Mira, Bartels, Clara, Peterseim, Daniel, und Weitz, Martin. . „Thermo-optical interactions in a dye-microcavity photon Bose-Einstein condensate.“ New Journal of Physics 19. doi: 10.1088/1367-2630/aa964c.
- Verfürth, B. . „Numerical homogenization for indefinite H(curl)-problems.“ In Proceedings of Equadiff 2017 Conference, herausgegeben von K Mikula, D Sevcovic und J Urban.
- Jerrard, R., und Seis, C. . „On the Vortex Filament Conjecture for Euler Flows.“ Archive for Rational Mechanics and Analysis 224 (1): 135–172. doi: 10.1007/s00205-016-1070-3.
- Schlichting, A., und Seis, C. . „Convergence rates for upwind schemes with rough coefficients.“ SIAM Journal on Numerical Analysis 55 (2): 812–840. doi: 10.1137/16M1084882.
- Crippa, Gianluca, Nobili, Camilla, Seis, Christian, und Spirito, Stefano. . „Eulerian and Lagrangian solutions to the continuity and Euler equations with $L^1$ vorticity.“ SIAM Journal on Mathematical Analysis 49 (5): 3973–3998.. doi: 10.1137/17M1130988.
- Seis, Christian. . „Optimal stability estimates for continuity equations.“ Oberwolfach Reports 14 (1). doi: 10.4171/OWR/2017/7.
Online First
- Grebhahn, A, Engwer, C, Bolten, M, und Apel, S. . „Variability of Stencil Computations for Porous Media.“ Concurrency and Computation: Practice and Experience Special Issue on Advanced Stencil-Code Engineering.
- Engwer, C, Falgout, R, und Yang, UM. . „A Framework of Stencil Computations for PDE based Applications with Examples from DUNE and hypre.“ Concurrency and Computation: Practice and Experience Special Issue on Advanced Stencil-Code Engineering.
accepted / in Press (not yet published)
- Herrmann, M, und Matthies, K. im Druck. „Uniqueness of solitary waves in the high-energy limit of FPU-type chains.“ Beitrag präsentiert auf der Patterns in Dynamics, Berlin
- Hefter, M, Jentzen, A, und Kurniawan, R. im Druck. „Counterexamples to regularities for the derivative processes associated to stochastic evolution equations.“ Stochastics and Partial Differential Equations: Analysis and Computations.
Eingereicht / In Begutachtung
- Buhr, Andreas, und Smetana, Kathrin. . „Randomized Local Model Order Reduction.“ arXiv:1706.09179.
Veröffentlicht
- Henning, P, Ohlberger, M, und Verfürth, B. . „Analysis of multiscale methods for time-harmonic Maxwell's equations.“ Proc. Appl. Math. Mech. 16 (1): 559–560. doi: 10.1002/pamm.201610268.
- Smetana, Kathrin Patera Anthony T. . „Optimal local approximation spaces for component-based static condensation procedures.“ SIAM J. Sci. Comput. 38 (5): A3318––A3356.. doi: 10.1137/15M1009603.
- Himpe, C, und Ohlberger, M. . „A note on the cross Gramian for non-symmetric systems.“ System Science and Control Engineering 4 (1): 199–208. doi: 10.1080/21642583.2016.1215273.
- Lehrenfeld, Christoph. . „High order unfitted finite element methods on level set domains using isoparametric mappings.“ Comp. Meth. Appl. Mech. Eng. 300 (1): 716–733. doi: 10.1016/j.cma.2015.12.005.
- Absil, P-A, Gousenbourger, P-Y, Striewski, P, und Wirth, B. . „Differentiable piecewise-Bezier interpolation on Riemannian manifolds.“ Beitrag präsentiert auf der European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges (Belgium)
- Absil, P-A, Gousenbourger, Pierre-Yves, Striewski, Paul Wirth, und Benedikt. . „Differentiable piecewise-Bézier surfaces on Riemannian manifolds.“ SIAM Journal on Imaging Sciences 9 (4): 1788–1828. doi: 10.1137/16M1057978.
- Wirth, B. . „On the Gamma-limit of joint segmentation and registration functionals based on phase fields.“ Interfaces and Free Boundaries 18 (4): 441–477.
- Buscher, K, Wang, H, Zhang, X, Striewski, P, Wirth, B, Saggu, G, Lütke-Enking, S, Mayadas, TN, Ley, K, Sorokin, L, und Song, J. . „Protection from septic peritonitis by rapid neutrophil recruitment through omental high endothelial venules.“ Nature Communications 7: 10828..
- Lu, J, Wirth, B, und Yang, H. . „Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis.“ Journal of the Mechanics and Physics of Solids 89: 194–210.
- Kohn, Robert V., und Wirth, Benedikt. . „Optimal fine-scale structures in compliance minimization for a shear load.“ Communications on Pure and Applied Mathematics 69: 1572–1610. doi: 10.1002/cpa.21589.
- Ohlberger, M, Rave, S, und Schindler, F. . „Model Reduction for Multiscale Lithium-Ion Battery Simulation.“ In Numerical Mathematics and Advanced Applications ENUMATH 2015, Bd. 112 aus Lecture Notes in Computational Science and Engineering, herausgegeben von B Karasözen, M Manguoğlu, M Teuer-Sezgin, S Göktepe und Ö Uğur. Springer. doi: 10.1007/978-3-319-39929-4_31.
- Henning, P, Ohlberger, M, und Verfürth, B. . „A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations.“ SIAM J. Numer. Anal. 54 (6): 3493–3522. doi: 10.1137/15M1039225.
- Lehrenfeld, C, und Reusken, A. . „Optimal Preconditioners for Nitsche-XFEM Discretizations of Interface Problems.“ Numerische Mathematik 2016. doi: 10.1007/s00211-016-0801-6.
- Falconi, Delgado C, Lehrenfeld, C, Marschall, H, Meyer, C, Abiev, R, Bothe, D, Reusken, A, Schlüter, M, und Wörner, M. . „Numerical and Experimental Analysis of Local Flow Phenomena in Laminar Taylor Flow in a Square Mini-Channel.“ Physics of Fluids 28 (1): 012109..
- Ohlberger, M, und Smetana, K. . „Approximation of skewed interfaces with tensor-based model reduction procedures: application to the reduced basis hierarchical model reduction approach.“ J. Comp. Phys. 321: 1185–1205. doi: 10.1016/j.jcp.2016.06.021.
- Schindler, F. . „Model reduction for parametric multi-scale problems.“ Dissertationsschrift, Westfälische Wilhelms-Universität Münster.
- Zeppieri, C.I. . „Stochastic homogenisation of singularly-perturbed integral functionals.“ Ann. Mat. Pura Appl. 195.
- Bevan, JJ, und Zeppieri, CI. . „A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation.“ Calc. Var. Partial Diff. Equations 55.
- Barchiesi, Marco, Lazzaroni, Giuliano, und Zeppieri, Caterina Ida. . „A bridging mechanism in the homogenisation of brittle composites with soft inclusions.“ SIAM Journal on Mathematical Analysis 48 (2): 1178–1209. doi: 10.1137/15M1007343.
- Herrmann, M. . „High-energy waves in superpolynomial FPU-type chains.“ Journal of Nonlinear Science 2016. doi: 10.1007/s00332-016-9331-8.
- Herrmann, M, Niethammer, B, und Velázquez, JJL. . „Instabilities and oscillations in coagulation equations with kernels of homogeneity one.“ Quarterly of Applied Mathematics 75-1. doi: 10.1090/qam/1454.
- Mannweiler, D., Suhr, S., Modersitzki, J., und Burger, M. . „Variational method for motion corrected reconstruction with MRI information in positron emission tomography.“ In Bd. null aus IEEE Nuclear Science Symposium and Medical Imaging Conference Wiley-IEEE Press. doi: 10.1109/NSSMIC.2015.7582045.
- Burger, M., Gilboa, G., Moeller, M., Eckardt, L., und Cremers, D. . „Spectral decompositions using one-homogeneous functionals.“ SIAM Journal on Imaging Sciences 9 (3): 1374–1408. doi: 10.1137/15M1054687.
- Burger, M., Rossmanith, C., und Zhang, X. . „Simultaneous reconstruction and segmentation for dynamic SPECT imaging.“ Inverse Problems 32 (10). doi: 10.1088/0266-5611/32/10/104002.
- Burger, M., Lorz, A., und Wolfram, M. . „On a Boltzmann mean field model for knowledge growth.“ SIAM Journal on Applied Mathematics 76 (5): 1799–1818. doi: 10.1137/15M1018599.
- Gilboa, G., Moeller, M., und Burger, M. . „Nonlinear Spectral Analysis via One-Homogeneous Functionals: Overview and Future Prospects.“ Journal of Mathematical Imaging and Vision 56 (2): 300–319. doi: 10.1007/s10851-016-0665-5.
- Burger, M., Hittmeir, S., Ranetbauer, H., und Wolfram, M. . „Lane formation by side-stepping.“ SIAM Journal on Mathematical Analysis 48 (2): 981–1005. doi: 10.1137/15M1033174.
- Burger, M., und Pietschmann, J. . „Flow characteristics in a crowded transport model.“ Nonlinearity 29 (11): 3528–3550. doi: 10.1088/0951-7715/29/11/3528.
- Burger, M. . „Bregman distances in inverse problems and partial differential equations.“ In Advances in Mathematical Modeling, Optimization, and Optimal Control, Bd. 109 aus Springer Optimization and Its Applications, herausgegeben von A.Korytowski J.Hiriard-Urrurty und M.Szymkat H.Maurer. Springer International Publishing. doi: 10.1007/978-3-319-30785-5_2.
- Wagner, S., Lucka, F., Vorwerk, J., Herrmann, C., Nolte, G., Burger, M., und Wolters, C. . „Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem.“ NeuroImage 140 (null): 163–173. doi: 10.1016/j.neuroimage.2016.04.005.
- Nüßing, A, Wolters, CH, Brinck, H, und Engwer, C. . „The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem.“ IEEE Trans Biomed Eng 63 (12): 2564–2575. doi: 10.1109/TBME.2016.2590740.
- Milk, R, Rave, S, und Schindler, F. . „pyMOR - Generic algorithms and interfaces for model order reduction.“ SIAM Journal on Scientific Computing 38 (5): S194–S216. doi: 10.1137/15M1026614.
- Engwer, C, und Schumacher, L. . „A phase field approach to pressurized fractures using discontinuous Galerkin methods.“ Mathematics and Computers in Simulation 137: –.. doi: 10.1016/j.matcom.2016.11.001.
- Ohlberger, M, Rave, S, und Schindler, F. . „Adaptive Localized Model Reduction.“ Oberwolfach Reports 13 (3): 2406–2409. doi: 10.4171/OWR/2016/42.
- Henning, P, und Ohlberger, M. . „A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift.“ Discrete and Continuous Dynamical Systems - Series S 9 (5): 1393–1420. doi: 10.3934/dcdss.2016056.
- Heeren, B, Rumpf, M, Schröder, P, Wardetzky, M, und Wirth, B. . „Splines in the space of shells.“ Computer Graphics Forum 35 (5): 111–120.
- Brunken, Julia, Leibner, Tobias, Ohlberger, Mario, und Smetana, Kathrin. . „Problem adapted hierachical model reduction for the Fokker-Planck equation.“ In ALGORITMY 2016 Proceedings of contributed papers and posters, herausgegeben von Angela Sevcovic Daniel Handlovicova. Bratislava: Publishing House of Slovak University of Technology.
- Wagner, S, Burger, M, und Wolters, CH. . „An optimization approach for well-targeted transcranial direct current stimulation.“ SIAM Journal on Applied Mathematics 76 (6): 2154–2174. doi: 10.1137/15M1026481.
- Engwer, C, Ranner, T, und Westerheide, S. . „An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces.“ In Proceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoké Tatry, Podbanské, Slovakia, March 13-18, 2016, herausgegeben von A. Handlovičová und D. Ševčovič. Publishing House of Slovak University of Technology.
- Bastian, P, Engwer, C, Fahlke, J, Geveler, M, Göddeke, D, Iliev, O, Ippisch, O, Milk, R, J, M, Müthing, S, Ohlberger, M, Ribbrock, D, und Turek, S. . „Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE.“ In Software for Exascale Computing - SPPEXA 2013-2015, Bd. 113 aus Lecture Notes in Computational Science and Engineering, herausgegeben von Bungartz Hans-Joachim, Neumann Philipp und E.Nagel Wolfgang. doi: 10.1007/978-3-319-40528-5_2.
- Bastian, P, Engwer, C, Fahlke, J, Geveler, M, Göddeke, D, Iliev, O, Ippisch, O, Milk, R, J, M, Müthing, S, Ohlberger, M, Ribbrock, D, und Turek, S. . „Hardware-based Efficiency Advances in the EXA-DUNE Project.“ In Software for Exascale Computing - SPPEXA 2013-2015, Bd. 113 aus Lecture Notes in Computational Science and Engineering, herausgegeben von Bungartz Hans-Joachim, Neumann Philipp und E.Nagel Wolfgang. Springer VDI Verlag. doi: 10.1007/978-3-319-40528-5_1.
- Kang, Kyungeun, und Stevens, Angela. . „Blowup and Global Solutions in a Chemotaxis-Growth System.“ Nonlinear Analysis: Theory, Methods and Applications 2016 (135): 57–72. doi: 10.1016/j.na.2016.01.017.
- Ohlberger, M, und Rave, S. . „Reduced Basis Methods: Success, Limitations and Future Challenges.“ In roceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016, herausgegeben von Handlovičova and D. Sevčovič A.. Bratislava: Publishing House of Slovak University of Technology.
- Brancolini, A, und Wirth, B. . „Optimal energy scaling for micropatterns in transport networks.“ SIAM Journal on Mathematical Analysis 49 (1): 311–359.
- Brancolini, A, und Wirth, B. . „Equivalent formulations for the branched transport and urban planning problems.“ Journal de Mathématiques Pures et Appliquées 106: 695–724.
- Friedrich, M, Piovano, P, und Stefanelli, U. . „The geometry of C60: A rigorous approach via Molecular Mechanics.“ SIAM J. Appl. Math. 76: 2009–2029. doi: 10.1137/16M106978X.
- E, W, Jentzen, A, und Shen, H. . „Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations.“ Nonlinear Analysis: Theory, Methods and Applications 142: 152–193. doi: 10.1016/j.na.2016.03.001.
- Becker, S, Jentzen, A, und Kloeden, PE. . „An exponential Wagner-Platen type scheme for SPDEs.“ SIAM Journal on Numerical Analysis 54 (4): 2389–2426. doi: 10.1137/15M1008762.
- Jentzen, A, Müller-Gronbach, T, und Yaroslavtseva, L. . „On stochastic differential equations with arbitrary slow convergence rates for strong approximation.“ Communications in Mathematical Sciences 14 (6): 1477–1500. doi: 10.4310/CMS.2016.v14.n6.a1.
- Erbar, M, Fathi, M, Laschos, V, und Schlichting, A. . „Gradient flow structure for McKean-Vlasov equations on discrete spaces.“ Discrete and Continuous Dynamical Systems - Series A 36 (12): 6799–6833. doi: 10.3934/dcds.2016096.
- Ranocha, H, Öffner, P, und Sonar, T. . „Summation-by-parts operators for correction procedure via reconstruction.“ Journal of Computational Physics 311: 299–328. doi: 10.1016/j.jcp.2016.02.009.
- Fehr, J, Heiland, J, Himpe, C, und Saak, J. . „Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.“ AIMS Mathematics 1 (3): 261--281. doi: 10.3934/Math.2016.3.261.
- Hilhorst, Danielle, Matano, Hiroshi, Thanh, Nam Nguyen, und Weber, Hendrik. . „On the Large Time Behavior of the Solutions of a Nonlocal Ordinary Differential Equation with Mass Conservation.“ Journal of Dynamics and Differential Equations 28 (3-4): 707–731. doi: 10.1007/s10884-015-9465-7.
- Adams, Stefan, Kister, Alexander, und Weber, Hendrik. . „Sample path large deviations for Laplacian models in (1+1)-dimensions.“ Electronic Journal of Probability 21: 1–36. doi: 10.1214/16-EJP8.
- Herrmann, M, und Mikikits-Leitner, A. . „KdV waves in atomic chains with nonlocal interactions.“ Discrete and Continuous Dynamical Systems - Series A 36. doi: 10.3934/dcds.2016.36.2047.
- Carstensen, C., Reddy, B., und Schedensack, M. . „A natural nonconforming FEM for the Bingham flow problem is quasi-optimal.“ Numerische Mathematik 133 (1): 37–66. doi: 10.1007/s00211-015-0738-1.
- Schedensack, M. . „A new discretization for mth-Laplace equations with arbitrary polynomial degrees.“ SIAM Journal on Numerical Analysis 54 (4): 2138–2162. doi: 10.1137/15M1013651.
- Kreuzer, C., und Schedensack, M. . „Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems.“ IMA Journal of Numerical Analysis 36 (2): 593–617. doi: 10.1093/imanum/drv019.
- Carstensen, C., Gallistl, D., und Schedensack, M. . „L2 best approximation of the elastic stress in the Arnold-Winther FEM.“ IMA Journal of Numerical Analysis 36 (3): 1096–1119. doi: 10.1093/imanum/drv051.
- Brenner, S., Oh, M., Pollock, S., Porwal, K., Schedensack, M., und Sharma, N. . „A $C^0$ interior penalty method for elliptic optimal control problems with pointwise state constraints in three dimensions.“ In Topics in Numerical Partial Differential Equations and Scientific Computing, Bd. 160 aus The IMA Volumes in Mathematics and its Applications, herausgegeben von Susanne C. Brenner. doi: 10.1007/978-1-4939-6399-7.
- Seis, C. . „A quantitative theory for the continuity equation.“ Annales de l'Institut Henri Poincaré C. Analyse non linéaire 34 (7): 1837–1850. doi: 10.1016/j.anihpc.2017.01.001.
- Mugnai, L., Seis, C., und Spadaro, E. . „Global solutions to the volume-preserving mean-curvature flow.“ Calculus of Variations and Partial Differential Equations 55 (1): 1–23. doi: 10.1007/s00526-015-0943-x.
Online First
- Lehrenfeld, C, und Schöberl, J. . „High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows.“ Comp. Meth. Appl. Mech. Eng. 2016. doi: 10.1016/j.cma.2016.04.025.
- Grah, J., Harrington, J., Koh, S., Pike, J., Schreiner, A., Burger, M., Schönlieb, C., und Reichelt, S. . „Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy.“ Methods null (null). doi: 10.1016/j.ymeth.2017.02.001.
- Bruna, M., Burger, M., Ranetbauer, H., und Wolfram, M. . „Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures.“ Journal of Nonlinear Science null (null): 1–33. doi: 10.1007/s00332-016-9348-z.
- Haskovec, Jan Markowich Peter, und Perthame, Benoît Schlottbom Matthias. . „Notes on a PDE system for biological network formation.“ Nonlinear Analysis: Theory, Methods & Applications null. doi: 10.1016/j.na.2015.12.018.
Eingereicht / In Begutachtung
- Lehrenfeld, C, und Reusken, A. . „L2-estimates for a high order unfitted finite element method for elliptic interface problems.“ arXiv eprints.
- Lehrenfeld, C, und Reusken, A. . „Analysis of a high order unfitted finite element method for elliptic interface problems.“ arXiv preprint arXiv:1602.02970 1602.02970.
- Brinkmann, Eva-Maria, Burger, Martin, Rasch, Julian, und Sutour, Camille. . „Bias-Reduction in Variational Regularization.“ Journal of Mathematical Imaging and Vision Special Issue MIA 2016.
- Engwer, C, Henning, P, M\ralqvist, A, und Peterseim, D. . „Efficient implementation of the Localized Orthogonal Decomposition method.“ arXiv.
- Hefter, M, Jentzen, A, und Kurniawan, R. . „Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces.“ arXiv.
Veröffentlicht
- Burger, Martin, Elvetun, Ole, und Schlottbom, Matthias. . „Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem.“ Inverse Problems 31 (12). doi: 10.1088/0266-5611/31/12/125002.
- Leibner, Tobias. . Numerical methods for kinetic equations (Master's thesis)
- Henning, P, und Ohlberger, M. . „Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems.“ Discrete and Continuous Dynamical Systems - Series S 8 (1): 119–150. doi: 10.3934/dcdss.2015.8.119.
- Egger, H., Pietschmann, J., und Schlottbom, M. . „Identification of nonlinear heat conduction laws.“ Journal of Inverse and Ill-Posed Problems 23 (5): 429–437. doi: 10.1515/jiip-2014-0030.
- Egger, H., Pietschmann, J., und Schlottbom, M. . „Identification of chemotaxis models with volume-filling.“ SIAM Journal on Applied Mathematics 75 (2): 275–288. doi: 10.1137/140967222.
- Herrman, M, und Matthies, K. . „Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains.“ Nonlinearity 28 (8). doi: 10.1088/0951-7715/28/8/2767.
- Burger, M., Esposito, T., und Zeppieri, C. . „Second-order edge-penalization in the ambrosio-tortorelli functional.“ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 13 (4): 1354–1389. doi: 10.1137/15M1020848.
- Brinkmann, E., Burger, M., und Grah, J. . „Regularization with sparse vector fields: From image compression to TV-type reconstruction.“ In Scale Space and Variational Methods in Computer Vision - 5th International Conference, SSVM 2015, Proceedings, Bd. 9087 aus Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Springer. doi: 10.1007/978-3-319-18461-6_16.
- Helin, T., und Burger, M. . „Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems.“ Inverse Problems 31 (8). doi: 10.1088/0266-5611/31/8/085009.
- Heins, P., Moeller, M., und Burger, M. . „Locally sparse reconstruction using the l1,∞-norm.“ Inverse Problems and Imaging 9 (4): 1093–1137. doi: 10.3934/ipi.2015.9.1093.
- Burger, M., Kaltenbacher, B., und Neubauer, A. . „Iterative solutionmethods.“ In Handbook of Mathematical Methods in Imaging: Volume 1, Second Edition, Bd. null , herausgegeben von O Scherzer. Springer. doi: 10.1007/978-1-4939-0790-8_9.
- Schmidt, C., Wagner, S., Burger, M., Rienen, U., und Wolters, C. . „Impact of uncertain head tissue conductivity in the optimization of transcranial direct current stimulation for an auditory target.“ Journal of Neural Engineering 12 (4). doi: 10.1088/1741-2560/12/4/046028.
- Wirth, B. . „Nachwuchswissenschaftler in Deutschland - die Sicht eines Rückkehrers.“ Forschung und Lehre 2015 (5): 365..
- Ohlberger, Mario, und Smetana, Kathrin. . „A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.“ Oberwolfach Reports 2/2015: 141–144. doi: 10.4171/OWR/2015/2.
- Himpe, C, und Ohlberger, M. . „The Versatile Cross Gramian.“ In Bd. Morepas 3 aus ScienceOpen Posters scienceopen. doi: 10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1.
- Benner, P, Ohlberger, M, Patera, A, Rozza, G, Sorensen, D, und Urban, K. . „Model order reduction of parameterized systems (MoRePaS).“ Advances in Computational Mathematics 41 (5): 955–960. doi: 10.1007/s10444-015-9443-y.
- Buhr, A, und Ohlberger, M. . „Interactive Simulations Using Localized Reduced Basis Methods.“ In IFAC-PapersOnLine, Bd. 48(1) doi: 10.1016/j.ifacol.2015.05.134.
- Mohring, Jan, Milk, Rene, Ngo, Adrian, Klein, Ole, Iliev, Oleg, Ohlberger, Mario, und Bastian, Peter. . „Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo.“ In Proceedings of 10th International Conference on Large-Scale Scientific Computations, Sozopol 2015, Bd. 9374 aus Lecture Notes in Computational Science, herausgegeben von I. Lirkov, S.D. Margenov und J. Wasniewski. Springer International Publishing. doi: 10.1007/978-3-319-26520-9_15.
- Himpe, C, und Ohlberger, M. . „The Empirical Cross Gramian for Parametrized Nonlinear Systems.“ In Bd. 48(1) aus IFAC-PapersOnLine doi: 10.1016/j.ifacol.2015.05.163.
- Ohlberger, M, und Schindler, F. . „Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment.“ SIAM J. Sci. Comput. 37 (6): A2865–A2895.. doi: 10.1137/151003660.
- Himpe, C, und Ohlberger, M. . „Accelerating the Computation of Empirical Gramians and Related Methods.“ Beitrag präsentiert auf der 5th International Workshop on Model Reduction in Reacting Flows, Spreewald doi: 10.5281/zenodo.46643.
- Lehrenfeld, C, und Reusken, A. . „Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport.“ In Computational Methods for Complex Liquid-Fluid Interfaces, herausgegeben von Press CRC.
- Lehrenfeld, C. . „The Nitsche XFEM-DG Space-Time Method and its Implementation in Three Space Dimensions.“ SIAM J. Sci. Comput. 37: A245–A270.. doi: 10.1137/130943534.
- Lehrenfeld, C. . „On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems.“ Dissertationsschrift, RWTH Aachen.
- Rumpf, M, Simon, S, Stahn, K, und Wirth, B. . „Bezier curves in the space of images.“ In Bd. 9087 aus Lecture Notes in Computer Science Springer.
- Elsey, Matt, und Wirth, Benedikt. . „Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images.“ Journal of Scientific Computing 63 (1): 279–306. doi: 10.1007/s10915-014-9892-3.
- Bredies, K, Pock, T, und Wirth, B. . „A convex, lower semi-continuous approximation of Euler's elastica energy.“ SIAM Journal of Mathematical Analysis 47 (1): 566–613.
- Rumpf, Martin, und Wirth, Benedikt. . „Variational time discretization of geodesic calculus.“ IMA Journal of Numerical Analysis 35 (3): 1011–1046. doi: 10.1093/imanum/dru027.
- Fuhrmann, Jan, und Stevens, Angela. . „A free boundary problem for cell motion.“ Differential and Integral Equations 28 (7-8): 695–732. doi: 10.57262/die/1431347860.
- Kaulmann, S, Flemisch, B, Haasdonk, B, Lie, K, und Ohlberger, M. . „The Localized Reduced Basis Multiscale method for two-phase flows in porous media.“ International Journal for Numerical Methods in Engineering 5 (102): 1018–1040. doi: 10.1002/nme.4773.
- Himpe, C, und Ohlberger, M. . „Data-driven combined state and parameter reduction for inverse problems.“ Advances in Computational Mathematics 41 (5): 1343–1364. doi: 10.1007/s10444-015-9420-5.
- Henning, P, Ohlberger, M, und Schweizer, B. . „Adaptive Heterogeneous Multiscale Methods for immiscible two-phase flow in porous media.“ Computational Geosciences 1 (19): 99–114. doi: 10.1007/s10596-014-9455-6.
- Burger, M., Eckardt, L., Gilboa, G., und Moeller, M. . „Spectral representations of one-homogeneous functionals.“ In Scale Space and Variational Methods in Computer Vision - 5th International Conference, SSVM 2015, Proceedings, Bd. 9087 aus Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Springer. doi: 10.1007/978-3-319-18461-6_2.
- Engwer, C, Hunt, A, und Surulescu, C. . „Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings.“ Mathematical Medicine and Biology 2015. doi: 10.1093/imammb/dqv030.
- Giese, W, Eigel, M, Westerheide, S, Engwer, C, und Klipp, E. . „Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models.“ Physical Biology 12 (6): 066014.. doi: 10.1088/1478-3975/12/6/066014.
- Engwer, C, Knappitsch, M, und Surulescu, C. . „A multiscale model for glioma spread including cell-fibre interactions and proliferation.“ Mathematical Biosciences and Engineering 13 (2): 443–460. doi: 10.3934/mbe.2015011.
- Engwer, C, Johannsen, K, und Nüßing, A. . „Algebraic multigrid for discontinuous Galerkin methods using local transformations.“ In Proceedings of the 22th Conference on Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering Springer.
- Engwer, C, und Müthing, S. . „Concepts for flexible parallel Multi-Domain Simulations.“ In Proceedings of the 22th Conference on Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering
- Engwer, C, Hillen, T, Knappitsch, M, und Surulescu, C. . „Glioma Follow White Matter Tracts; a Multiscale DTI-based Model.“ Journal of Mathematical Biology 71 (3). doi: 10.1007/s00285-014-0822-7.
- Hamel, Francois, Otani, Mitsuharu, Stevens, Angela, und Webb, Jeffrey R. L., Hrsg. . Mathematical Methods in the Applied Sciences, Bd. 38/16, Special Issue: Nonlinear Phenomena in Biology, Physics and Mechanics Hoboken, New Jersey, USA: John Wiley & Sons.
- Stevens, Angela. . „Mathematik und Biowissenschaften.“ In Studien- und Berufsplaner Mathematik, Bd. 5 aus Studien- und Berufsplaner Mathematik, herausgegeben von Springer Fachmedien Wiesbaden. Wiesbaden: Springer Fachmedien Wiesbaden. doi: 10.1007/978-3-658-04129-8.
- Burger, Martin, Esposito, Teresa, und Zeppieri, Caterina Ida. . „Second-order edge-penalization in the Ambrosio-Tortorelli functional.“ Multiscale Model. Simul. 13 (4): 1354–1389.
- Müller, Stefan, Scardia, Lucia, und Zeppieri, Caterina Ida. . „Gradient theory for geometrically nonlinear plasticity via the homogenization of dislocations.“ In Analysis and Computation of Microstructure in Finite Plasticity, Bd. 78 aus Lecture Notes in Applied and Computational Mechanics, herausgegeben von Sergio Conti und Klaus Hackl.
- Smetana, Kathrin. . „A new certification framework for the port reduced static condensation reduced basis element method.“ Computer Methods in Applied Mechanics and Engineering 283: 352–383. doi: 10.1016/j.cma.2014.09.020.
- Friedrich, M, und Schmidt, B. . „On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime.“ Netw. Heterog. Media 10: 321–342. doi: 10.3934/nhm.2015.10.321.
- Friedrich, M, und Schmidt, B. . „An analysis of crystal cleavage in the passage from atomistic models to continuum theory.“ Arch. Ration. Mech. Anal. 217: 263–308. doi: 10.1007/s00205-014-0833-y.
- Hairer, M, Hutzenthaler, M, und Jentzen, A. . „Loss of regularity for Kolmogorov equations.“ Annals of Probability 43 (2): 468–527. doi: 10.1214/13-AOP838.
- Jentzen, A, und Röckner, M. . „A Milstein scheme for SPDEs.“ Foundations of Computational Mathematics 15 (2): 313–362. doi: 10.1007/s10208-015-9247-y.
- Hutzenthaler, M, und Jentzen, A. . „Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients.“ Memoirs of the American Mathematical Society 236 (1112): v+99.. doi: 10.1090/memo/1112.
- Koenders, C, Glassmeier, K, Richter, I, Ranocha, H, und Motschmann, U. . „Dynamical features and spatial structures of the plasma interaction region of 67P/Churyumov-Gerasimenko and the solar wind.“ Planetary and Space Science 105: 101–116. doi: 10.1016/j.pss.2014.11.014.
- Mourrat, Jean-Christophe, und Weber, Hendrik Xu Weijun. . „Construction of ϕ4/3 diagrams for pedestrians. In From Particle Systems to Partial Differential Equations.“ In From Particle Systems to Partial Differential Equations , Bd. 209 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von Patrícia Gonçalves und Ana Jacinta Soares. Cham: Springer International Publishing. doi: 10.1007/978-3-319-66839-0_1.
- Hairer, Martin, und Weber, Hendrik. . „Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions.“ Annales de la Faculté des sciences de Toulouse: Mathématiques 6 / 24 (1): 55–92. doi: 10.5802/afst.1442.
- Pinski, F.J., Simpson, G., Stuart, A.M., und Weber, H. . „Algorithms for Kullback--Leibler Approximation of Probability Measures in Infinite Dimensions.“ SIAM Journal on Scientific Computing 37 (6). doi: 10.1137/14098171X.
- Pinski, F.J., Simpson, G., Stuart, A.M., und Weber, H. . „Kullback--Leibler Approximation for Probability Measures on Infinite Dimensional Spaces.“ SIAM Journal on Mathematical Analysis 47 (6): 4091–4742. doi: 10.1137/140962802.
- Bredies, Kristian, Pock, Thomas, und Wirth, Benedikt. . „A convex, lower semicontinuous approximation of Euler’s elastica energy.“ SIAM Journal on Mathematical Analysis 47 (1): 566–613. doi: 10.1137/130939493.
- Carstensen, C., Köhler, K., Peterseim, D., und Schedensack, M. . „Comparison results for the Stokes equations.“ Applied Numerical Mathematics 95: 118–129. doi: 10.1016/j.apnum.2013.12.005.
- Carstensen, C., Gallistl, D., und Schedensack, M. . „Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems.“ Mathematics of Computation 84 (293): 1061–1087. doi: 10.1090/S0025-5718-2014-02894-9.
- Carstensen, C., und Schedensack, M. . „Medius analysis and comparison results for first-order finite element methods in linear elasticity.“ IMA Journal of Numerical Analysis 35 (4): 1591–1621. doi: 10.1093/imanum/dru048.
- Schedensack, M. . „A class of mixed finite element methods based on the Helmholtz decomposition in computational mechanics.“ Dissertationsschrift, Humboldt-Universität zu Berlin.
- Korman, J., McCann, R., und Seis, C. . „An elementary approach to linear programming duality with application to capacity constrained transport.“ Journal of Convex Analysis 22 (3): 797–808.
- Seis, C. . „Scaling bounds on dissipation in turbulent flows.“ Journal of Fluid Mechanics 777: 591–603. doi: 10.1017/jfm.2015.384.
- McCann, R., und Seis, C. . „The Spectrum of a Family of Fourth-Order Nonlinear Diffusions Near the Global Attractor.“ Communications in Partial Differential Equations 40 (2): 191–218. doi: 10.1080/03605302.2014.963605.
- Korman, J., McCann, R., und Seis, C. . „Dual potentials for capacity constrained optimal transport.“ Calculus of Variations and Partial Differential Equations 54 (1): 573–584. doi: 10.1007/s00526-014-0795-9.
Online First
- Burger, M., Elvetun, O., und Schlottbom, M. . „Analysis of the Diffuse Domain Method for Second Order Elliptic Boundary Value Problems.“ Foundations of Computational Mathematics null (null). doi: 10.1007/s10208-015-9292-6.
accepted / in Press (not yet published)
- Engwer, C, Gräser, C, Müthing, S, und Sander, O. im Druck. „The interface for functions in the dune-functions module.“ arXiv.
- Barchiesi, M, Brancolini, A, und Julin, V. im Druck. „Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality.“ Annals of Probability 2015.
- Burger, M, Dirks, H, und Frerking, L. im Druck. „On Optical Flow Models for Variational Motion Estimation.“ Radon Book Series 2016.
Eingereicht / In Begutachtung
- Engwer, C, und Schumacher, L. . „Phase Field Approach to Fluid Filled Fractures using Discontinuous Galerkin Methods.“ Mathematics and Computers in Simulation -.
- Engwer, C, Vorwerk, J, Ludewig, J, und Wolters, C. . „A Discontinuous Galerkin Methods for the EEG Forward Problem.“ arXiv 2015.
- Friedrich, M, und Schmidt, B. . A quantitative geometric rigidity result in SBD
- Friedrich, M. . A Korn-Poincaré-type inequality for special functions of bounded deformation
- Seis, C. . Invariant manifolds for the porous medium equation
Veröffentlicht
- Moeller, Michael H. M.H., Brinkmann, Eva Maria E.M., Burger, Martin M., und Seybold, Tamara T. . „Color Bregman TV.“ SIAM Journal on Imaging Sciences 7 (4): 2806. doi: 10.1137/130943388.
- Burger, Martin, und Lucka, Felix. . „Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators.“ Inverse Problems 30 (11). doi: 10.1088/0266-5611/30/11/114004.
- Burger, Martin M., Müller, Jahn J., Papoutsellis, E.E., und Schönlieb, Carola Bibiane C.B. . „Total variation regularization in measurement and image space for PET reconstruction.“ Inverse Problems 30 (10). doi: 10.1088/0266-5611/30/10/105003.
- Egger, H., und Schlottbom, M. . „Stationary radiative transfer with vanishing absorption.“ Mathematical Models and Methods in Applied Sciences 24 (5): 973–990. doi: 10.1142/S0218202513500735.
- Egger, H., Pietschmann, J., und Schlottbom, M. . „Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem.“ Inverse Problems 30 (3). doi: 10.1088/0266-5611/30/3/035009.
- Egger, H., und Schlottbom, M. . „Numerical methods for parameter identification in stationary radiative transfer.“ Computational Optimization and Applications 62 (1): 67–83. doi: 10.1007/s10589-014-9657-9.
- Egger, H., Pietschmann, J., und Schlottbom, M. . „Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales.“ Inverse Problems 30 (2). doi: 10.1088/0266-5611/30/2/025004.
- Egger, H., und Schlottbom, M. . „Diffusion asymptotics for linear transport with low regularity.“ Asymptotic Analysis 89 (null): 365–377. doi: 10.3233/ASY-141235.
- Egger, H., und Schlottbom, M. . „An Lp theory for stationary radiative transfer.“ Applicable Analysis 93 (6): 1283–1296. doi: 10.1080/00036811.2013.826798.
- Marschall, H, Boden, S, Lehrenfeld, C, Falconi, Delgado C, Hampel, U, Reusken, A, Wörner, M, und Bothe, D. . „Validation of Interface Capturing and Tracking Techniques with different Surface Tension Treatments against a Taylor Bubble Benchmark Problem.“ Comput. & Fluids 102: 336–352. doi: 10.1016/j.compfluid.2014.06.030.
- Herrmann, M, Niethammer, B, und Velázquez, JJL. . „Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control.“ Archive for Rational Mechanics and Analysis 124 (3): 803–866. doi: 10.1007/s00205-014-0782-5.
- Ansini, Nadia, Dal Maso, Gianni, und Zeppieri, Caterina Ida. . „New results on Γ-limits of integral functionals.“ Annales de l'Institut Henri Poincaré C. Analyse non linéaire 31: 185–202.
- Müller, Stefan, Scardia, Lucia, und Zeppieri, Caterina Ida. . „Geometric rigidity for incompatible fields and an application to strain-gradient plasticity.“ Indiana University Mathematics Journal 63 (5): 1365–1396. doi: 10.1512/iumj.2014.63.5330.
- Heeren, B, Rumpf, M, Schröder, P, Wardetzky, M, und Wirth, B. . „Exploring the geometry of the space of shells.“ Computer Graphics Forum 33 (5).
- Kohn, Robert V., und Wirth, Benedikt. . „Optimal fine-scale structures in compliance minimization for a uniaxial load.“ Proceedings of the Royal Society A 470 (2170): 20140432–20140448.
- Haasdonk, B, und Ohlberger, M. . „Wenn die Probleme zahlreicher werden: Reduzierte Basis Methoden f\ür effiziente und gesicherte numerische Simulation.“ GAMM Rundbrief 2014/1: 6–13.
- Brancolini, A., und Solimini, S. . „Fractal regularity results on optimal irrigation patterns.“ Journal de Mathématiques Pures et Appliquées 2014 (Vol. 102, n. 5). doi: 10.1016/j.matpur.2014.02.008.
- Wirth, B, Sobey, I, und Eisenträger, A. . „Conditions for choking in a poroelastic flow model.“ The IMA Journal of Applied Mathematics 79 (2): 254–273.
- Elsey, M, und Wirth, B. . „Fast automated detection of crystal distortion and crystal defects in polycrystal images.“ SIAM Multiscale Modeling and Simulation 12 (1): 1–24. doi: 10.1137/130916515.
- Freistühler, Heinrich, und Fuhrmann, Jan Stevens Angela. . „Traveling waves emerging in a diffusive moving filament system.“ In Managing complexity, reducing perplexity, Modeling biological systems, Bd. 67 aus Springer Proceedings in Mathematics and Statistics, herausgegeben von Giulia Ajmone-Marsan und Marcello Delitala. Cham: Springer VDI Verlag. doi: 10.1007/978-3-319-03759-2_10.
- Stevens, Angela. . Nordrhein-Westfälische Akademie der Wissenschaften und der Künste - Naturwissenschaften und Medizin, Bd. 485, Mathematische Modellierung von Strukturbildung in zellulären Systemen Paderborn: Ferdinand Schöningh.
- Xu, Q, Sawatzky, A, Anastasio, M, und Schirra, C. . „Sparsity-Regularized Image Reconstruction of Decomposed K-edge Data in Spectral CT.“ Physics in Medicine and Biology 59 (10). doi: 10.1088/0031-9155/59/10/N65.
- Xu, Q, Sawatzky, A, und Anastasio, M. . „A Multi-Channel Image Reconstruction Method for Grating-Based X-ray Phase-Contrast Computed Tomography.“ Beitrag präsentiert auf der SPIE Medical Imaging 2014, San Diego, California, USA doi: 10.1117/12.2043732.
- Burger, M., Fetecau, R., und Huang, Y. . „Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion.“ SIAM Journal on Applied Dynamical Systems 13 (1): 397–424. doi: 10.1137/130923786.
- Moller, M., Burger, M., Dieterich, P., und Schwab, A. . „A framework for automated cell tracking in phase contrast microscopic videos based on normal velocities.“ Journal of Visual Communication and Image Representation 25 (2): 396–409. doi: 10.1016/j.jvcir.2013.12.002.
- Fuhrmann, J, Ohlberger, M, und Rohde, C. . Springer Proceedings in Mathematics & Statistics, Bd. 77, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects - FVCA 7, Berlin, June 2014 Springer International Publishing. doi: 10.1007/978-3-319-05684-5.
- Fuhrmann, J, Ohlberger, M, und Rohde, C. . Springer Proceedings in Mathematics & Statistics, Bd. 78, Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems - FVCA 7, Berlin, June 2014 Springer International Publishing. doi: 10.1007/978-3-319-05591-6.
- Girke, S, Klöfkorn, R, und Ohlberger, M. . „Efficient Parallel Simulation of Atherosclerotic Plaque Formation Using Higher Order Discontinuous Galerkin Schemes.“ In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, Bd. 78 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von J Fuhrmann, M Ohlberger und C Rohde. Springer International Publishing. doi: 10.1007/978-3-319-05591-6_61.
- Ohlberger, M, und Schindler, F. . „A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method.“ In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, Bd. 77 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von C Rohde. Springer International Publishing. doi: 10.1007/978-3-319-05684-5_41.
- Ohlberger, M, Rave, S, Schmidt, S, und Zhang, S. . „A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries.“ In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, Bd. 78 aus Springer Proceedings in Mathematics & Statistics, herausgegeben von J Fuhrmann, M Ohlberger und C Rohde. Springer. doi: 10.1007/978-3-319-05591-6_69.
- Ohlberger, M, und Smetana, K. . „A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.“ SIAM Journal on Scientific Computing 36 (2): A714–A736.. doi: 10.1137/130939122.
- Berninger, H, Ohlberger, M, Sander, O, und Smetana, K. . „Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions.“ Math. Models and Methods in Appl. Sciences 24 (5): 901–936. doi: 10.1142/S0218202513500711.
- Himpe, C, und Ohlberger, M. . „Model Reduction for Complex Hyperbolic Networks.“ Beitrag präsentiert auf der 13th European Control Conference (ECC), June 24-27, 2014, Strasbourg, France Wiley-IEEE Press. doi: 10.1109/ECC.2014.6862188.
- Himpe, C, und Ohlberger, M. . „Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems.“ Mathematical Problems in Engineering 2014: 1–13. doi: 10.1155/2014/843869.
- Henning, Patrick, Ohlberger, Mario, und Schweizer, Benn. . „An adaptive Multiscale Finite Element Method.“ Multiscale Mod. Simul. 12 (3): 1078–1107. doi: 10.1137/120886856.
- Mikula, K, Ohlberger, M, und Urban, J. . „Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations.“ Applied Numerical Mathematics 85: 16–37. doi: 10.1016/j.apnum.2014.06.002.
- Buhr, A, Engwer, C, Ohlberger, M, und Rave, S. . „A Numerically Stable A Posteriori Error Estimator for Reduced Basis Approximations of Elliptic Equations.“ In 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, herausgegeben von Onate XO E. und A Huerta. Barcelona: CIMNE.
- John, V, und Schumacher, L. . „A study of isogeometric analysis for scalar convection–diffusion equations.“ Applied Mathematics Letters 27: 43–48. doi: 10.1016/j.aml.2013.08.004.
- Vorwerk, J, Wagner, S, Aydin, Ü, Engwer, C, und Wolters, C. . „New Methodology for the Forward Problem in EEG/MEG Source Analysis and in Brain Stimulation.“ Biomedical Engineering / Biomedizinische Technik 59: 657..
- Engwer, C. . „DTI-based multi-scale modelling and simulation of glioma growth.“ Oberwolfach Reports 2014.
- Bastian, P, Engwer, C, Göddeke, D, Iliev, O, Ippisch, O, Ohlberger, M, Turek, S, Fahlke, J, Kaulmann, S, Müthing, S, und Ribbrock, D. . „EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications.“ In Euro-Par 2014: Parallel Processing Workshops, Bd. 8806 aus Lecture Notes in Computer Science, herausgegeben von L. Lopes, J. Žilinskas, A. Costan, R.G. Cascella, G. Kecskemeti, E. Jeannot, M. Cannataro, L. Ricci, S. Benkner, S. Petit, V. Scarano, J. Gracia, S. Hunold, S.L. Scott, S. Lankes, C. Lengaue, J. Carretero, J. Breitbart und M. Alexander. Springer International Publishing. doi: 10.1007/978-3-319-14313-2_45.
- Giese, W, Eigel, M, Westerheide, S, Engwer, C, und Klipp, E. . „Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models.“ doi: 10.1088/1478-3975/12/6/066014.
- Engwer, C, Kunisch, K, und Nagaiah, C. . „Boundary control of bidomainequations with state dependentswitching source functions in theionic model.“ Journal of Computational Physics 273: 227–242.
- Engwer, C, und Fahlke, J. . „Scalable hybrid parallelization strategies for the DUNE grid interface.“ In Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2013, Bd. 103 aus Lecture Notes in Computational Science and Engineering doi: 10.1007/978-3-319-10705-9_57.
- Engwer, C, und Westerheide, S. . „Heterogenous coupling for implicitly described domains.“ In Domain Decomposition Methods in Science and Engineering XXI, Bd. 98 aus Lecture Notes in Computational Science and Engineering, herausgegeben von Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi und Olof Widlund. Cham: Springer International Publishing. doi: 10.1007/978-3-319-05789-7_78.
- Remmel, H, Paech, B, Engwer, C, und Bastian, P. . „A Case Study on a Quality Assurance Process for a Scientific Framework.“ IEEE Computing in Science and Engineering 16 (3): 58–66.
- Friedrich, M, und Schmidt, B. . „An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem.“ J. Nonlin. Sci. 24: 145–183. doi: 10.1007/s00332-013-9187-0.
- Menz, G, und Schlichting, A. . „Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape.“ Annals of Probability 42 (5): 1809–1884. doi: 10.1214/14-AOP908.
- Himpe, C, und Ohlberger, M. . „Combined State and Parameter Reduction.“ In Bd. 14 aus Proceedings in Applied Mathematics and Mechanics (PAMM) doi: 10.1002/pamm.201410393.
- Hairer, Martin, Maas, Jan, und Weber, Hendrik. . „Approximating Rough Stochastic PDEs.“ Communications on Pure and Applied Mathematics 67 (5): 776–870. doi: 10.1002/cpa.21495.
- Otto, Felix, Weber, Hendrik, und Westdickenberg, Maria G. . „Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size.“ Electronic Journal of Probability 19: 1–76. doi: 10.1214/EJP.v19-2813.
- Gallistl, D., Schedensack, M., und Stevenson, R. . „A remark on newest vertex bisection in any space dimension.“ Computational Methods in Applied Mathematics 14 (3): 317–320. doi: 10.1515/cmam-2014-0013.
- Seis, C. . „Long-time asymptotics for the porous medium equation: The spectrum of the linearized operator.“ Journal of Differential Equations 256 (3): 1191–1223. doi: 10.1016/j.jde.2013.10.013.
- Suhr, Sebastian, Tenbrinck, Danie, Burger, Martin, und Modersitzki, Jan. . „Registration of noisy images via maximum a-posteriori estimation.“ Lecture notes in computer science 8545 LNCS: 240. doi: 10.1007/978-3-319-08554-8_24.
- Burger, Martin M., Caffarelli, Luis A. L.A., Markowich, Peter P., und Wolfram, Marie Therese M.T. . „On the asymptotic behavior of a boltzmann-type price formation model.“ Communications in Mathematical Sciences 12 (7): 1361. doi: 10.4310/CMS.2014.v12.n7.a10.
- Burger, Martin, Caffarelli, Luis A., und Markowich, Peter A. . „Partial differential equation models in the socio-economic sciences.“ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372 (2028). doi: 10.1098/rsta.2013.0406.
- Burger, Martin M., Di Francesco, Marco M., Markowich, Peter P., und Wolfram, Marie Therese M.T. . „Mean field games with nonlinear mobilities in pedestrian dynamics.“ Discrete and Continuous Dynamical Systems - Series B 19 (5): 1333. doi: 10.3934/dcdsb.2014.19.1311.
- Burger, Martin, Modersitzki, Jan, und Tenbrinck, Daniel. . „Mathematical methods in biomedical imaging.“ GAMM-Mitteilungen / GAMM-Reports 37 (2): 183. doi: 10.1002/gamm.201410008.
- Engbers, Ralf R., Burger, Martin M., und Capasso, Vincenzo V. . „Inverse problems in geographical economics: Parameter identification in the spatial Solow model.“ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372 (2028). doi: 10.1098/rsta.2013.0402.
accepted / in Press (not yet published)
- Sawatzky, A, Xu, Q, Schirra, C, und Anastasio, M. im Druck. „Proximal ADMM for Multi-Channel Image Reconstruction in Spectral X-ray CT.“ IEEE Transactions on Medical Imaging -.
- Sawatzky, A. im Druck. „Performance of First-Order Algorithms for TV Penalized Weighted Least-Squares Denoising Problem.“ Beitrag präsentiert auf der ICISP 2014, Cherbourg, Normandy, France
Eingereicht / In Begutachtung
- Hutzenthaler, M, Jentzen, A, und Noll, M. . „Strong convergence rates and temporal regularity for Cox--Ingersoll--Ross processes and Bessel processes with accessible boundaries.“ arXiv.
Veröffentlicht
- Gigengack, F, Ruthotto, L, Jiang, X, Modersitzki, J, Burger, M, Hermann, S, und Schäfers, KP. . „Atlas-based whole-body PET-CT segmentation using a passive contour distance.“ Lecture notes in computer science 7766 LNCS: 82–92.
- Himpe, C, und Ohlberger, M. . „A Unified Software Framework for Empirical Gramians.“ Journal of Mathematics 2013 (2013): 1–6. doi: 10.1155/2013/365909.
- Primi, Ivano, Stevens, Angela, und Velázquez, Juan J. L. . „Pattern forming instabilities driven by non-diffusive interaction.“ Networks and Heterogeneous Media 2013 (8, no. 1): 397–432. doi: 10.3934/nhm.2013.8.397.
- Schöberl, J, und Lehrenfeld, C. . „Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes.“ In Advanced Finite Element Methods and Applications, Bd. 66 aus Lecture Notes in Applied and Computational Mechanics, herausgegeben von Thomas Apel und Olaf Steinbach. Springer VDI Verlag.
- Lehrenfeld, C, und Reusken, A. . „Analysis of a DG-XFEM Discretization for a Class of Two-Phase Mass Transport Problems.“ SIAM J. Numer. Anal. 51: 958–983. doi: 10.1137/120875260.
- Aland, S, Lehrenfeld, C, Marschall, H, Meyer, C, und Weller, S. . „Accuracy of Two-Phase Flow Simulations.“ In Proc. Appl. Math. Mech., Bd. 13 aus Proc. Appl. Math. Mech. Springer. doi: 10.1002/pamm.201310278.
- Ansini, N, Dal, Maso G, und Zeppieri, C.I. . „Γ-convergence and H-convergence of linear elliptic operators.“ J. Math. Pures Appl. 99: 321–329.
- Dassisti, M., Maddalena, F., Brancolini, A., Chimienti, M., und Granieri, L. . „Variational techniques for assessing the technological signature of flat surfaces.“ Optimization and Engineering 14 (1): 155–174. doi: 10.1007/s11081-011-9173-z.
- Bredies, K, Pock, T, und Wirth, B. . „Convex relaxation of a class of vertex penalizing functionals.“ Journal of Mathematical Imaging and Vision 47 (3): 278–302. doi: 10.1007/s10851-012-0347-x.
- Elsey, M, und Wirth, B. . „Segmentation of Crystal Defects via Local Analysis of Crystal Distortion.“ In Proceedings of the 8'th International Conference on Computer Vision Theory and Applications (VISAPP'13)
- Elsey, M, und Wirth, B. . „A simple and efficient scheme for phase field crystal simulation.“ ESAIM: M2AN 47 (5): 1413–1432. doi: 10.1051/m2an/2013074.
- Rumpf, M, und Wirth, B. . „Discrete geodesic calculus in the space of viscous fluidic objects.“ SIAM Journal on Imaging Sciences 6 (4).
- Franken, M, Rumpf, M, und Wirth, B. . „A Phase Field based PDE Constraint Optimization Approach to Time Discrete Willmore Flow.“ International Journal of Numerical Analysis and Modeling 10 (1): 116–138.
- Berkels, B, Fletcher, T, Heeren, B, Rumpf, M, und Wirth, B. . „Discrete geodesic regression in shape space.“ In 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
- Sawatzky, A, Brune, C, Kösters, T, Wübbeling, F, und Burger, M. . „EM-TV Methods for Inverse Problems with Poisson Noise.“ In Level Set and PDE Based Reconstruction Methods in Imaging, herausgegeben von M Burger und S Osher. doi: 10.1007/978-3-319-01712-9_2.
- Burger, M., Di, Francesco M., und Franek, M. . „Stationary states of quadratic diffusion equations with long-range attraction.“ Communications in Mathematical Sciences 11 (3): 709–738. doi: 10.4310/CMS.2013.v11.n3.a3.
- Pietschmann, J.-F., Wolfram, M.-T., Burger, M., Trautmann, C., Nguyen, G., Pevarnik, M., Bayer, V., und Siwy, Z. . „Rectification properties of conically shaped nanopores: Consequences of miniaturization.“ Physical Chemistry Chemical Physics 15 (39): 16917–16926. doi: 10.1039/c3cp53105h.
- Burger, M., Caffarelli, L., Markowich, P.A., und Wolfram, M.-T. . „On a Boltzmann-type price formation model.“ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2157). doi: 10.1098/rspa.2013.0126.
- Moeller, M., und Burger, M. . „Multiscale methods for polyhedral regularizations.“ SIAM Journal on Optimization 23 (3): 1424–1456. doi: 10.1137/110858136.
- Burger, M., Haskovec, J., und Wolfram, M.-T. . „Individual based and mean-field modeling of direct aggregation.“ Physica D: Nonlinear Phenomena 260 (null): 145–158. doi: 10.1016/j.physd.2012.11.003.
- Benning, M., Brune, C., Burger, M., und Muller, J. . „Higher-order TV methods - Enhancement via Bregman iteration.“ Journal of Scientific Computing 54 (null): 269–310. doi: 10.1007/s10915-012-9650-3.
- Burger, M., Flemming, J., und Hofmann, B. . „Convergence rates in ℓ1-regularization if the sparsity assumption fails.“ Inverse Problems 29 (2). doi: 10.1088/0266-5611/29/2/025013.
- Burger, M., Modersitzki, J., und Ruthotto, L. . „A hyperelastic regularization energy for image registration.“ SIAM Journal on Scientific Computing 35 (1). doi: 10.1137/110835955.
- Lang, T., Dechant, M., Sanchez, V., Wistuba, J., Boiani, M., Pilatz, A., Stammler, A., Middendorff, R., Schuler, G., Bhushan, S., Tchatalbachev, S., Wubbeling, F., Burger, M., Chakraborty, T., Mallidis, C., und Meinhardt, A. . „Structural and functional integrity of spermatozoa is compromised as a consequence of acute uropathogenic E. Coli-associated epididymitis.“ Biology of Reproduction 89 (3). doi: 10.1095/biolreprod.113.110379.
- Burger, M., Pietschmann, J.-F., und Wolfram, M.-T. . „Identification of nonlinearities in transport-diffusion models of crowded motion.“ Inverse Problems and Imaging 7 (4): 1157–1182. doi: 10.3934/ipi.2013.7.1157.
- Sawatzky, A., Brune, C., Kosters, T., Wubbeling, F., und Burger, M. . „EM-TV methods for inverse problems with poisson noise.“ In Level Set and PDE-based Reconstruction Methods, Bd. 2090 aus Lecture Notes in Mathematics, herausgegeben von Martin Osher Stanley Burger. Springer VDI Verlag. doi: 10.1007/978-3-319-01712-9-2.
- Burger, M., und Osher, S. . „A guide to the TV zoo.“ In Level Set and PDE-based Reconstruction Methods, Bd. 2090 aus Lecture Notes in Mathematics, herausgegeben von Martin Osher Stanley Burger. unbekannt / n.a. / unknown. doi: 10.1007/978-3-319-01712-9-1.
- Herrmann, M. . „Ground waves in atomic chains with bi-monomial double-well potential.“ Nonlinear Analysis: Theory, Methods and Applications 76: 41–51. doi: 10.1016/j.na.2012.07.013.
- Herrmann, M, Matthies, K, Schwetlick, H, und Zimmer, J. . „Subsonic phase transition waves in bistable lattice models with small spinodal region.“ SIAM Journal on Mathematical Analysis 45 (5): 2625–2645. doi: 10.1137/120877878.
- Helmers, M, und Herrmann, M. . „Interface dynamics in discrete forward-backward diffusion equations.“ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 11 (4): 1261–1297. doi: 10.1137/130915959.
- Albrecht, F, und Ohlberger, M. . „The localized reduced basis multi-scale method with online enrichment.“ Oberwolfach Reports 7: 406–409. doi: 10.4171/OWR/2013/07.
- Ohlberger, M, und Rave, S. . „Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing.“ C. R. Acad. Sci. Paris, Ser. I 351: 901–906. doi: 10.1016/j.crma.2013.10.028.
- Ohlberger, M, und Schaefer, M. . „Error Control Based Model Reduction for Parameter Optimization of Elliptic Homogenization Problems.“ In Proceedings of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations doi: 10.3182/20130925-3-FR-4043.00053.
- Janssen, AM, Rampersad, SM, Lucka, F, Lanfer, B, Lew, S, Aydin, Ü, Wolters, CH, Stegeman, DF, und Oostendorp, TF. . „The influence of sulcus width on simulated electric fields induced by transcranial magnetic stimulation.“ Physics in Medicine and Biology 58 (14): 4881.. doi: 10.1088/0031-9155/58/14/4881.
- Sawatzky, Alex, Tenbrinck, Daniel, Jiang, Xiaoyi, und Burger, Martin. . „A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models.“ Journal of Mathematical Imaging and Vision 47 (3): 179–209.
- Pursiainen, S, Lucka, F, und Wolters, CH. . „Complete electrode model in EEG: relationship and differences to the point electrode model (vol 57, pg 999, 2012).“ Physics in Medicine and Biology 58 (185): 185–185.. doi: 10.1088/0031-9155/58/1/185.
- Henning, P, Ohlberger, M, und Schweizer, B. . „Homogenization of the degenerate two-phase flow equations.“ Math. Models and Methods in Appl. Sciences 23 (12): 2323–2352. doi: 10.1142/S0218202513500334.
- Ohlberger, M, Albrecht, F, Drohmann, M, Henning, P, Kaulmann, S, und Schweizer, B. . „Model reduction for multiscale problems.“ Oberwolfach Reports 39: 2228–2230. doi: 10.4171/OWR/2013/39.
- Remmel, H, Paech, B, Engwer, C, und Bastian, P. . „Design and Rationale of a Quality Assurance Process for a Scientific Framework.“ In Proceeding of the 2013 International workshop on Software engineering for computational science and engineering doi: 10.1109/SECSE.2013.6615100.
- Heimann, F, Engwer, C, Ippisch, O, und Bastian, P. . „An Unfitted Interior Penalty Discontinuous Galerkin Method for Incompressible Navier-Stokes Two-Phase Flow.“ International Journal for Numerical Methods in Fluids 71 (3): 269–293. doi: 10.1002/fld.3653.
- Burger, M, Dirks, H, und Müller, J. . „Inverse problems in imaging.“ Large Scale Inverse Problems. Computational Methods and Applications in the Earth Sciences (M. Cullen, MA Freitag, S. Kindermann, and R. Scheichl, eds.), Radon Ser. Comput. Appl. Math 13: 135–180.
- Blömker, D, und Jentzen, A. . „Galerkin approximations for the stochastic Burgers equation.“ SIAM Journal on Numerical Analysis 51 (1): 694–715. doi: 10.1137/110845756.
- Hutzenthaler, M, Jentzen, A, und Kloeden, PE. . „Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations.“ Annals of Applied Probability 23 (5): 1913–1966. doi: 10.1214/12-AAP890.
- Hairer, Martin, und Weber, Hendrik. . Rough Burgers-like equations with multiplicative noise doi: 10.1007/s00440-011-0392-1.
- Hairer, Martin, und Weber, Hendrik. . „Rough Burgers-like equations with multiplicative noise.“ Probability Theory and Related Fields 157 (3-4): 71–126. doi: 10.1007/s00440-013-0538-4.
- Röger, Matthias, und Weber, Hendrik. . „Tightness for a stochastic Allen–Cahn equation.“ Stochastics and Partial Differential Equations: Analysis and Computations 1: 175–203. doi: 10.1007/s40072-013-0004-4.
- Carstensen, C., Gallistl, D., und Schedensack, M. . „Discrete reliability for Crouzeix-Raviart FEMs.“ SIAM Journal on Numerical Analysis 51 (5): 2935–2955. doi: 10.1137/130915856.
- Carstensen, C., Gallistl, D., und Schedensack, M. . „Quasi-optimal adaptive pseudostress approximation of the Stokes equations.“ SIAM Journal on Numerical Analysis 51 (3): 1715–1734. doi: 10.1137/110852346.
- Otto, F., Seis, C., und Slepčev, D. . „Crossover of the coarsening rates in demixing of binary viscous liquids.“ Communications in Mathematical Sciences 11 (2): 441–464.
- Seis, C. . „Maximal mixing by incompressible fluid flows.“ Nonlinearity 26 (12): 3279–3289. doi: 10.1088/0951-7715/26/12/3279.
- Seis, C. . „Laminar Boundary Layers in Convective Heat Transport.“ Communications in Mathematical Physics 324 (3): 995–1031. doi: 10.1007/s00220-013-1826-7.
- Mugnai, Luca, und Seis, Christian. . „On the coarsening rates for attachment-limited kinetics.“ SIAM Journal on Mathematical Analysis 45 (1): 324–344. doi: 10.1137/120865197.
- Burger, Martin, Di Francesco, Marco, Markowich, Peter, und Wolfram, Marie Therese. . „On a mean field game optimal control approach modeling fast exit scenarios in human crowds.“ Beitrag präsentiert auf der Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, Firenze doi: 10.1109/CDC.2013.6760360.
- Burger, M, Möller, M, Benning, M, und Osher, S. . „An adaptive inverse scale space method for compressed sensing.“ Mathematics of Computation 82: 269–299. doi: 10.1090/S0025-5718-2012-02599-3.
Online First
- Hegemann, Jan Cantarero Alejandro, und Richardson, Casey L Teran Joseph M. . „An explicit update scheme for inverse parameter and interface estimation of piecewise constant coefficients in linear elliptic PDEs.“ SIAM Journal on Scientific Computing 35.
Veröffentlicht
- Stück, R, Burger, M, und Hohage, T. . „The iteratively regularized Gauss-Newton method with convex constraints and applications in 4Pi microscopy.“ Inverse Problems 28 (1). doi: 10.1088/0266-5611/28/1/015012.
- Möller, M, Wittman, T, Bertozzi, AL, und Burger, M. . „A variational approach for sharpening high dimensional images.“ SIAM Journal on Imaging Sciences 5 (1): 150–178. doi: 10.1137/100810356.
- Engbers, R, Benning, M, Heins, P, Schäfers, K, und Burger, M. . „Sparse recovery in myocardial blood flow quantification via PET.“ Beitrag präsentiert auf der IEEE NSS/MIC, San Diego
- Müller, J, Brune, C, Sawatzky, A, Kösters, T, Schäfers, KP, und Burger, M. . „Reconstruction of short time PET scans using Bregman iterations.“ Beitrag präsentiert auf der IEEE NSS/MIC, San Diego
- Burger, M, Schlake, B, und Wolfram, M-T. . „Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries.“ Nonlinearity 25 (4): 961–990. doi: 10.1088/0951-7715/25/4/961.
- Lucka, F. . „Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors.“ Inverse Problems 28 (12): 125012.. doi: 10.1088/0266-5611/28/12/125012.
- Lanfer, B, Scherg, M, Dannhauer, M, Knösche, TR, Burger, M, und Wolters, CH. . „Influences of skull segmentation inaccuracies on EEG source analysis.“ NeuroImage 62 (1): 418–31. doi: 10.1016/j.neuroimage.2012.05.006.
- Lucka, Felix Pursiainen Sampsa, und Burger, Martin Wolters Carsten H. . „Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents.“ NeuroImage 61 (4): 1364–1382. doi: 10.1016/j.neuroimage.2012.04.017.
- Lucka, Felix, Pursiainen, Sampsa, und Wolters, Carsten H. . „Complete electrode model in EEG: relationship and differences to the point electrode model.“ Physics in Medicine and Biology 57 (4): 999–1017. doi: 10.1088/0031-9155/57/4/999.
- Lehrenfeld, Christoph Reusken Arnold. . „Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem.“ SIAM J. Sci. Comput. 34: 2740–2759. doi: 10.1137/110855235.
- Koutschan, Christoph, Lehrenfeld, Christoph, und Schöberl, Joachim. . „Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwells Equations.“ In Numerical and Symbolic Scientific Computing: Progress and Prospects, herausgegeben von Langer PP Ulrich. Springer VDI Verlag. doi: 10.1007/978-3-7091-0794-2_6.
- Scardia, Lucia, und Zeppieri, Caterina Ida. . „Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy.“ SIAM Journal on Mathematical Analysis 44 (4): 2372–2400. doi: 10.1137/110824851.
- Ansini, Nadia, und Zeppieri, Caterina Ida. . „Asymptotic analysis of nonsymmetric linear operators via Γ-convergence.“ SIAM Journal on Mathematical Analysis 44 (3): 1617–1635. doi: 10.1137/110834330.
- Sobey, I, Eisenträger, A, Wirth, B, und Czosnyka, M. . „Simulation of cerebral infusion tests using a poroelastic model.“ International Journal of Numerical Analysis and Modeling Series B 3 (1): 52–64.
- Ring, W, und Wirth, B. . „Optimization methods on Riemannian manifolds and their application to shape space.“ SIAM Journal on Optimization 22 (2): 596–627. doi: 10.1137/11082885X.
- Penzler, P, Rumpf, M, und Wirth, B. . „A Phase-Field Model for Compliance Shape Optimization in Nonlinear Elasticity.“ ESAIM: Control, Optimisation and Calculus of Variations 18 (1): 229–258. doi: 10.1051/cocv/2010045.
- Heeren, B, Rumpf, M, Wardetzky, M, und Wirth, B. . „Time-Discrete Geodesics in the Space of Shells.“ Computer Graphics Forum 31 (5): 1755–1764. doi: 10.1111/j.1467-8659.2012.03180.x.
- Engbers, R., Benning, M., Heins, P., Schafers, K., und Burger, M. . „Sparse recovery in myocardial blood flow quantification via PET.“ In Bd. null doi: 10.1109/NSSMIC.2011.6153707.
- Burger, M., Franek, M., und Schonlieb, C.-B. . „Regularized regression and density estimation based on optimal transport.“ Applied Mathematics Research eXpress 2012 (2): 209–253. doi: 10.1093/amrx/abs007.
- Muller, J., Brune, C., Sawatzky, A., Kosters, T., Schafers, K.P., und Burger, M. . „Reconstruction of short time PET scans using Bregman iterations.“ In Bd. null doi: 10.1109/NSSMIC.2011.6153884.
- Gigengack, F., Ruthotto, L., Kosters, T., Jiang, X., Modersitzki, J., Burger, M., Wolters, C.H., und Schafers, K.P. . „Pipeline for motion correction in dual gated PET.“ In Bd. null doi: 10.1109/NSSMIC.2012.6551681.
- Gigengack, F., Ruthotto, L., Burger, M., Wolters, C.H., Jiang, X., und Schafers, K.P. . „Mass-preserving motion correction of PET: Displacement field vs. spline transformation.“ In Bd. null doi: 10.1109/NSSMIC.2011.6152559.
- Gigengack, F., Ruthotto, L., Burger, M., Wolters, C.H., Jiang, X., und Schafers, K.P. . „Mass-preserving motion correction of dual gated cardiac PET.“ In Bd. null doi: 10.1109/NSSMIC.2011.6153658.
- Tenbrinck, D., Sawatzky, A., Jiang, X., Burger, M., Haffner, W., Willems, P., Paul, M., und Stypmann, J. . „Impact of physical noise modeling on image segmentation in echocardiography.“ In Bd. null doi: 10.2312/VCBM/VCBM12/033-040.
- Gigengack, F., Ruthotto, L., Kosters, T., Jiang, X., Modersitzki, J., Burger, M., Hermann, S., und Schafers, K.P. . „Atlas-based segmentation using passive contours.“ In Bd. null doi: 10.1109/NSSMIC.2012.6551688.
- Ruthotto, L., Gigengack, F., Burger, M., Wolters, C.H., Jiang, X., Schafers, K.P., und Modersitzki, J. . „A simplified pipeline for motion correction in dual gated cardiac PET.“ In Bd. null doi: 10.1007/978-3-642-28502-8-11.
- Herrmann, M, Schwetlick, H, und Zimmer, J. . „On selection criteria for problems with moving inhomogeneities.“ Continuum Mechanics and Thermodynamics 24 (1): 21–36. doi: 10.1007/s00161-011-0206-9.
- Herrmann, M. . „Oscillatory waves in discrete scalar conservation laws.“ Mathematical Models and Methods in Applied Sciences 22 (1): 1150002, 21.. doi: 10.1142/S021820251200585X.
- Herrmann, M, Laurençot, P, und Niethammer, B. . „Self-similar solutions to a kinetic model for grain growth.“ Journal of Nonlinear Science 22 (3): 399–427. doi: 10.1007/s00332-011-9122-1.
- Herrmann, M, Niethammer, B, und Velázquez, JJL. . „Kramers and non-Kramers phase transitions in many-particle systems with dynamical constraint.“ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 10 (3): 818–852. doi: 10.1137/110851882.
- Bernard-Champmartin, A, Deriaz, E, Hoch, P, Samba, G, und Schaefer, M. . „Extension of centered hydrodynamical schemes to unstructured deforming conical meshes: the case of circles.“ In CEMRACS'11: Multiscale Coupling of Complex Models in Scientific Computing EDP Sciences. doi: 10.1051/proc/201238008.
- Wagner, S., Vorwerk, J., Ruthotto, L., Kugel, H., Burger, M., Knösche, T., Maess, B., und Wolters, C.H. . „Sensitivity of EEG leads to volume conductor properties.“ Biomedical Engineering / Biomedizinische Technik 57 Suppl 1: 793–793. doi: 10.1515/bmt-2012-4065.
- Vorwerk, J, Clerc, M, Burger, M, und Wolters, CH. . „Comparison of boundary element and finite element approaches to the EEG forward problem.“ Biomedical Engineering / Biomedizinische Technik 57 Suppl 1.
- Wagner, S, Lucka, F, Burger, M, Grasedyck, L, Haueisen, J, und Wolters, CH. . „Comparison of direct and reciprocal forward modeling approaches in EEG source analysis.“ Biomedical Engineering / Biomedizinische Technik 57 1: –.. doi: 10.1515/bmt-2012-4069.
- Wagner, S., Vorwerk, J., Ruthotto, L., Kugel, H., Burger, M., Knösche, T., Maess, B., und Wolters, C.H. . „Sensitivity of EEG leads to volume conductor properties.“ Biomedical Engineering / Biomedizinische Technik 57 (SI-1-Track-O): 793–793. doi: 10.1515/bmt-2012-4065.
- Lucka, F, Pursiainen, S, Burger, M, und Wolters, CH. . „Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: depth localization and source separation for focal primary currents.“ NeuroImage 61 (4): 1364–1382. doi: 10.1016/j.neuroimage.2012.04.017.
- Ruthotto, L, Kugel, H, Olesch, J, Fischer, B, Modersitzki, J, Burger, M, und Wolters, CH. . „Diffeomorphic susceptibility artifact correction of diffusion-weighted magnetic resonance images.“ Physics in Medicine and Biology 57 (18): 5715–5731.
- Drohmann Martin, Haasdonk Bernard, und Ohlberger, Mario. . „Reduced Basis Model Reduction of Parametrized Two-Phase Flow in Porous Media.“ In 7th Vienna International Conference on Mathematical Modelling, Bd. 45 aus IFAC Proceedings Volumes doi: 10.3182/20120215-3-AT-3016.00128.
- Drohmann, M, Haasdonk, B, und Ohlberger, M. . „Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation.“ SIAM Journal on Scientific Computing 34: A937–A969.. doi: 10.1137/10081157X.
- Ohlberger, M. . „Error control based model reduction for multiscale problems.“ In Proceedings of Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, herausgegeben von University of Technology in Bratislava Slovak und House of STU Publishing.
- Bastian, P, Berninger, H, Dedner, A, Engwer, C, Henning, P, Kornhuber, R, Kröner, D, Ohlberger, M, Sander, O, Schiffler, G, Shokina, N, und Smetana, K. . „Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management.“ In Progress in Industrial Mathematics at ECMI 2010, Bd. 17 aus Mathematics in Industry, Springer. doi: 10.1007/978-3-642-25100-9_65.
- Ohlberger, M, und Schaefer, M. . „A reduced basis method for parameter optimization of multiscale problems.“ In Submitted to Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012
- Gigengack, F, Ruthotto, L, Burger, M, Wolters, C, Jiang, X, und Schafers, K. . „Motion Correction in Dual Gated Cardiac PET Using Mass-Preserving Image Registration.“ IEEE Transactions on Medical Imaging 31 (3): 698–712.
- Espejo, Elio E., Stevens, Angela, und Suzuki, Takashi. . „Simultaneous Blowup and Mass Separation During Collapse in an Interacting System of Chemotactic Species.“ Differential and Integral Equations 25 (3-4): 251–288. doi: 10.57262/die/1356012736.
- Gigengack, F, Ruthotto, L, Burger, M, Wolters, C, Jiang, X, und Schäfers, K. . „Motion correction in dual gated cardiac PET using mass preserving image registration.“ IEEE Transactions on Medical Imaging 31 (3): 171–174. doi: 10.1109/TMI.2011.2175402.
- Möller, M, Wittman, T, Bertozzi, A, und Burger, M. . „A variational approach for sharpening high-dimensional images.“ SIAM Journal on Imaging Sciences 5 (1): 150–178. doi: 10.1137/100810356.
- Stück, R, Burger, M, und Hohage, T. . „The iteratively regularized Gauss-Newton method with convex constraints and applications in 4pi-microscopy.“ Inverse Problems 28. doi: 10.1088/0266-5611/28/1/015012.
- Rave, S. . „On Finitely Summable K-Homology.“ Dissertationsschrift, Universität Münster.
- Albrecht, F, Haasdonk, B, Kaulmann, S, und Ohlberger, M. . „The Localized Reduced Basis Multiscale Method.“ Beitrag präsentiert auf der Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske Bratislava: Publishing House of Slovak University of Technology.
- Remmel, H, Paech, B, Engwer, C, und Bastian, P. . „System Testing for a Scientific Framework Using a Regression Test Environment.“ Computing in Science and Engeneering 14 (2): 38–45. doi: 10.1109/MCSE.2011.115.
- Engwer, C, und Heimann, F. . „DUNE-UDG: A Cut-Cell Framework for Unfitted Discontinuous Galerkin Methods.“ In Advances in DUNE, herausgegeben von A Dedner, B Flemisch und R Klöfkorn. Springer. doi: 10.1007/978-3-642-28589-9_7.
- Jentzen, A, und Röckner, M. . „Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise.“ Journal of Differential Equations 252 (1): 114–136. doi: 10.1016/j.jde.2011.08.050.
- Hutzenthaler, M, Jentzen, A, und Kloeden, PE. . „Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients.“ Annals of Applied Probability 22 (4): 1611–1641.
- Hairer, Martin, Ryser, Marc D., und Weber, Hendrik. . „Triviality of the 2D stochastic Allen-Cahn equation.“ Electronic Journal of Probability 17 (39): 1–14. doi: 10.1214/EJP.v17-1731.
- Stevens, Angela, und Velazquez, Juan J. L. . „Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory.“ Preprint. MiS Preprint Repository
- Carstensen, C, Peterseim, D, und Schedensack, M. . „Comparison results of finite element methods for the Poisson model problem.“ SIAM J. Numer. Anal. 50 (6): 2803–2823. doi: 10.1137/110845707.
Online First
- Kelkel, J, und Surulescu, C. . „A multiscale approach to cell migration in tissue networks.“ Mathematical Models and Methods in the Applied Sciences 22 (3).
accepted / in Press (not yet published)
- Gigengack, F, Ruthotto, L, Modersitzki, J, Burger, M, Wolters, C, Jiang, X, und Schäfers, K. im Druck. „A simplified pipeline for motion correction in dual gated cardiac PET.“ Beitrag präsentiert auf der Bildverarbeitung für die Medizin, Berlin
Veröffentlicht
- Lucka, F, Pursiainen, S, Burger, M, und Wolters, CH. . „Hierarchical bayesian models for eeg inversion: Depth localization and source separation for focal sources in realistic FE head models.“
- Burger, M. . „Inverse problems in ion channel modelling.“ Inverse Problems 27 (8). doi: 10.1088/0266-5611/27/8/083001.
- Sanchez, V, Wistuba, J, Wubbeling, F, Burger, M, Schlatt, S, und Mallidis, C. . „Detection of Sperm DNA damage by Raman microspectroscopy.“ doi: 10.1016/j.fertnstert.2011.07.900.
- Mallidis, C, Wistuba, J, Bleisteiner, B, Damm, OS, Gross, P, Wubbeling, F, Fallnich, C, Burger, M, und Schlatt, S. . „In situ visualization of damaged DNA in human sperm by Raman microspectroscopy.“ Human Reproduction 26 (7): 1641–1649. doi: 10.1093/humrep/der122.
- Richardson, Casey L, Hegemann, Jan, Sifakis, Eftychios, Hellrung, Jeffrey, und Teran, Joseph M. . „An XFEM method for modeling geometrically elaborate crack propagation in brittle materials.“ International Journal for Numerical Methods in Engineering 88: 1042–1065. doi: 10.1002/nme.3211.
- Brenier, Y., Otto, F., und Seis, C. . „Upper bounds on coarsening rates in demixing binary viscous liquids.“ SIAM Journal on Mathematical Analysis 43 (1): 134. doi: 10.1137/090775142.
- Kelkel, J, und Surulescu, C. . „On some models for cancer cell migration through tissue.“ Mathematical Biosciences and Engineering 8: 575–589.
- Ohlberger, M, und Smetana, K. . „A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems.“ In Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011) held in Paris, France, 6-8 June 2011, herausgegeben von D.et al. Aubry. CIMNE.
- Drohmann, M, Haasdonk, B, und Ohlberger, M. . „Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations.“ In Finite Volumes for Complex Applications VI - Problems & Perspectives, Bd. 4 (1) aus Springer Proceedings in Mathematics, herausgegeben von J.et al. Fort. Springer. doi: 10.1007/978-3-642-20671-9_39.
- Haasdonk, B, und Ohlberger, M. . „Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition.“ Mathematical and Computer Modelling of Dynamical Systems 17 (2): 145–161. doi: 10.1080/13873954.2010.514703.
- Mikula, K, und Ohlberger, M. . „Inflow-Implicit/Outflow-Explicit scheme for solving advection equations.“ In Finite Volumes for Complex Applications VI - Problems & Perspectives, Bd. 4(1) aus Springer Proceedings in Mathematics, herausgegeben von J.et al. Fort. Springer. doi: 10.1007/978-3-642-20671-9_72.
- Stevens, Angela. . „Angewandte Analysis.“ In Facettenreiche Mathematik: Einblicke in die moderne mathematische Forschung für alle, die mehr von Mathematik verstehen wollen, , herausgegeben von Katrin Wendland und Annette Werner. Wiesbaden: Vieweg Verlag. doi: 10.1007/978-3-8348-8173-1_17.
- Wirth, B, Warnecke, M, Schmenk, B, Seide, G, und Gries, T. . „Filament breaches during air-gap spinning.“ Chemical Fibers International 61: 38–39.
- Lehrenfeld, Christoph. . „Nitsche-XFEM for a Transport Problem in Two- Phase Incompressible Flows.“ In Proc. Appl. Math. Mech., Bd. 11 John Wiley & Sons. doi: 10.1002/pamm.201110296.
- Heins, P. . Sparse Model-Based Reconstruction in Dynamic Positron Emission Tomography
- Cicalese, Marco, Spadaro, Emanuele Nunzio, und Zeppieri, Caterina Ida. . „Asymptotic analysis of a second-order singular perturbation model for phase transitions.“ Calculus of Variations and Partial Differential Equations 41 (1-2): 127–150. doi: 10.1007/s00526-010-0356-9.
- Brancolini, A., und Solimini, S. . „On the Hölder regularity of the landscape function.“ Interfaces and Free Boundaries 13 (2): 191–222. doi: 10.4171/IFB/254.
- Wirth, B, Gerhard, J, und Marquardt, W. . „Robust optimisation with normal vectors on critical manifolds of transient stability loss.“ Journal of Nonlinear Science 21: 57–92. doi: 10.1007/s00332-010-9076-8.
- Wirth, Benedikt, Gerhard, Johannes, und Marquardt, Wolfgang. . „Stability-preserving optimization in the presence of fast disturbances.“ IEEE Transactions on Automatic Control 56 (11): 2683–2687. doi: 10.1109/TAC.2011.2160029.
- Wirth, B, Bar, L, Rumpf, M, und Sapiro, G. . „A Continuum Mechanical Approach to Geodesics in Shape Space.“ International Journal of Computer Vision 93 (3): 293–318. doi: 10.1007/s11263-010-0416-9.
- Rumpf, M, und Wirth, B. . „An elasticity-based covariance analysis of shapes.“ International Journal of Computer Vision 92 (3): 281–295. doi: 10.1007/s11263-010-0358-2.
- Rumpf, M, und Wirth, B. . „Variational methods in shape analysis.“ In Handbook of Mathematical Methods in Imaging, herausgegeben von O Scherzer. Springer VDI Verlag. doi: 10.1007/978-0-387-92920-0_31.
- Müller, J, Brune, C, Sawatzky, A, Kösters, T, Wübbeling, F, Schäfers, K, und Burger, M. . „Reconstruction of short time PET scans using Bregman iterations.“ Beitrag präsentiert auf der IEEE NSS/MIC 2011, Valencia, Spain doi: 10.1109/NSSMIC.2011.6153884.
- Herrmann, M. . „Action minimising fronts in general FPU-type chains.“ Journal of Nonlinear Science 21 (1): 33–55. doi: 10.1007/s00332-010-9075-9.
- Budáč, O, Herrmann, M, Niethammer, B, und Spielmann, A. . „On a model for mass aggregation with maximal size.“ Kinetic and Related Models 4 (2): 427–439. doi: 10.3934/krm.2011.4.427.
- Dreyer, W, Guhlke, C, und Herrmann, M. . „Hysteresis and phase transition in many-particle storage systems.“ Continuum Mechanics and Thermodynamics 23 (3): 211–231. doi: 10.1007/s00161-010-0178-1.
- Herrmann, M, und Niethammer, B. . „Kramers' formula for chemical reactions in the context of Wasserstein gradient flows.“ Communications in Mathematical Sciences 9 (2): 623–635. doi: 10.4310/CMS.2011.v9.n2.a15.
- Herrmann, M. . „Homoclinic standing waves in focusing DNLS equations.“ Discrete and Continuous Dynamical Systems - Series A 31 (3): 737–752. doi: 10.3934/dcds.2011.31.737.
- Mallidis, C, Wistuba, J, Bleisteiner, B, Damm, OS, Gross, P, Wübbeling, F, Fallnich, C, Burger, M, und Schlatt, S. . „In situ visualization of damaged DNA in human sperm by Raman microspectroscopy.“ Human Reproduction 26 (7): 1641–1649.
- Lucka, Felix Pursiainen Sampsa, und Burger, Martin Wolters Carsten H. . „Hierarchical Bayesian Models for EEG Inversion: Depth Localization and Source Separation for Focal Sources in Realistic FE Head Models.“ Beitrag präsentiert auf der Annual meeting of the DGBMT, Freiburg De Gruyter.
- Horstmann, Dirk, und Stevens, Angela. . „Origins of Theoretical Biology.“ European Communications in Mathematical and Theoretical Biology 2011 (14): 94–103.
- Burger, M, Markowich, P, und Pietschmann, J. . „Continuous limit of a crowd motion and herding model: Analysis and numerical simulations.“ Kinetic and Related Methods 4: 1025–1047.
- Surulescu, C, und Surulescu, N. . „Mathematical modeling with stochastic processes and stochastic differential equations.“ European Communications in Mathematical and Theoretical Biology 14: 106–117.
- Sawatzky, A. . „(Nonlocal) Total Variation in Medical Imaging.“ Dissertationsschrift, WWU Münster.
- Capasso, Vincenzo, Engbers, Ralf, und La, Torre Davide. . „Population dynamics in a spatial Solow model with a convex-concave production function.“ In Mathematical and Statistical Methods for Actuarial Sciences and Finance, herausgegeben von Cira Perna und Marilena Sibillo. Springer.
- Lucka, F., Pursiainen, S., Burger, M., und Wolters, C. . „Hierarchical bayesian models for EEG inversion: Depth localization and source separation for focal sources in realistic FE head models.“ Biomedical Engineering / Biomedizinische Technik 56: 1–4. doi: 10.1515/BMT.2011.817.
- Remmel, H, Paech, B, Engwer, C, und Bastian, P. . „Supporting the Testing of Scientific Frameworks with Software Product Line Engineering: A Proposed Approach.“ In Proceeding of the 4th international workshop on Software engineering for computational science and engineering doi: 10.1145/1985782.1985785.
- Bastian, P, Engwer, C, Fahlke, J, und Ippisch, O. . „An Unfitted Discontinuous Galerkin Method for Pore-Scale Simulations of Solute Transport.“ Mathematics and Computers in Simulation 81 (10): 2051–2061. doi: 10.1016/j.matcom.2010.12.024.
- Jentzen, A. . „Higher order pathwise numerical approximations of SPDEs with additive noise.“ SIAM Journal on Numerical Analysis 49 (2): 642–667. doi: 10.1137/080740714.
- Hutzenthaler, M, Jentzen, A, und Kloeden, PE. . „Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients.“ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467 (2130): 1563–1576. doi: 10.1098/rspa.2010.0348.
- Jentzen, A, Kloeden, P, und Winkel, G. . „Efficient simulation of nonlinear parabolic SPDEs with additive noise.“ Annals of Applied Probability 21 (3): 908–950. doi: 10.1214/10-AAP711.
- Jentzen, A, und Kloeden, PE. . CBMS-NSF Regional Conference Series in Applied Mathematics, Bd. 83, Taylor approximations for stochastic partial differential equations Selbstverlag / Eigenverlag. doi: 10.1137/1.9781611972016.
- Hutzenthaler, M, und Jentzen, A. . „Convergence of the stochastic Euler scheme for locally Lipschitz coefficients.“ Foundations of Computational Mathematics 11 (6): 657–706. doi: 10.1007/s10208-011-9101-9.
- Otto, F., und Seis, C. . „Rayleigh-Bénard convection: Improved bounds on the Nusselt number.“ Journal of Mathematical Physics 52 (8). doi: 10.1063/1.3623417.
- Seis, C. . „On the coarsening rates in demixing binary viscous liquids.“ Oberwolfach Reports 8 (4). doi: 10.4171/OWR/2011/55.
- Seis, Christian. . „Scaling laws in two models for thermodynamically driven fluid flows.“ Dissertationsschrift, Universität Leipzig.
- Haasdonk, B, Dihlmann, M, und Ohlberger, M. . „A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space.“ Mathematical and Computer Modelling of Dynamical Systems 2011 (17 (4)): 423–442. doi: 10.1080/13873954.2011.547674.
- Brune, C, Sawatzky, A, und Burger, M. . „Primal and Dual Bregman Methods with Application to Optical Nanoscopy.“ International Journal of Computer Vision 92 (2): 211–229. doi: 10.1007/s11263-010-0339-5.
- Burger, M, Matevosyan, N, und Wolfram, M. . „A level set based shape optimization method for an elliptic obstacle problem.“ : 619–649.
- Henning, P, und Ohlberger, M. . „A Note on Homogenization of Advection-Diffusion Problems with Large Expected Drift.“ Zeitschrift für Analysis und ihre Anwendungen 2011 (30(3)): 319–339. doi: 10.4171/ZAA/1437.
- Benning, M, und Burger, M. . „Error estimates for general fidelities.“ El. Trans. Numer. Anal. 38: 44–68.
Eingereicht / In Begutachtung
- Märkl, C, und Surulescu, C. . „Mathematical analysis and numerical simulations for a system modeling acid-mediated tumor cell invasion.“
- Winkel, C, Neumann, S, Surulescu, C, und Scheurich, P. . „A minimal mathematical model for the dynamics of (TNF-) receptor signaling.“
- Meral, G., und Surulescu, C. . „Mathematical modeling, analysis and numerical simulations for the influence of heat shock proteins on tumor invasion.“
Veröffentlicht
- Scharf, O, Gorlatch, S, Blanke, F, Hemker, C, Westerheide, S, Priebs, T, Bartenhagen, C, Ploss, A, Glinka, F, und Meilaender, D. . „Scalable distributed simulation of large dense crowds using the Real-Time Framework (RTF).“ Lecture notes in computer science 6271 LNCS (PART 1): 572–583.
- Benning, M, Heins, P, und Burger, M. . „A solver for dynamic PET reconstructions based on forward-backward- splitting.“ Beitrag präsentiert auf der ICNAAM 2010, Crete doi: 10.1063/1.3498318.
- Mallidis, C, Wistuba, J, Bleisteiner, B, Gross, P, Wubbeling, F, Fallnich, C, Burger, M, und Schlatt, S. . „Confocal Raman microspectroscopy, the future for semen analysis?“ doi: 10.1111/j.1365-2605.2010.01106.x.
- Burger, M, Carrillo, J, und Wolfram, MT. . „A mixed finite element method for nonlinear diffusion equations.“ Kinetic and Related Methods 3: 59–83.
- Dawood, M, Brune, C, Jiang, X, Büther, F, Burger, M, Schober, O, Schäfers, M, und Schäfers, K. . „A continuity equation based optical flow method for cardiac motion correction in 3D PET data.“ In Medical Imaging and Augmented Reality: 5th International Workshop, MIAR 2010, Beijing, China, September 19-20, 2010, Proceedings (Lecture Notes in ... Vision, Pattern Recognition, and Graphics), herausgegeben von Liao Hongen, Eddie Edwards P.J. und Pan Xiaochuan. Berlin Heidelberg: Springer. doi: 10.1007/978-3-642-15699-1_10.
- Capasso, Vincenzo, Engbers, Ralf, und La, Torre Davide. . „On a spatial Solow model with technological diffusion and nonconcave production function.“ Nonlinear Analysis: Real World Applications 11 (5): 3858–3876. doi: 10.1016/j.nonrwa.2010.01.016.
- Kelkel, J, und Surulescu, C. . „On a stochastic reaction-diffusion system modeling pattern formation on seashells.“ JMB 60: 765–796.
- Surulescu, C. . „On a Time-Dependent Fluid-Solid Coupling in 3D with Nonstandard Boundary Conditions. Steps Towards Modeling Blood Flow.“ Acta Applicandae Mathematica 110: 1087–1104.
- Surulescu, Cand Surulescu N. . „A Nonparametric Approach to Cell Dispersal.“ Int. J. of Biomathematics and Biostatistics 1: 109–128.
- Maurer, H, und Semmler, W. . „An optimal control model of oil discovery and extraction.“ Applied Mathematics and Computation 217 (3): 1163–1169. doi: 10.1016/j.amc.2010.03.075.
- Ledzewicz, U, Marriott, J, Maurer, H, und Schättler, H. . „Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment.“ Mathematical Medicine and Biology 27 (2): 157–179. doi: 10.1093/imammb/dqp012.
- Zhang, X, Burger, M, Bresson, X, und Osher, S. . „Bregmanized nonlocal regularization for deconvolution and sparsereconstruction.“ SIAM Journal on Imaging Sciences 3 (3): 253–276. doi: 10.1137/090746379.
- Surulescu, C. . „On a time-dependent fluid-solid coupling in 3D with nonstandard boundary conditions: steps towards modeling blood flow.“ Acta Applicandae Mathematicae 110 (3): 1087–1104. doi: 10.1007/s10440-009-9495-4.
- Kelkel, J, und Surulescu, C. . „On a stochastic reaction-diffusion system modeling pattern formation on seashells.“ Journal of Mathematical Biology 60 (6): 765–796. doi: 10.1007/s00285-009-0284-5.
- Mikula, K, und Ohlberger, M. . „A New Inflow-Implicit/Outflow-Explicit Finite Volume Method for Solving Variable Velocity Advection Equations.“
- Ohlberger, M, und Smetana, K. . „A new problem adapted hierarchical model reduction technique based on reduced basis methods and dimensional splitting.“
- Drohmann, M, Haasdonk, B, und Ohlberger, M. . „Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation.“
- Kang, Kyungkeun, Stevens, Angela, und Velázquez, Juan J. L. . „Qualitative behavior of a Keller-Segel model with non-diffusive memory.“ Communications in Partial Differential Equations 35 (2): 245–274. doi: 10.1080/03605300903473400.
- Wiebel, Alexander, Chan, Raymond, Wolf, Christina, Robitzki, Andrea, Stevens, Angela, und Scheuermann, Gerik. . „Topological flow structure in a mathematical model for rotation-mediated cell aggregation.“ In Topological Methods in Data Analysis and Visualization - Theory, Algorithms, and Applications, Mathematics and Visualization, herausgegeben von Valerio Pascucci, Xavier Tricoche, Hans Hagen und Julien Tierny. Berlin / Heidelberg: Springer VDI Verlag. doi: 10.1007/978-3-642-15014-2_16.
- Espejo, Elio E., Stevens, A., und Velázquez, Juan J. L. . „A note on nonsimultaneous blow-up for a drift-diffusion model.“ Differential and Integral Equations 23 (5-6): 451–462. doi: 10.57262/die/1356019306.
- Lehrenfeld, Christoph. . Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems
- Dal, Maso G, und Zeppieri, C.I. . „Homogenization of fiber reinforced brittle materials: The intermediate case.“ Advances in Calculus of Variations 3 (4): 345–370. doi: 10.1515/ACV.2010.011.
- Bianchini, S., und Brancolini, A. . „Estimates on path functionals over Wasserstein spaces.“ SIAM Journal on Mathematical Analysis 42 (3): 1179–1217. doi: 10.1137/100782693.
- Benning, M., Heins, P., und Burger, M. . „A solver for dynamic PET reconstructions based on forward-backward- splitting.“ In Bd. 1281 doi: 10.1063/1.3498318.
- Sobey, I, Eisenträger, A, Wirth, B, und Czosnyka, M. . „Multi-fluid poro-elastic modelling of the CSF infusion test.“ In 6th World Congress of Biomechanics (WCB 2010), IFMBE Proceedings, Bd. 31
- Herrmann, M, und Segatti, A. . „Infinite harmonic chain with heavy mass.“ Communications on Pure and Applied Analysis 9 (1): 61–75. doi: 10.3934/cpaa.2010.9.61.
- Herrmann, M, und Rademacher, JDM. . „Riemann solvers and undercompressive shocks of convex FPU chains.“ Nonlinearity 23 (2): 277–304. doi: 10.1088/0951-7715/23/2/004.
- Herrmann, M. . „Unimodal wavetrains and solitons in convex Fermi-Pasta-Ulam chains.“ Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140 (4): 753–785. doi: 10.1017/S0308210509000146.
- Herrmann, M, und Rademacher, JDM. . „Heteroclinic travelling waves in convex FPU-type chains.“ SIAM Journal on Mathematical Analysis 42 (4): 1483–1504. doi: 10.1137/080743147.
- Herrmann, M. . „Heteroclinic standing waves in defocusing DNLS equations: variational approach via energy minimization.“ Applicable Analysis 89 (10): 1591–1602. doi: 10.1080/00036811.2010.492504.
- Benning, M, Heins, P, und Burger, M. . „A Solver for Dynamic PET Reconstruction based on Forward-Backward Splitting.“ Beitrag präsentiert auf der ICNAAM 2010
- Sawatzky, A, und Burger, M. . „Edge-Preserving Regularization for the Deconvolution of Biological Images in Nanoscopy.“ Beitrag präsentiert auf der ICNAAM 2010, Rhodes, Greece doi: 10.1063/1.3498325.
- Gigengack, F., Ruthotto, L., Burger, M., Wolters, C., Jiang, X., und Schafers, K. . „Motion correction of cardiac PET using mass-preserving registration.“ In Bd. null doi: 10.1109/NSSMIC.2010.5874418.
- Jentzen, A, und Kloeden, PE. . „A unified existence and uniqueness theorem for stochastic evolution equations.“ Bulletin of the Australian Mathematical Society 81 (1): 33–46. doi: 10.1017/S0004972709000677.
- Jentzen, A, Leber, F, Schneisgen, D, Berger, A, und Siegmund, S. . „An improved maximum allowable transfer interval for $L^p$-stability of networked control systems.“ IEEE Transactions on Automatic Control 55 (1): 179–184. doi: 10.1109/TAC.2009.2033771.
- Jentzen, A, und Kloeden, P. . „Taylor expansions of solutions of stochastic partial differential equations with additive noise.“ Annals of Probability 38 (2): 532–569. doi: 10.1214/09-AOP500.
- Jentzen, A. . „Taylor expansions of solutions of stochastic partial differential equations.“ Discrete and Continuous Dynamical Systems - Series B 14 (2): 515–557. doi: 10.3934/dcdsb.2010.14.515.
- Weber, Hendrik. . „On the short time asymptotic of the stochastic Allen-Cahn equation.“ Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 46 (4): 965–975. doi: 10.1214/09-AIHP333.
- Weber, Hendrik. . „Sharp Interface Limit for Invariant Measures of a Stochastic Allen-Cahn Equation.“ Communications on Pure and Applied Mathematics 63 (8): 1071–1109. doi: 10.1002/cpa.20323.
- Moeller, M, Burger, M, Dieterich, P, und Schwab, A. . „A Framework for Automated Cell Tracking in Phase Contrast Microscopic Videos based on Normal Velocities.“
- Benning, M. . Improved Dynamic PET via Kinetic Models and Operator Splitting
- Wolfram, M, Burger, M, und Siwy, Z. . „Mathematical modeling and simulation of nanopore blocking by precipitation.“ J. Phys.: Cond. Matt. 22: 45401.. doi: 10.1088/0953-8984/22/45/454101.
- Burger, MDi Francesco M, und Pietschmann, JSchlake B. . „Nonlinear cross-diffusion with size exclusion.“ SIAM Journal on Mathematical Analysis 42 (6): 2842–2871. doi: 10.1137/100783674.
- Burger, M, Nielsen, B, und Mardal, K. . „Stability analysis of the inverse transmembrane potential problem in electrocardiography.“ Inverse Problems 26 (10): 105012.. doi: 10.1088/0266-5611/26/10/105012.
- Dedner, A, Klöfkorn, R, Nolte, M, und Ohlberger, M. . „A generic interface for parallel and adaptive scientific computing: Abstraction principles and the DUNE-FEM module.“ Computing 90 (3-4): 165–196. doi: 10.1007/s00607-010-0110-3.
- Burger, M, Carrillo, J, und Wolfram, M. . „A mixed finite element method for nonlinear diffusion equations.“ Kinetic and Related Methods 3: 59–83.
- Mikula, K, und Ohlberger, M. . „A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach.“ SIAM Journal on Scientific Computing 32 (3): 1527–1544. doi: 10.1137/09075946X.
- Zhang, X, Burger, M, und Osher, S. . „A unified primal-dual algorithm framework based on Bregman iteration.“ J Sci Comp 3.
- Henning, P, und Ohlberger, M. . „The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift.“ Networks and Heterogeneous Media 5 (4): 711–744. doi: 10.3934/nhm.2010.5.711.
accepted / in Press (not yet published)
- Engwer, C, Bastian, P, und Kuttanikkad, SP. im Druck. „An Unfitted Discontinuous Galerkin Finite Element Method for Pore Scale Simulations.“ In 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing, Lecture Notes in Computer Science Springer.
- Schellmann, M, Gorlatch, S, Meiländer, D, Kösters, T, Schäfers, K, Wübbeling, F, und Burger, M. . „Parallel medical image reconstruction: From graphics processors to grids.“ Lecture notes in computer science 5698 LNCS: 457–473.
- Büther, F, Dawood, M, Stegger, L, Wübbeling, F, Schäfers, M, Schober, O, und Schäfers, KP. . „List mode-driven cardiac and respiratory gating in PET.“ Journal of Nuclear Medicine 50 (5): 674–681. doi: 10.2967/jnumed.108.059204.
- Bachmayr, M, und Burger, M. . „Iterative total variation schemes for nonlinear inverse problems.“ Inverse Problems 25.
- Henning, P, und Ohlberger, M. . „The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains.“ Numer. Math. 113: 601–629. doi: 10.1007/s00211-009-0244-4.
- Buther, F, Dawood, M, Stegger, L, Wübbeling, F, Schäfers, M, Schober, O, und Schafers, KP. . „List mode-driven cardiac and respiratory gating.“ PET. J. Nucl. Med. 50: 674–681.
- Kelkel, J, und Surulescu, C. . „A weak solution approach to a reaction-diffusion system modeling pattern formation on seashells.“ MMAS 32: 2267–2286.
- Osmolovskii, NP, und Maurer, H. . „Second order sufficient optimality conditions for a control problem with continuous and bang-bang control components: Riccati approach.“ In System modeling and optimization, IFIP Adv. Inf. Commun. Technol. Berlin: Springer VDI Verlag. doi: 10.1007/978-3-642-04802-9_24.
- Maurer, H, und Vossen, G. . „Sufficient conditions and sensitivity analysis for optimal bang-bang control problems with state constraints.“ In System modeling and optimization, IFIP Adv. Inf. Commun. Technol. Berlin: Springer VDI Verlag. doi: 10.1007/978-3-642-04802-9_4.
- d'Onofrio, A, Ledzewicz, U, Maurer, H, und Schättler, H. . „On optimal delivery of combination therapy for tumors.“ Mathematical Biosciences 222 (1): 13–26. doi: 10.1016/j.mbs.2009.08.004.
- Göllmann, L, Kern, D, und Maurer, H. . „Optimal control problems with delays in state and control variables subject to mixed control-state constraints.“ Optimal Control Applications and Methods 30 (4): 341–365. doi: 10.1002/oca.843.
- Brune, C, Maurer, H, und Wagner, M. . „Detection of intensity and motion edges within optical flow via multidimensional control.“ SIAM Journal on Imaging Sciences 2 (4): 1190–1210. doi: 10.1137/080725064.
- Kelkel, J, und Surulescu, C. . „A weak solution approach to a reaction-diffusion system modeling pattern formation on seashells.“ Mathematical Methods in the Applied Sciences 32 (17): 2267–2286. doi: 10.1002/mma.1133.
- Primi, Ivano, Stevens, Angela, und Velázquez, Juan J. L. . „Mass-selection in alignment models with non-deterministic effects.“ Communications in Partial Differential Equations 34 (5): 419–456. doi: 10.1080/03605300902797171.
- Espejo, Elio E., Stevens, Angela, und Velazquez, Juan J. L. . „Simultaneous finite time blow-up in a two species model for chemotaxis.“ Analysis 29 (3): 317–338. doi: 10.1524/anly.2009.1029.
- Kang, Kyungkeun, Perthame, Benoit, Stevens, Angela, und Velázquez, Juan J. L. . „An integro-differential equation model for alignment and orientational aggregation.“ Journal of Differential Equations 246 (4): 1387–1421. doi: 10.1016/j.jde.2008.11.006.
- Dkhil, Fathi, und Stevens, Angela. . „Traveling wave speeds in rapidly oscillating media.“ Discrete and Continuous Dynamical Systems - Series A 25 (1): 89–108. doi: 10.3934/dcds.2009.25.89.
- DiBenedetto, Emmanuele, Perthame, Benoit, und Stevens, Angela, Hrsg. .„Mathematical biology. Abstracts from the workshop held May 3-9, 2009. Organized by Emmanuele DiBenedetto, Benoit Perthame and Angela Stevens.“ Sonderausgabe Oberwolfach Reports 2. doi: 10.4171/OWR/2009/24.
- Braides, A, und Zeppieri, C.I. . „Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy.“ Interfaces and Free Boundaries 11 (1): 61–108.
- Cicalese, M, DeSimone, A, und Zeppieri, C.I. . „Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers.“ Networks and Heterogeneous Media 4 (4): 667–708. doi: 10.3934/nhm.2009.4.667.
- Brancolini, A., Buttazzo, G., Santambrogio, F., und Stepanov, E. . „Long-term planning versus short-term planning in the asymptotical location problem.“ ESAIM: Control, Optimisation and Calculus of Variations 15 (3): 509–524. doi: 10.1051/cocv:2008034.
- Wirth, B, und Sobey, I. . „Analytic solution of the linear unsteady poroelastic equations in a spherically symmetric brain during an infusion test.“ Mathematical Medicine and Biology 26: 25–61.
- Wirth, B, Bar, L, Rumpf, M, und Sapiro, G. . „Geodesics in Shape Space via Variational Time Discretization.“ In 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Bd. 5681 aus Lecture Notes in Computer Science doi: 10.1007/978-3-642-03641-5_22.
- Rumpf, M, und Wirth, B. . „An Elasticity Approach to Principal Modes of Shape Variation.“ In Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, Bd. 5567 aus Lecture Notes in Computer Science
- Rumpf, M, und Wirth, B. . „A nonlinear elastic shape averaging approach.“ SIAM Journal on Imaging Sciences 2 (3): 800–833. doi: 10.1137/080738337.
- Herrmann, M, Laurençot, P, und Niethammer, B. . „Self-similar solutions for fat tails for a coagulation equation with nonlocal drift.“ Comptes Rendus Mathématique 347 (15-16): 909–914. doi: 10.1016/j.crma.2009.05.006.
- Herrmann, M. . „Periodic travelling waves in convex Klein-Gordon chains.“ Nonlinear Analysis: Theory, Methods and Applications 71 (11): 5501–5508. doi: 10.1016/j.na.2009.04.039.
- Herrmann, M, Niethammer, B, und Velázquez, JJL. . „Self-similar solutions for the LSW model with encounters.“ Journal of Differential Equations 247 (8): 2282–2309. doi: 10.1016/j.jde.2009.07.021.
- Engwer, C. . „An Unfitted Discontinuous Galerkin Scheme for Micro-scale Simulations and Numerical Upscaling.“ Dissertationsschrift, Universität Heidelberg.
- Bastian, P, und Engwer, C. . „An unfitted finite element method using discontinuous Galerkin.“ International Journal for Numerical Methods in Engineering 79 (12): 1557–1576. doi: 10.1002/nme.2631.
- Jentzen, A, und Kloeden, PE. . „Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise.“ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465 (2102): 649–667. doi: 10.1098/rspa.2008.0325.
- Jentzen, A, und Neuenkirch, A. . „A random Euler scheme for Carathéodory differential equations.“ Journal of Computational and Applied Mathematics 224 (1): 346–359. doi: 10.1016/j.cam.2008.05.060.
- Jentzen, A, Kloeden, PE, und Neuenkirch, A. . „Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients.“ Numerische Mathematik 112 (1): 41–64. doi: 10.1007/s00211-008-0200-8.
- Jentzen, A, und Kloeden, PE. . „Pathwise Taylor schemes for random ordinary differential equations.“ BIT Numerical Mathematics 49 (1): 113–140. doi: 10.1007/s10543-009-0211-6.
- Jentzen, A. . „Pathwise numerical approximation of SPDEs with additive noise under non-global Lipschitz coefficients.“ Potential Analysis 31 (4): 375–404. doi: 10.1007/s11118-009-9139-3.
- Jentzen, A, Kloeden, PE, und Neuenkirch, A. . „Pathwise convergence of numerical schemes for random and stochastic differential equations.“ In Foundations of computational mathematics, Hong Kong 2008, Bd. 363 aus London Math. Soc. Lecture Note Ser., herausgegeben von F Cucker, A Pinkus und MJ Todd. Cambridge University Press. doi: 10.1017/CBO9781139107068.006.
- Jentzen, A, und Kloeden, PE. . „The numerical approximation of stochastic partial differential equations.“ Milan Journal of Mathematics 77: 205–244. doi: 10.1007/s00032-009-0100-0.
- Ohlberger, M. . „A review of a posteriori error control and adaptivity for approximations of nonlinear conservation laws.“ International Journal for Numerical Methods in Fluids 59 (International Journal for Numerical Methods in Fluids): 333–354. doi: 10.1002/fld.1686.
- Henning, P, und Ohlberger, M. . „A-posteriori error estimate for a heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift.“
- Brune, C, Sawatzky, A, und Burger, M. . „Bregman-EM-TV Methods with Application to Optical Nanoscopy.“ Beitrag präsentiert auf der SSVM 2009, Voss, Norway doi: 10.1007/978-3-642-02256-2_20.
- Burger, M, He, L, und Schönlieb, C. . „Cahn-Hilliard inpainting and a generalization for grayvalue image.“ SIAM J. Imag. Sci. 3: 3..
- Brune, C, Maurer, H, und Wagner, M. . „Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control.“ SIAM J. Imag. Sci. 2 (4): 1190–1210. doi: 10.1137/080725064.
- Haasdonk, B, und Ohlberger, M. . „Efficient reduced models for parametrized dynamical systems by offline/online decomposition.“
- Burger, M, Kaltenbacher, B, und Neubauer, A. . „Iterative solution methods.“ In Handbook of Mathematical Methods in Imaging, herausgegeben von O Scherzer. Springer VDI Verlag.
- Albrecht, F. . Local Discontinuous Galerkin Verfahren für die Stokes Gleichungen und Homogenisierung in porösen Medien (Diplomarbeit)
- Schellmann, M, Gorlatch, S, Meiländer, D, Kösters, T, Wübbeling, F, und Burger, M. . „Parallel medical image reconstruction: From graphics processors to grids.“ Beitrag präsentiert auf der 10th International Conference PaCT, Novosibirsk, Russia
- Drohmann, M, Haasdonk, B, und Ohlberger, M. . „Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries.“ Beitrag präsentiert auf der Proceedings of ALGORITMY 2009
- Drohmann, M. . Reduzierte Basis Methoden für ungesättigte Grundwasserströmungen
- Steinstraeter, O, Sillekens, S, Junghoefer, M, Burger, M, und Wolters, C. . „Sensitivity of beamformer source analysis to deficiencies in forward modeling.“ Human Brain Mapping 31: 1907–1927.
- Haasdonk, B, und Ohlberger, M. . „Space-adaptive reduced basis simulation for time-dependent problems.“
- Sawatzky, A, Brune, C, Müller, J, und Burger, M. . „Total Variation Processing of Images with Poisson Statistics.“ In Bd. 5702 aus LNCS, herausgegeben von X Jiang und N Petkov. Berlin: Springer. doi: 10.1007/978-3-642-03767-2_65.
- Haasdonk, B, und Ohlberger, M. . „Reduced Basis Method for Explicit Finite Volume Approximations of Nonlinear Conservation Laws.“ In Hyperbolic problems: theory, numerics and applications, Bd. 67 aus Proc. Sympos. Appl. Math. Providence, RI: American Mathematical Society.
- Busby, M, Blum, C, Tibben, M, Fibikar, S, Calzaferri, G, Subramaniam, V, und De, Cola L. . „Time, space, and spectrally resolved studies on J-aggregate interactions in zeolite L nanochannels.“ Journal of the American Chemical Society 130 (33): 10970–10976. doi: 10.1021/ja801178p.
- Dawood, M, Kösters, T, Fieseler, M, Büther, F, Jiang, X, Wübbeling, F, und Schäfers, KP. . „Motion correction in respiratory gated cardiac PET/CT using multi-scale optical flow.“ doi: 10.1007/978-3-540-85990-1_19.
- Haasdonk, B, Ohlberger, M, und Rozza, G. . „A reduced basis method for evolution schemes with parameter-dependent explicit operators.“ Electronic transactions on numerical analysis 32: 145–161.
- Dawood, M, Kösters, T, Fieseler, M, Büther, F, Jiang, X, Wübbeling, F, und Schäfers, K. . „Multi-scale optical flow for respiratory motion correction in cardiac PET/CT.“ Beitrag präsentiert auf der MICCAI, New York
- Surulescu, C. . „On the Time-Dependent Motion of a Viscous Incompressible Fluid Through a Tube with Compliant Walls.“ Studia UBB Mathem LIII: 77–95.
- Maurer, H, und Pesch, HJ. . „Direct optimization methods for solving a complex state-constrained optimal control problem in microeconomics.“ Applied Mathematics and Computation 204 (2): 568–579. doi: 10.1016/j.amc.2008.05.035.
- Dedner, A, und Ohlberger, M. . „A new $hp$-adaptive DG scheme for conservation laws based on error control.“ In Hyperbolic Problems: Theory, Numerics, Applications, herausgegeben von Serre Benzoni-Gavage. Berlin. doi: 10.1007/978-3-540-75712-2_15.
- Haasdonk, B, Ohlberger, M, und Rozza, G. . „A reduced basis method for evolution schemes with parameter-dependent explicit operators.“ Electronic transactions on numerical analysis 32: 145–161.
- Klöfkorn, R, Kröner, D, und Ohlberger, M. . „Parallel and adaptive simulation of fuel cells in 3d.“ In Computational science and high performance computing III, Bd. 101 aus Notes Numer. Fluid Mech. Multidiscip. Des. Berlin: Springer VDI Verlag. doi: 10.1007/978-3-540-69010-8_7.
- Stevens, Angela, und Velázquez, Juan J. L. . „Partial differential equations and non-diffusive structures.“ Nonlinearity 21 (12): T283–T289. doi: 10.1088/0951-7715/21/12/T04.
- Wirth, B, und Sobey, I. . „A model for an inverse power constitutive law for cerebral compliance.“ Mathematical Medicine and Biology 25: 113–131. doi: 10.1093/imammb/dqn006.
- Dreyer, W, und Herrmann, M. . „Numerical experiments on the modulation theory for the nonlinear atomic chain.“ Physica D: Nonlinear Phenomena 237 (2): 255–282. doi: 10.1016/j.physd.2007.09.003.
- Henseler, R, Herrmann, M, Niethammer, B, und Velázquez, JJL. . „A kinetic model for grain growth.“ Kinetic and Related Models 1 (4): 591–617. doi: 10.3934/krm.2008.1.591.
- Giannoulis, J, Herrmann, M, und Mielke, A. . „Lagrangian and Hamiltonian two-scale reduction.“ Journal of Mathematical Physics 49 (10): 103505, 42.. doi: 10.1063/1.2956487.
- Benning, M, Kösters, T, Wübbeling, F, Schäfers, K, und Burger, M. . „A Nonlinear Variational Method for Improved Quantification of Myocardial Blood Flow Using Dynamic H215O PET.“ Beitrag präsentiert auf der IEEE NSS/MIC 2008, Dresden
- Burger, M, He, L, Markowich, P, und Schönlieb, C. . „A generalization of Cahn-Hilliard inpainting for gray-value images.“ In PAMM Special Issue: ICIAM 07
- Burger, M, Chu, S, Markowich, P, und Schönlieb, C. . „Cahn-Hilliard inpainting and the Willmore functional.“ In PAMM Special Issue: ICIAM 07
- Arning, K, Burger, M, Eisenberg, B, Engl, H, und He, L. . „Inverse problems related to ion channels.“ In PAMM Special Issue: ICIAM 07
- Sawatzky, A, Brune, C, Wübbeling, F, Kösters, T, Schäfers, K, und Burger, M. . „Accurate EM-TV algorithm in PET with low SNR.“ Beitrag präsentiert auf der IEEE NSS/MIC 2008, Dresden, Deutschland doi: 10.1109/NSSMIC.2008.4774392.
- P, Bastian, M, Blatt, A, Dedner, C, Engwer, Klöfkorn, Rober, R, Kornhuber, M, Ohlberger, und O, Sander. . „A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part {II}: Implementation and Tests in {DUNE}.“ Computing 82 (2--3): 121–138. doi: 10.1007/s00607-008-0004-9.
- Bastian, P, Blatt, M, Dedner, A, Engwer, C, Klöfkorn, R, Ohlberger, M, und Sander, O. . „A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part I: Abstract framework.“ Computing 82 (2--3): 103–119. doi: 10.1007/s00607-008-0003-x.
- Bastian, P, Chavarria-Krauser, A, Engwer, C, Jäger, W, Marnach, S, und Ptashnyk, M. . „Modelling in vitro growth of dense root networks.“ Journal of Theoretical Biology 254 (1): 99–109. doi: 10.1016/j.jtbi.2008.04.014.
- Bastian, P, Bauer, J, Chavarria-Krauser, A, Engwer, C, Jager, W, Marnach, S, Ptashnyk, M, und Wetterauer, B. . „Modeling and Simulation of Hairy Root Growth.“ In Mathematics-Key Technology for the Future: Joint Projects Between Universities and Industry 2004-2007, herausgegeben von H Krebs und W Jäger. Springer VDI Verlag. doi: 10.1007/978-3-540-77203-3_8.
- Burger, M, und Pinnau, R. . „A Globally Covergent Gummel Map for Optimal Dopant Profiling.“ Math. Models Meth. Appl. Sci. 19.
- Goldsmith, F, Ohlberger, M, Schumacher, J, Steinkamp, K, und Ziegler, C. . „A non-isothermal PEM fuel cell model including two water transport mechanisms in the membrane.“ Journal of Fuel Cell Science and Technology 5 (Journal of Fuel Cell Science and Technology): 5.. doi: 10.1115/1.2822884.
- Burger, M. . „A note on sparse reconstruction methods.“ In J Phys Conference Series, herausgegeben von G Uhlmann.
- Haasdonk, B, und Ohlberger, M. . „Adaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes.“ In Finite Volumes for Complex Applications V , herausgegeben von Robert Eymard und Jean-Marc Hérard. London: ISTE Ltd and John Wiley & Sons Inc.
- Burger, M, Dolak-Struss, Y, und Schmeiser, C. . „Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions.“ Commun. Math. Sci. 6: 1–28.
- Burger, M, Landa, Y, Tanushev, N, und Tsai, R. . „Discovering point sources in unknown environments.“ Beitrag präsentiert auf der WAFR 2008
- Burger, M. . „Finite element approximation of elliptic partial differential equations on implicit surfaces.“ Comp. Vis. Sci..
- Burger, M, Stöcker, C, und Voigt, A. . „Finite element based level set methods for higher order flows.“ J. Sci. Comp. 35: 77–98.
- Brune, C, Maurer, H, und Wagner, M. . „aaa Kantenerkennung im optischen Fluss als mehrdimensionales Steuerungsproblem.“ BTU Cottbus.
- Burger, MDi Francesco M. . „Large time behavior of nonlocal aggregation models with nonlinear diffusion.“ Networks and Heterogeneous Media 3: 749–785.
- Schlake, B. . Mathematical Models for Pedestrian Motion
- Burger, M, Pinnau, R, und Wolfram, M. . „On-/Off-State design of semiconductor doping profiles.“ Commun. Math. Sci. 6: 1021–1041.
- Klöfkorn, R, Kröner, D, und Ohlberger, M. . „Parallel adaptive simulation of PEM fuel cells.“ In Mathematics – Key Technology for the Future, herausgegeben von Krebs und Jäger.
- Haasdonk, B, und Ohlberger, M. . „Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations.“ M2AN Math. Model. Numer. Anal. 42 (2): 277–302. doi: 10.1051/m2an:2008001.
- Favaro, P, Soatto, S, Burger, M, und Osher, S. . „Shape from Defocus via Diffusion.“ IEEE Transactions PAMI 30: 518–531.
- Burger, M, Chu, S, Markowich, P, und Schönlieb, C. . „The Willmore functional and instabilities in the Cahn-Hilliard equation.“ Commun. Math. Sci. 6: 309–329.
- Fuhrmann, Jan, Käs, Josef, und Stevens, Angela. . „Initiation of cytoskeletal asymmetry for cell polarization and movement.“ Journal of Theoretical Biology 249 (2): 278–288. doi: 10.1016/j.jtbi.2007.08.013.
- Burger, M, Frick, K, Osher, S, und Scherzer, O. . „Inverse total variation flow.“ SIAM Multiscale Mod. Simul. 6: 366–395.
- Ben, Ameur H, Burger, M, und Hackl, B. . „On some geometric inverse problems in linear elasticity.“ Math. Meth. Appl. Sci. 30: 625–647.
- Klöfkorn, R, Kröner, D, und Ohlberger, M. . „Parallel and adaptive simulaiton of fuel cells in 3D.“
- Sawatzky, A. . Reflektoren in der Ultraschall-Tomographie
- Benning, M, Lee, E, Pao, H, und Yacoubou-Djima, K. . „Statistical Filtering of Global Illumination for Computer Graphics.“
- Burger, M, Eisenberg, B, und Engl, H. . „Inverse problems related to ion channel selectivity.“ SIAM J. Appl. Math. 67: 960–989.
- Dedner, A, Makridakis, C, und Ohlberger, M. . „Error control for a class of Runge-Kutta discontinuous Galerkin methods for nonlinear conservation laws.“ SIAM J. Numer. Anal. 45: 514–538.
- Surulescu, C. . „On the Stationary Interaction of a Navier-Stokes Fluid With an Elastic Tube Wall.“ Applicable Analyis 86: 149–165.
- Schweizer, B, Surovtsova, I, und Surulescu, C. . „Fluid Flows and Free Boundaries.“ In Reactive Flows, Diffusion and Transport, herausgegeben von W Jäger und Rand Warnatz J. Rannacher. Springer VDI Verlag.
- Osmolovskii, NP, und Maurer, H. . „Equivalence of second order optimality conditions for bang-bang control problems. {II}. Proofs, variational derivatives and representations.“ Control and Cybernetics 36 (1): 5–45.
- Su, B, und Burger, M. . „Global weak solutions of non-isothermal front propagation problem.“ Electronic Research Announcements of the American Mathematical Society 13: 46–52. doi: 10.1090/S1079-6762-07-00173-4.
- Burger, M, Capasso, V, und Micheletti, A. . „An extension of the Kolmogorov-Avrami formula to inhomogeneous birth-and-growth processes.“, herausgegeben von G Aletti, M Burger, A Micheletti und D Morale. Berlin: Springer VDI Verlag. doi: 10.1007/978-3-540-44446-6_6.
- Surulescu, C. . „On the stationary interaction of a Navier-Stokes fluid with an elastic tube wall.“ Applicable Analysis 86 (2): 149–165. doi: 10.1080/00036810601108756.
- Schweizer, B, Bodea, S, Surulescu, C, und Surovtsova, I. . „Fluid flows and free boundaries.“ In Reactive flows, diffusion and transport Berlin: Springer VDI Verlag. doi: 10.1007/978-3-540-28396-6_1.
- Ohlberger, M, und Schweizer, B. . „Modelling of interfaces in unsaturated porous media.“ Discrete Contin. Dyn. Syst., Nr. Dynamical Systems and Differential Equations. Proceedings of the 6th AIMSInternational Conference, suppl.: 794–803.
- Ansini, N, Babadjian, J.F., und Zeppieri, C.I. . „The Neumann sieve problem and dimensional reduction: A multiscale approach.“ Mathematical Models and Methods in Applied Sciences 17 (5): 681–735. doi: 10.1142/S0218202507002078.
- Braides, A, und Zeppieri, C.I. . „A note on equi-integrability in dimension reduction problems.“ Calculus of Variations and Partial Differential Equations 29 (2): 231–238. doi: 10.1007/s00526-006-0065-6.
- Rave, S. . Über die Entscheidbarkeit gewisser Prädikate in der Theorie der C*-Algebren Münster.
- Kloeden, PE, und Jentzen, A. . „Pathwise convergent higher order numerical schemes for random ordinary differential equations.“ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463 (2087): 2929–2944. doi: 10.1098/rspa.2007.0055.
- Burger, M, Hausser, F, Stöcker, C, und Voigt, A. . „A level set approach to anisotropic flows with curvature regularization.“ J. Comp. Phys. 225: 183–205.
- Haasdonk, B, und Ohlberger, M. . „Basis Construction for Reduced Basis Methods by Adaptive Parameter Grids.“
- Brune, C. . Berechnung des optischen Flusses und Kantenerkennung mit Optimierungsmethoden
- Henning, P. . Die Heterogene Mehrskalenmethode f\�r elliptische Differentialgleichungen in perforierten Gebieten
- Burger, M, Resmerita, E, und He, L. . „Error estimation for Bregman iterations and inverse scale space methods.“ Computing 81: 109–135.
- Fuhrmann, J, Haasdonk, B, Holzbecher, E, und Ohlberger, M. . „Guest Editorial for Special Issue on Modelling and Simulation of PEM-FC.“ Journal of Fuel Cell Science and Technology 2007 (Journal of Fuel Cell Science and Technology).
- Lunkenheimer, PP, Redmann, K, Kling, N, Jiang, XJ, Rothaus, K, Cryer, CW, Wubbeling, F, Niederer, P, Heitz, PU, Ho, SY, und Anderson, RH. . „Three-dimensional architecture of the left ventricular myocardium.“ Anatomical Record Part A: Discoveries in Molecular Cellular and Evolutionary Biology 288A (6): 565–578. doi: 10.1002/ar.a.20326.
- Burri, A, Dedner, A, Diehl, D, Klöfkorn, R, und Ohlberger, M. . „A general object oriented framework for discretizing nonlinear evolution equations.“
- Stainko, R, und Burger, M. . „A one-shot approach to topology optimization with stress constraints.“ Beitrag präsentiert auf der IUTAM Symposium on Topological Design Optimization of Structures, Machines, and Materials , herausgegeben von M Bendsoe, N Ohlhoff und O Sigmund. Berlin: Springer.
- Burri, A, Dedner, A, Klöfkorn, R, und Ohlberger, M. . „An efficient implementation of an adaptive and parallel grid in DUNE.“
- Burger, M, Capasso, V, und Micheletti, A. . „An extension of the Avrami-Kolmogorov formula to inhomogeneous birth-and-growth processes.“ Beitrag präsentiert auf der Math Everywhere, Milano , herausgegeben von G Aletti, M Burger, A Micheletti und D Morale. Berlin: Springer.
- Berkels, B, Burger, M, Droske, M, Nemitz, O, und Rumpf, M. . „Cartoon extraction based on anisotropic image classification.“ Beitrag präsentiert auf der Vision, Modeling, and Visualization Proceedings
- Aletti, G, Burger, M, Micheletti, A, und Morale, D. . Deterministic and Stochastic Modelling in Biomedicine, Economics, and Industry
- He, L, Burger, M, und Osher, S. . „Iterative total variation regularization with non-quadratic fidelity.“ J. Math. Imaging Vision 26: 167–184.
- Burger, M, Capasso, V, und Pizzocchero, L. . „Mesoscale averaging of nucleation and growth processes.“ SIAM Multiscale Mod. Simul. 5: 564–592.
- Burger, M, Gilboa, G, Osher, S, und Xu, J. . „Nonlinear inverse scale space methods.“ Commun. Math. Sci. 4: 179–212.
- Burger, M, Capasso, V, und Morale, D. . „On an aggregation model with long and short range interactions.“ Nonlinear Analysis: Real World Applications 8: 939–958.
- Burger, M, Hinze, M, und Pinnau, R. . „Optimization models for semiconductor dopant profiling.“ In Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photons, and Biological Systems, herausgegeben von C Cercignani und E Gabetta. Boston: Birkhäuser Verlag.
- Burger, M, und Stainko, R. . „Phase-field relaxation of topology optimization with local stress constraints,.“ SIAM J. Control. Optim. 45: 1447–1466.
- Haasdonk, B, und Ohlberger, M. . „Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations.“
- Su, B, und Burger, M. . „Weak solutions of a polymer crystal growth model.“
- Burger, M. . „Surface diffusion including adatoms.“ Comm. Math. Sci. 4: 1–51.
- Burger, M, DiFrancesco, M, und Dolak-Struss, Y. . „The Keller-Segel model for chemotaxis: linear vs. nonlinear diffusion.“ SIAM J. Math. Anal. 38: 1288–1315.
- Ohlberger, M, und Vovelle, J. . „Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method.“ Math. Comp. 75: 113–150.
- Lunkenheimer, P, P, Redmann, K, Kling, N, Rothaus, K, Jiang, X, Cryer, C, Wübbeling, F, Niederer, P, Heitz, U, Ph, Ho, Y, S, H, R, und erson. . „The three-dimensional architecture of the left ventricular myocardium.“ The anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology 288A (6): 565–578.
- Surulescu, C. . „On the Stationary Motion of a Stokes Fluid in a Thick Elastic Tube: A 3D/3D Interaction Problem.“ AMUC 75: 95–106.
- Surulescu, C, und Surulescu, N. . „A Note on an Individual Bioequivalence Setting.“ J. Inequal. Pure Appl. Math. 7: 8..
- Vossen, G, und Maurer, H. . „On {$L^1$}-minimization in optimal control and applications to robotics.“ Optimal Control Applications and Methods 27 (6): 301–321. doi: 10.1002/oca.781.
- Osmolovskii, NP, und Maurer, H. . „Second order optimality conditions for controls with continuous and bang-bang components.“ In Systems, control, modeling and optimization, IFIP Int. Fed. Inf. Process. New York: Springer VDI Verlag. doi: 10.1007/0-387-33882-9_28.
- Burger, M, und Kaltenbacher, B. . „Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems.“ SIAM Journal on Numerical Analysis 44 (1): 153–182. doi: 10.1137/040613779.
- Surulescu, C, und Surulescu, N. . „A note on an individual bioequivalence setting.“ Journal of inequalities in pure and applied mathematics 7 (3): Article 100, 8 pp. (electronic)..
- Surulescu, C. . „On the stationary motion of a Stokes fluid in a thick elastic tube: a 3D/3D interaction problem.“ Acta Mathematica Universitatis Comenianae 75 (1): 95–106.
- Bastian, P, Blatt, M, Engwer, C, Dedner, A, Klöfkorn, R, Kuttanikkad, SP, Ohlberger, M, und Sander, O. . „The Distributed and Unified Numerics Environment (DUNE).“ In Proc. of the 19th Symposium on Simulation Technique in Hannover, September 12 - 14
- Dkhil, Fathi, und Stevens, Angela. . „Traveling wave speeds of nonlocally perturbed reaction diffusion equations.“ Asymptotic Analysis 46 (1): 81–91.
- Hwang, Hyung Ju, Kang, Kyungkeun, und Stevens, Angela. . „Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit.“ Indiana University Mathematics Journal 55 (1): 289–316. doi: 10.1512/iumj.2006.55.2677.
- DiBenedetto, Emmanuele, Perthame, Benoit, und Stevens, Angela, Hrsg. .„Mathematical biology. Abstracts from the workshop held May 14-20, 2006. Organized by Emmanuele DiBenedetto, Benoit Perthame and Angela Stevens.“ Sonderausgabe Oberwolfach Reports 2. doi: 10.4171/OWR/2006/24.
- Brancolini, A., Buttazzo, G., und Santambrogio, F. . „Path functionals over Wasserstein spaces.“ Journal of the European Mathematical Society 8 (3): 415–434.
- Sobey, I, und Wirth, B. . „Effect of nonlinear permeability in a spherical model of hydrocephalus.“ Mathematical Medicine and Biology 23: 339–361. doi: 10.1093/imammb/dql015.
- Wirth, B, und Sobey, I. . „An axisymmetric and fully 3D poroelastic model for the onset and treatment of hydrocephalus.“ Mathematical Medicine and Biology 23: 363–388. doi: 10.1093/imammb/dql014.
- Dreyer, W, Herrmann, M, und Mielke, A. . „Micro-macro transition in the atomic chain via Whitham's modulation equation.“ Nonlinearity 19 (2): 471–500. doi: 10.1088/0951-7715/19/2/013.
- Herrmann, M, Naldzhieva, M, und Niethammer, B. . „On a thermodynamically consistent modification of the Becker-Döring equations.“ Physica D: Nonlinear Phenomena 222 (1-2): 116–130. doi: 10.1016/j.physd.2006.08.004.
- Giannoulis, J, Herrmann, M, und Mielke, A. . „Continuum descriptions for the dynamics in discrete lattices: derivation and justification.“ In Analysis, modeling and simulation of multiscale problems, herausgegeben von A Mielke. Springer VDI Verlag. doi: 10.1007/3-540-35657-6_16.
- Dreyer, W, Herrmann, M, und Rademacher, JDM. . „Wave trains, solitons and modulation theory in FPU chains.“ In Analysis, modeling and simulation of multiscale problems, herausgegeben von A Mielke. Springer VDI Verlag. doi: 10.1007/3-540-35657-6_17.
Veröffentlicht
- Hwang, Hyung Ju, Kang, Kyungkeun, und Stevens, Angela. . „Drift-diffusion limits of kinetic models for chemotaxis: A generalization.“ Discrete and Continuous Dynamical Systems - Series B 5 (2): 319–334. doi: 10.3934/dcdsb.2005.5.319.
- Natterer, F, und Wubbeling, F. . „Marching schemes for inverse acoustic scattering problems.“ Numerische Mathematik 100 (4): 697–710. doi: 10.1007/s00211-004-0580-3.
- Burger, M. . „A model hierarchy for surface diffusion: the small slope case.“ Beitrag präsentiert auf der 5th MATHMOD, Vienna , herausgegeben von F Breitenecker und I Troch.
- Dedner, A, Makridakis, C, und Ohlberger, M. . „A new stable discontinuous Galerkin approximation for non-linear conservation laws on adaptively refined grids.“
- Ohlberger, M. . „A posterior error estimates for the heterogenoeous mulitscale finite element method for elliptic homogenization problems.“ SIAM Multiscale Mod. Simul. 4 (1): 88–114.
- Burger, M, und Osher, S. . „A survey on level set methods for inverse problems and optimal design.“ European J. Appl. Math. 16: 263–301.
- Ohlberger, M. . „Error control for approximations of non-linear conservation laws.“
- Burger, M, und Hofinger, A. . „Greedy algorithms for neural network training with data noise.“ Computing 74: 1–22.
- Wolfram, M, und Burger, M. . „Inverse dopant profiling for highly doped semiconductor devices.“ Beitrag präsentiert auf der 5th MATHMOD, Vienna , herausgegeben von F Breitenecker und I Troch.
- Burger, M, Gilboa, G, Osher, S, und Xu, J. . „Nonlinear inverse scale space methods for image restoration.“ In Bd. 3752 aus LNCS, herausgegeben von N Paragios. Berlin: Springer.
- Burger, M. . „Numerical simulation of anisotropic surface diffusion with curvature-dependent energy.“ J. Comp. Phys. 203: 602–625.
- Burger, M, und Hintermueller, M. . „Projected gradient flows for BV / level set relaxation.“ PAMM 5 (PAMM): 11–14.
- Burger, M, und Gu, H. . „Symbolic preprocessing of finite element methods for parameter-dependent geometric differential equations.“ Beitrag präsentiert auf der Workshop on Symbolic-Numerical Computation 2005
- Bastian, P, Droske, M, Engwer, C, Klöfkorn, R, Neubauer, T, Ohlberger, M, und Rumpf, M. . „Towards a unified framework for scientific computing.“
- Osher, S, Burger, M, Goldfarb, D, Xu, J, und Yin, W. . „An iterative regularization method for total variation based image restoration.“ SIAM Multiscale Modelling and Simulation 4: 460–489.
- Ohlberger, M. . „A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems.“ Multiscale Model. Simul. 4: 88–114.
- Osmolovskii, NP, und Maurer, H. . „Equivalence of second order optimality conditions for bang-bang control problems. I. Main results.“ Control and Cybernetics 34 (3): 927–950.
- Maurer, H, Büskens, C, Kim, JR, und Kaya, CY. . „Optimization methods for the verification of second order sufficient conditions for bang-bang controls.“ Optimal Control Applications and Methods 26 (3): 129–156. doi: 10.1002/oca.756.
- Malanowski, K, Maurer, H, und Pickenhain, S. . „Second order sufficient conditions for optimal control subject to first order state constraints.“ In Control and boundary analysis, Lect. Notes Pure Appl. Math. Chapman & Hall.
- Engwer, C, und Bastian, P. . „A Discontinuous Galerkin Method for Simulations in Complex Domains.“
- Bastian, P, und Engwer, C. . „Solving partial differential equations in complicated domains.“ Oberwolfach Reports 4.
- Stevens, Angela, und Søgaard-Andersen, Lotte. . „Making waves: Pattern formation by a cell-surface-associated signal.“ Trends in Microbiology 13 (6): 249–252. doi: 10.1016/j.tim.2005.04.002.
- Hwang, Hyung Ju, Kang, Kyungkeun, und Stevens, Angela. . „Global solutions of nonlinear transport equations for chemosensitive movement.“ SIAM Journal on Mathematical Analysis 36 (4): 1177–1199. doi: 10.1137/S0036141003431888.
- Brancolini, A., und Buttazzo, G. . „Optimal networks for mass transportation problems.“ ESAIM: Control, Optimisation and Calculus of Variations null (11): 88–101. doi: 10.1051/cocv:2004032.
- Dreyer, W, Herrmann, M, Kunik, M, und Qamar, S. . „Kinetic schemes for selected initial and boundary value problems.“ In Analysis and numerics for conservation laws, herausgegeben von G Warnecke. Springer VDI Verlag. doi: 10.1007/3-540-27907-5_9.
Eingereicht / In Begutachtung
- Surulescu, C. . „The Time Dependent Motion of a Navier-Stokes Fluid Through a Vessel With an Elastic Cover.“
- Lunkenheimer, PP, Redmann, K, Florek, J, Fassnacht, U, Cryer, CW, Wubbeling, F, und Niederer, P. . „The forces generated within the musculature of the left ventricular wall.“ Heart 90 (2): 200–207. doi: 10.1136/hrt.2003.011650.
- Barth, T, und Ohlberger, M. . „Finite volume methods: foundation and analysis.“
- Burger, M. . „Growth of multiple crystals in polymer melts.“ European J. Appl. Math. 15: 347–363.
- Ohlberger, M. . „Higher order finite volume methods on selfadaptive grids for convection dominated reactive transport problems in porous media.“ Comp. Vis. Sci. 7 (1): 41–51.
- Burger, M, Hackl, B, und Ring, W. . „Incorporating topological derivatives into level set methods.“ J. Comp. Phys. 194: 344–362.
- Burger, M, Osher, S, und Yablonovitch, E. . „Inverse problem techniques for the design of photonic crystals.“ IEICE Transactions on Electronics 87 C: 258–265.
- Ben, Ameur H, Burger, M, und Hackl, B. . „Level set methods for geometric inverse problems in linear elasticity.“ Inverse Problems 20: 673–696.
- Burger, M. . „Levenberg-Marquardt level set methods for inverse obstacle problems.“ Inverse Problems 20: 673–696.
- Burger, M, Engl, H, Leitao, A, und Markowich, P. . „On inverse problems for semiconductor equations.“ Milan J. Math. 72: 273–314.
- Burger, M, Capasso, V, und Micheletti, A. . „Optimal control of polymer morphologies.“ J. Eng. Math. 49: 339–358.
- Favaro, P, Burger, M, und Soatto, S. . „Scene and motion reconstruction from defocused and motion blurred images via anisotropic diffusion.“ Beitrag präsentiert auf der ECCV , herausgegeben von T Padla und J Matas. Berlin: Springer.
- Burger, M, und Osher, S. . „Convergence rates of convex variational regularization.“ Inverse Problems 20: 1411–1421.
- Malanowski, K, Maurer, H, und Pickenhain, S. . „Second-order sufficient conditions for state-constrained optimal control problems.“ Journal of Optimization Theory and Applications 123 (3): 595–617. doi: 10.1007/s10957-004-5725-0.
- Maurer, H, und Osmolovskii, NP. . „Second order sufficient conditions for time-optimal bang-bang control.“ SIAM Journal on Control and Optimization 42 (6): 2239–2263. doi: 10.1137/S0363012902402578.
- Kim, JR, Lippi, GL, und Maurer, H. . „Minimizing the transition time in lasers by optimal control methods single-mode semiconductor laser with homogeneous transverse profile.“ Physica D: Nonlinear Phenomena 191 (3-4): 238–260. doi: 10.1016/j.physd.2003.12.002.
- Bastian, P, Droske, M, Engwer, C, Klöfkorn, R, Neubauer, T, Ohlberger, M, und Rumpf, M. . „Towards a Unified Framework for Scientific Computing.“ In Proceedings of the 15th Conference on Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering doi: 10.1007/3-540-26825-1_13.
- Dreyer, W, Herrmann, M, und Kunik, M. . „Kinetic solutions of the Boltzmann-Peierls equation and its moment systems.“ Continuum Mechanics and Thermodynamics 16 (5): 453–469. doi: 10.1007/s00161-003-0171-z.
- Horstmann, Dirk, und Stevens, Angela. . „A constructive approach to traveling waves in chemotaxis.“ Journal of Nonlinear Science 14 (1): 1–25. doi: 10.1007/s00332-003-0548-y.
- Lunkenheimer, PP, Redmann, K, Kimaun, D, Cryer, CW, Wubbeling, F, Konertz, W, Zytowsky, A, Hotz, H, Ho, SY, und Anderson, RH. . „A critical evaluation of results of partial left ventriculectomy.“ Journal of Cardiac Surgery 18 (3): 225–235. doi: 10.1046/j.1540-8191.2003.02026.x.
- Lunkenheimer, PP, Redmann, K, Cryer, CW, Wubbeling, F, Konertz, W, Batista, RJV, Ho, SY, und Anderson, RH. . „The relationship between structure and function: why does reshaping the left ventricle surgically not always result in functional improvement?“ Computers in Biology and Medicine 33 (3): 185–196. doi: 10.1016/S0010-4825(02)00085-9.
- Kröner, D, Küther, M, Ohlberger, M, und Rohde, C. . „A posteriori error estimates and adaptive methods for hyperbolic and convection dominates parabolic conservation laws.“
- Küther, M, und Ohlberger, M. . „Adaptive second order central schemes on unstructured staggered grids.“
- Burger, M, und Pinnau, R. . „Fast optimal design of semiconductor devices.“ SIAM J. Appl. Math. 64: 108–126.
- Burger, M. . „Growth and impingement in polymer melts.“ Beitrag präsentiert auf der FBP 2002, Trento Birkhäuser Verlag.
- Burger, M, und Markowich, P. . „Model reduction for semiconductor inverse dopant profiling.“ Beitrag präsentiert auf der 4th IMACS Symposium on Mathematical Modelling, Wien, Österreich , herausgegeben von F Breitenecker und I Troch.
- Burger, M, und Markowich, P. . „Model reduction for semiconductor inverse dopant profiling.“ In Proceedings of the 4th IMACS Symposium on Mathematical Modelling, herausgegeben von I Troch und F Breitenecker.
- Haasdonk, B, Ohlberger, M, Rumpf, M, Schmidt, A, und Siebert, K. . „Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations.“ Computing 70 (Computing): 181–204.
- Burger, M. . „A framework for the construction of level set methods for shape optimization and reconstruction.“ Interfaces and Free Boundaries 5: 301–329.
- Engwer, C. . Direkte Simulation von Transportprozessen im Boden zur Bestimmung makroskopischer Parameter
- Herbin, R, und Ohlberger, M. . „A posteriori error estimate for finite volume approximations of convection diffusion problems.“
- Ohlberger, M, und Rohde, C. . „Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems.“ IMA J. Numer. Anal. 22 (2): 253–280.
- Bürkle, D, und Ohlberger, M. . „Adaptive finite volume methods for displacement problems in porous media.“ Comp. Vis. Sci. 5 (2): 95–106.
- Burger, M, und Neubauer, A. . „Analysis of Tikhonov regularization for function approximation by neural networks.“ Neural Networks 16: 79–90.
- Haslinger, J, Bodenhofer, U, und Burger, M. . „Data-Driven construction of Sugeno controllers: analytical aspects and new numerical methods.“ Beitrag präsentiert auf der 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver
- Burger, M, Engl, H, und Markowich, P. . „Inverse doping problems for semiconductor devices.“ Beitrag präsentiert auf der Recent Progress in Computational and Applied PDEs , herausgegeben von T Chan und al et. Plenum Press.
- Burger, M, und Mühlhuber, W. . „Iterative regularization of parameter identification problems by SQP methods.“ Inverse Problems 18: 943–970.
- Klöfkorn, R, Kröner, D, und Ohlberger, M. . „Local adaptive methods for convection dominated problems.“ International Journal for Numerical Methods in Fluids 40 (1-2): 79–91.
- Burger, M, Capasso, V, und Micheletti, A. . „Mathematical modelling of the crystallization process of polymers.“ Beitrag präsentiert auf der 5th Hellenic Conference on Computer Mathematics and its Applications, Athens , herausgegeben von E Lipitakis. Athens: LEA.
- Capasso, V, Burger, M, Micheletti, A, und Salani, C. . „Mathematical models for polymer crystallization processes.“ In Mathematical modelling for polymer industry, herausgegeben von V Capasso. Springer VDI Verlag.
- Burger, M, Capasso, V, und Eder, G. . „Modelling crystallization of polymers in temperature fields.“ ZAMM 82: 51–63.
- Burger, M, Capasso, V, und Salani, C. . „Modelling multi-dimensional crystallization of polymers in interaction with heat transfer.“ Nonlinear Analysis: Real World Applications 3: 139–160.
- Burger, M, Haslinger, J, Engl, H, und Bodenhofer, U. . „Regularized data-driven construction of fuzzy controllers.“ J. Inverse Ill-Posed Problems 10: 319–344.
- Haslinger, J, Bodenhofer, U, und Burger, M. . „Tuning of fuzzy systems as an ill-posed problem.“ Beitrag präsentiert auf der ECMI 2000, Palermo , herausgegeben von M Anile, V Capasso und A Greco. Berlin: Springer.
- Karlsen, KH, und Ohlberger, M. . „A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.“ J. Math. Anal. Appl. 275: 439–458.
- Maurer, H, und Oberle, HJ. . „Second order sufficient conditions for optimal control problems with free final time: the Riccati approach.“ SIAM Journal on Control and Optimization 41 (2): 380–403. doi: 10.1137/S0363012900377419.
- Burger, M, und Mühlhuber, W. . „Numerical approximation of an SQP-type method for parameter identification.“ SIAM Journal on Numerical Analysis 40 (5): 1775–1797. doi: 10.1137/S0036142901389980.
- Haslinger, J, Bodenhofer, U, und Burger, M. . „Tuning of fuzzy systems as an ill-posed problem.“ Beitrag präsentiert auf der ECMI 2000, Palermo , herausgegeben von M Anile, V Capasso und A Greco. Berlin: Springer.
- Dreyer, W, Herrmann, M, und Kunik, M. . „Kinetic schemes and initial boundary value problems for the Euler system.“ Transport Theory and Statistical Physics 31 (1): 1–33. doi: 10.1081/TT-120003009.
- Lutscher, Frithjof, und Stevens, Angela. . „Emerging patterns in a hyperbolic model for locally interacting cell systems.“ Journal of Nonlinear Science 12 (6): 619–640. doi: 10.1007/s00332-002-0510-4.
- Burger, M. . „A level set method for inverse problems.“ Inverse Problems 17: 1327–1356.
- Ohlberger, M. . „A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations.“ Numerische Mathematik 87 (4): 737–761.
- Ohlberger, M. . A posteriori error estimates and adaptive methods for convection dominated transport processes
- Burger, M, und Neubauer, A. . „Error bounds for approximation with neural networks.“ J. Approx. Theory 112: 235–250.
- Haasdonk, B, Ohlberger, M, Rumpf, M, Schmidt, A, und Siebert, K. . „h-p-Multiresolution Visualization of Adaptive Finite Element Simulations.“
- Burger, M, Engl, H, Markowich, P, und Pietra, P. . „Identification of doping profiles in semiconductor device.“ Inverse Problems 17: 1765–1795.
- Burger, M. . „Iterative regularization of a parameter identification problem occurring in polymer crystallization.“ SIAM J. Numer. Anal. 39 (SIAM J. Numer. Anal.): 1029–1054.
- Burger, M, und Capasso, V. . „Mathematical modelling and simulation of non-isothermal crystallization of polymers.“ Math. Models and Methods in Appl. Sciences 11: 1029–1054.
- Burger, M, und Scherzer, O. . „Regularization methods for blind deconvolution and blind source separation problems.“ Mathematics of Control, Signals and Systems 14: 358–383.
- Ohlberger, M. . „A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations.“ M2AN Math. Model. Numer. Anal. 35: 355–387.
- Augustin, D, und Maurer, H. . „Second order sufficient conditions and sensitivity analysis for the optimal control of a container crane under state constraints.“ Optimization 49 (4): 351–368. doi: 10.1080/02331930108844537.
- Büskens, C, und Maurer, H. . „Real-time control of an industrial robot under control and state constraints.“ In Online optimization of large scale systems Berlin: Springer VDI Verlag.
- Büskens, C, und Maurer, H. . „*Sensitivity analysis and real-time control of parametric optimal control problems using nonlinear programming methods.“ In Online optimization of large scale systems Berlin: Springer VDI Verlag.
- Maurer, H, und Augustin, D. . „*Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods.“ In Online optimization of large scale systems Berlin: Springer VDI Verlag.
- Büskens, C, und Maurer, H. . „*Sensitivity analysis and real-time optimization of parametric nonlinear programming problems.“ In Online optimization of large scale systems Berlin: Springer VDI Verlag.
- Augustin, D, und Maurer, H. . „Sensitivity analysis and real-time control of a container crane under state constraints.“ In Online optimization of large scale systems Berlin: Springer VDI Verlag.
- Augustin, D, und Maurer, H. . „Computational sensitivity analysis for state constrained optimal control problems.“ Annals of Operations Research 101: 75–99. doi: 10.1023/A:1010960221295.
- Malanowski, K, und Maurer, H. . „Sensitivity analysis for optimal control problems subject to higher order state constraints.“ Annals of Operations Research 101: 43–73. doi: 10.1023/A:1010956104457.
- Maurer, H, und Mittelmann, HD. . „Optimization techniques for solving elliptic control problems with control and state constraints. {II}. Distributed control.“ Computational Optimization and Applications 18 (2): 141–160. doi: 10.1023/A:1008774521095.
- Micheletti, A, und Burger, M. . „Stochastic and deterministic simulation of nonisothermal crystallization of polymers.“ Journal of Mathematical Chemistry 30 (2): 169–193. doi: 10.1023/A:1017923703579.
- Natterer, F, und Wübbeling, F. . SIAM Monographs on Mathematical Modeling and Computation, Bd. 5, Mathematical methods in image reconstruction Philadelphia, PA: Selbstverlag / Eigenverlag. doi: 10.1118/1.1455744.
- Heinze, Steffen, Papanicolaou, George, und Stevens, Angela. . „Variational principles for propagation speeds in inhomogeneous media.“ SIAM Journal on Applied Mathematics 62 (1): 129–148. doi: 10.1137/s0036139999361148.
- Stevens, Angela. . „The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems.“ SIAM Journal on Applied Mathematics 61 (1): 183–212. doi: 10.1137/S0036139998342065.
- Burger, M, und Engl, H. . „Training neural networks with noisy data as an ill-posed problem.“ Adv. Comp. Math 13 (Adv. Comp. Math): 335–354.
- Kröner, D, und Ohlberger, M. . „A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multidimensions.“ Math. Comp. 69: 25–39.
- Büskens, C, und Maurer, H. . „Nonlinear programming methods for real-time control of an industrial robot.“ Journal of Optimization Theory and Applications 107 (3): 505–527. doi: 10.1023/A:1026491014283.
- Augustin, D, und Maurer, H. . „An example for computational sensitivity analysis of state constrained control problems.“ In Parametric optimization and related topics, V (Tokyo, 1997) Frankfurt am Main: Peter Lang.
- Augustin, D, und Maurer, H. . „Computational sensitivity analysis of state constrained control problems.“ In Optimization, dynamics, and economic analysis Heidelberg: Physica-Verlag.
- Mittelmann, HD, und Maurer, H. . „Solving elliptic control problems with interior point and {SQP} methods: control and state constraints.“ Journal of Computational and Applied Mathematics 120 (1-2): 175–195. doi: 10.1016/S0377-0427(00)00309-5.
- Büskens, C, und Maurer, H. . „S{QP}-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control.“ Journal of Computational and Applied Mathematics 120 (1-2): 85–108. doi: 10.1016/S0377-0427(00)00305-8.
- Büskens, C, und Maurer, H. . „Real-time control of robots with initial value perturbations via nonlinear programming methods.“ Optimization 47 (3-4): 383–405. doi: 10.1080/02331930008844488.
- Augustin, D, und Maurer, H. . „Second order sufficient conditions and sensitivity analysis for optimal multiprocess control problems.“ Control and Cybernetics 29 (1): 11–31.
- Maurer, H, und Mittelmann, HD. . „Optimization techniques for solving elliptic control problems with control and state constraints. I. Boundary control.“ Computational Optimization and Applications 16 (1): 29–55. doi: 10.1023/A:1008725519350.
- Stevens, Angela. . „A stochastic cellular automaton modeling gliding and aggregation of myxobacteria.“ SIAM Journal on Applied Mathematics 61 (1): 72–182. doi: 10.1137/S0036139998342053.
- Hillen, Thomas, und Stevens, Angela. . „Hyperbolic models for chemotaxis in 1-D.“ Nonlinear Analysis: Real World Applications 1 (3): 409–433. doi: 10.1016/S0362-546X(99)00284-9.
- Geßner, T, Haasdonk, B, Kende, R, Lenz, M, Metscher, M, Neubauer, R, Ohlberger, M, Rosenbaum, W, Rumpf, M, Schwörer, R, Spielberg, M, und Weikard, U. . „A Procedural Interface for Multiresolutional Visualization of General Numerical Data.“
- Ohlberger, M. . „Adaptive mesh refinement for single and two phase flow problems in porous media.“
- Ohlberger, M, und Rumpf, M. . „Adaptive protection operators in multiresolution scientific visualizations.“ IEEE Transactions on Visualization and Computer Graphics 5 (1): 74–94.
- Burger, M, Capasso, V, und Engl, H. . „Inverse problems related to crystallization of polymers.“ Inverse Problems 15 (Inverse Problems): 155–173.
- Ohlberger, M. . „Mixed finite element-finte volume methods for two-phase flow in porous media.“
- Burger, M, Capasso, V, Eder, G, und Engl, H. . „Modelling and parameter-identification in non-isothermal crystallization of polymers.“ Beitrag präsentiert auf der EcMI 98, Gothenburg , herausgegeben von L Arkeryd, J Bergh, P Brenner und R Pettersson. Stuttgart: B. G. Teubner Verlag.
- Grüne, L, Metscher, M, und Ohlberger, M. . „On numerical algorithm and interactive visualization for optimal control problems.“ Comp. Visual. Sci. 1 (4): 221–229.
- Maurer, H. . „Sufficient conditions and sensitivity analysis for economic control problems.“ Annals of Operations Research 88: 3–14. doi: 10.1023/A:1018942732605.
- Ohlberger, M, und Schwörer, R. . Challenges in Fluid Dynamics
- Sonoc, C. . „On the Pathwise Uniqueness of Solutions of Stochastic Differential Equations.“ Portugaliae Mathematica 55: 451–456.
- Büskens, C, und Maurer, H. . „Sensitivity analysis and real-time control of nonlinear optimal control systems via nonlinear programming methods.“ In Variational calculus, optimal control and applications (Trassenheide, 1996), Internat. Ser. Numer. Math. Basel: Birkhäuser Verlag.
- Maurer, H, Büskens, C, und Feichtinger, G. . „Solution techniques for periodic control problems: a case study in production planning.“ Optimal Control Applications and Methods 19 (3): 185–203. doi: 10.1002/(SICI)1099-1514(199805/06)19:3<185::AID-OCA627>3.0.CO;2-E.
- Malanowski, K, und Maurer, H. . „Sensitivity analysis for state constrained optimal control problems.“ Discrete and Continuous Dynamical Systems - Series A 4 (2): 241–272.
- Malanowski, K, Büskens, C, und Maurer, H. . „Convergence of approximations to nonlinear optimal control problems.“ In Mathematical programming with data perturbations, Lecture Notes in Pure and Appl. Math. New York: Marcel Dekker Verlag.
- Ohlberger, M. . „Convergence of a mixed finite element-finite volume method for the two phase flow in porous media.“ East-West journal of numerical mathematics 5 (3): 183–210.
- Neubauer, R, Ohlberger, M, Rumpf, M, und Schwörer, R. . „Efficient visualization of large-scale data on hierarchical meshes.“
- Ohlberger, M, und Rumpf, M. . „Hierarchical and adaptive visualization on nested grids.“ Computing 59 (Computing): 365–385.
- Sonoc, C. . „The Cauchy Problem for Seismic Wave Propagation.“ Analele Univ. de Vest din Timisoara, Seria Matematica/Informatica XXXV: 299–305.
- Othmer, Hans G., und Stevens, Angela. . „Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks.“ SIAM Journal on Applied Mathematics 57 (4): 1044–1081. doi: 10.1137/s0036139995288976.
- Stevens, Angela, und Schweitzer, Frank. . „Aggregation induced by diffusing and non-diffusing media.“ In Dynamics of Cell and Tissue Motion. Mathematics and Biosciences in Interaction., Mathematics and Biosciences in Interaction (MBI), herausgegeben von Wolfgang Alt, Andreas Deutsch und Graham Dunn. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-0348-8916-2_22.
- Stevens, Angela. . „Simulation of chemotaxis-equations in two space dimensions.“ In Nonlinear Physics of Complex Systems - Current Status and Future Trends, Bd. 476 aus Lecture Notes in Physics, herausgegeben von Jürgen Parisi, Stefan C. Müller und Walter Zimmermann. Berlin, Heidelberg: Springer. doi: 10.1007/BFb0105453.
- Natterer, F, und Wübbeling, F. . „A propagation-backpropagation method for ultrasound tomography.“ Inverse Problems 11 (6): 1225–1232. doi: 10.1088/0266-5611/11/6/007.
- Stevens, Angela. . „Trail Following and Aggregation of Myxobacteria.“ Journal of Biological Systems 3 (4): 1059–1068. doi: 10.1142/S0218339095000952.
- Natterer, F, und Wübbeling, F. . „A finite difference method for the inverse scattering problem at fixed frequency.“ In Inverse problems in mathematical physics (Saariselkä, 1992), Lecture Notes in Phys. Berlin: Springer VDI Verlag. doi: 10.1007/3-540-57195-7_18.
- Stevens, Angela. . „Aggregation of Myxobacteria - a many particle system.“ In Proceedings 1st European Conference on the Applications of Mathematics to Medicine & Biology (1990) , herausgegeben von Jacques Demongeot und Vincenzo Capasso. Winipeg: Wuerz Publishing Ltd.
- Stevens, Angela. . „A model for gliding and aggregation of Myxobacteria.“ In Nonlinear wave processes in excitable media, Bd. 244 aus NATO ASI Series, herausgegeben von Arun V. Holden, Mario Markus und Hans G. Othmer. Boston, MA: Springer Science+Business Media. doi: 10.1007/978-1-4899-3683-7_25.
- Stevens, Angela. . „Simulations of the aggregation and gliding behavior of Myxobacteria.“ In Biological motion, Bd. 89 aus Lecture Notes in Biomathematics, herausgegeben von Wolfgang Alt und Gerhard Hoffmann. Berlin / Heidelberg: Springer. doi: 10.1007/978-3-642-51664-1_36.
- Lempio, F, und Maurer, H. . „Differential stability in infinite-dimensional nonlinear programming.“ Applied Mathematics and Optimization 6 (2): 139–152. doi: 10.1007/BF01442889.
- Maurer, H. . „Differential stability in optimal control problems.“ Applied Mathematics and Optimization 5 (4): 283–295. doi: 10.1007/BF01442559.
- Maurer, H, und Zowe, J. . „First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems.“ Mathematical Programming 16 (1): 98–110. doi: 10.1007/BF01582096.
- Zowe, J, und Maurer, H. . „Optimality conditions for the programming problem in infinite dimensions.“ In Optimization and operations research (Proc. Workshop, Univ. Bonn, Bonn, 1977), Lecture Notes in Econom. and Math. Systems Berlin: Springer VDI Verlag.
- Lempio, F, und Maurer, H. . „Differentiable perturbations of infinite optimization problems.“ In Optimization and operations research (Proc. Workshop, Univ. Bonn, Bonn, 1977), Lecture Notes in Econom. and Math. Systems Berlin: Springer VDI Verlag.
- Maurer, H, und Zowe, J. . „Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems.“ In Optimization techniques (Proc. 8th {IFIP} Conf., Würzburg, 1977), Part 2 Berlin: Springer VDI Verlag. doi: 10.1007/BFb0006504.
- Maurer, H. . „On optimal control problems with bounded state variables and control appearing linearly.“ SIAM Journal on Control and Optimization 15 (3): 345–362. doi: 10.1137/0315023.
- Maurer, H. . „Numerical solution of singular control problems using multiple shooting techniques.“ Journal of Optimization Theory and Applications 18 (2): 235–257. doi: 10.1007/BF00935706.
- Maurer, H, und Heidemann, U. . „Optimale Steuerprozesse mit Zustandsbeschränkungen.“ In Optimization and optimal control (Proc. Conf., Oberwolfach, 1974) Berlin: Springer VDI Verlag.
- Maurer, H, und Gillessen, W. . „Application of multiple shooting to the numerical solution of optimal control problems with bounded state variables.“ Computing 15 (2): 105–126. doi: 10.1007/BF02252860.
- Maurer, H. . „An example of a continuous junction for a singular control problem of even order.“ SIAM Journal on Control and Optimization 13: 899–903. doi: 10.1137/0313055.