Research
Research Foci
- Numerical analysis for partial differential equations
- Error control and adaptivity for finite element and finite volume schemes
- Model reduction for parametrized partial differential equations
- Development and analysis of numerical multiscale methods
- Software development and scientific computing
Projects
In Process
- MaRDI – Mathematical Research Data Initiative - TA2: Scientific Computing ( – )
Subproject in DFG-Joint Project Hosted outside the University of Münster: DFG - National Research Data Infrastructure | Project Number: NFDI 29 /1 - EXC 2044 – Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure ( – )
Main DFG-Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C2: Multi-scale phenomena and macroscopic structures ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C4: Geometry-based modelling, approximation, and reduction ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
Finished
- ML-MORE – ML-MORE: Machine learning and model order reduction to predict the efficiency of catalytic filters. Subproject 1: Model Order Reduction ( – )
participations in bmbf-joint project: Federal Ministry of Education and Research | Project Number: 05M20PMA - LRB-Opt – Localized Reduced Basis Methods for PDE-constrained Parameter Optimization ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: OH 98/11-1; SCHI 1493/1-1 - pyMOR – pyMOR - Sustainable Software for Model Order Reduction ( – )
Individual Granted Project: DFG - Scientific Library Services and Information Systems | Project Number: RA 3055/1-1 - MALLi2 – Modellbasierte Abschätzung der Lebensdauer von gealterten Li-Batterien für die 2nd Life Anwendung als stationärer Stromspeicher ( – )
participations in bmbf-joint project: Federal Ministry of Education and Research | Project Number: 05M18PMA - GlioMaTh – Verbundprojekt 05M2016 - GlioMaTh: Gliomen, Mathematische Modelle und Therapieansätze - Teilprojekt 2 ( – )
participations in bmbf-joint project: Federal Ministry of Education and Research | Project Number: 05M16PMA - EXC 1003 A6 - Motion Analysis in Cellular Systems ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC1003/1 - EXA-DUNE – SPP 1648 - Subproject: EXA-DUNE - Flexible PDE Solvers, Numerical Methods, and Applications ( – )
Subproject in DFG-Joint Project Hosted outside the University of Münster: DFG - Priority Programme | Project Number: EN 1042/2-2; OH 98/5-2 - Wave propagation in periodic structures and negative refraction mechanisms ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: OH 98/6-1 - EXC 1003 FF-2015-07 - Mechanobiology, Mathematical Modeling and Simulation of Forces During Tissue Morphogenesis ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence - Derivation, analysis and validation of model reduction methods for the approximation of parameterized Maxwell equations ( – )
Individual Granted Project: CST AG - CRC 656 B07 - Mathematical Modelling of Atherosclerotic Plaque Formation Based on Data from Multiparametric Imaging ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre - MULTIBAT – Verbundprojekt 05M2013 - MULTIBAT: Multiskalenmodelle und Modellreduktionsverfahren zur Vorhersage der Lebensdauer von Lithium-Ionen-Batterien - Teilprojekt 1 ( – )
participations in bmbf-joint project: Federal Ministry of Education and Research | Project Number: 05M13PMA - EXA-DUNE – SPP 1648: Software for Exascale Computing - Subproject: EXA-DUNE - Flexible PDE Solvers, Numerical Methods, and Applications ( – )
Subproject in DFG-Joint Project Hosted outside the University of Münster: DFG - Priority Programme | Project Number: EN 1042/2-1; OH 98/5-1 - Multi-scale analysis of two-phase flow in porous media with complex heterogenities ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: OH 98/4-2 - Reduced basis methods for model reduction of nonlinear parameterized evolution equations ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: OH 98/2-2 - Multi-scale – Multi-scale analysis of two-phase flow in porous media with complex heterogeneities ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: 568656 - SFB 656 PM09 – CRC 656 PM09 - Modeling of blood flow for a arteriosclerosis model ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre - RBevol – Reduced basis methods for model reduction of nonlinear parameterized evolution equations ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: OH 98/2-1 - AdaptHydroMod – Co-operative Project "Adaptive hydrological modeling with application in water resource management", Sub-project "Multi-scale modelling and system reduction for ground water flow" ( – )
participations in bmbf-joint project: Federal Ministry of Education and Research | Project Number: 03OMPAF1
- MaRDI – Mathematical Research Data Initiative - TA2: Scientific Computing ( – )
Publications
- Wenzel, Tizian, Haasdonk, Bernard, Kleikamp, Hendrik, Ohlberger, Mario, and Schindler, Felix. . “Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.” in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I. Lirkov and S. Margenov. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- Keil, Tim, Ohlberger, Mario, and Schindler, Felix. . “Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.” in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I Lirkov and S Margenov. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Biedinger, Christine, Fiedler, Jochen, Reidelbach, Marco, Shehu, Aurela, Schmidt, Burkhard, Koprucki, Thomas, Iglezakis, Dorothea, and 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, Vol. 2048 of Communications in Computer and Information Science, edited by Emmanouel Garoufallou and Fabio Sartori. Heidelberg: Springer. doi: 10.1007/978-3-031-65990-4_14.
- Singh, A, Thale, S, Leibner, T, Lamparter, L, Ricker, A, Nüsse, H, Klingauf, J, Galic, M, Ohlberger, M, and 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 , and Felix Schindler, Julia . . “Local training and enrichment based on a residual localization strategy.” in Proceedings of the Conference Algoritmy 2024, Vol. 8 of Proceedings of the Conference Algoritmy, edited by P Frolkovič, K Mikula and D Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Schmidt, Burkhard, Shehu, Aurela, Reidelbach, Marco, Biedinger, Christine, Fiedler, Jochen, Koprucki, Thomas, Iglezakis, Dorothea, and Göddeke, Dominik. Forthcoming. “Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics.” in Proceedings of the 18th International Conference on Metadata and Semantics Research 2024 Heidelberg: Springer.
- Kleikamp, Hendrik, and Ohlberger, Mario. . “Adaptive Model Hierarchies for Multi-Query Scenarios.” arXiv doi: 10.48550/arXiv.2411.17252.
- Engwer, Christian, Ohlberger, Mario, and 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.
- Kleikamp, Hendrik, and Wenzel, Tizian. . “Kernel Methods in the Deep Ritz framework: Theory and practice.” arXiv doi: 10.48550/arXiv.2410.03503.
- Kartmann, Michael, Keil, Tim, Ohlberger, Mario, Volkwein, Stephan, and 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, and Renelt, Lukas. . “Construction of local reduced spaces for Friedrichs' systems via randomized training.” contribution to the Central-European Conference on Scientific Computing, ALGORITMY, Podbanské
- Gander, Martin J, Ohlberger, Mario, and Rave, Stephan. . “A Parareal algorithm without Coarse Propagator?” arXiv doi: 10.48550/arXiv.2409.02673.
- Kleikamp, Hendrik, and Renelt, Lukas. . “Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems.” arXiv doi: 10.48550/arXiv.2408.15900.
- Kleikamp, Hendrik. . “Application of an adaptive model hierarchy to parametrized optimal control problems.” in
- Keil Tim, Ohlberger . . “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.
- Landstorfer, M, Ohlberger, M, Rave, S, and 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.
- Ohlberger, M., Banholzer, S., Haasdonk, B., Keil, T., Mechelli, L., Oguntola, M, Schindler F., Volkwein, S., and Wenzel, T. . “Model Reduction and Learning for PDE Constrained Optimization.” contribution to the Oberwolfach Workshop on Optimization Problems for PDEs in Weak Space-Time Form, Oberwolfach doi: 10.4171/OWR/2023/13.
- Schleuß, Julia, Smetana, Kathrin, and Maat, Lukas . . “Randomized quasi-optimal local approximation spaces in time.” SIAM Journal on Scientific Computing, № 45 (3) doi: 10.1137/22M1481002.
- Julia Schleuß, Kathrin . . “DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions.” arXiv doi: 10.48550/arXiv.2302.00348.
- Himpe, Christian, and Grundel, sara. . “System Order Reduction for Gas and Energy Networks.” contribution to the 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Aachen doi: 10.1002/pamm.202200201.
- Renelt, Lukas, Ohlberger, Mario, and Engwer, Christian. . “An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.” in Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, Springer Proceedings in Mathematics & Statistics, edited by Emmanuel Franck, Jürgen Fuhrmann, Michel-Dansac and Laurent Navoret. Heidelberg: Springer. doi: 10.1007/978-3-031-40860-1_30.
- Kleikamp, Hendrik, Lazar, Martin, and Molinari, Cesare. Forthcoming. “Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems.” arXiv doi: 10.48550/arXiv.2307.15590.
- Haasdonk, B, Kleikamp, H, Ohlberger, M, Schindler, F, and 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.
- Gavrilenko Pavel, Haasdonk , Iliev Oleg, Ohlberger , Schindler Felix, Toktaliev , and Wenzel Tizian, Youssef . . “A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows.” in Large-Scale Scientific Computing, Vol. 13127 of Lecture Notes in Computer Science (LNCS), edited by Margenov Lirkov Ivan. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-030-97549-4_43.
- Keil Tim, Ohlberger . . “Model Reduction for Large Scale Systems.” in Large-Scale Scientific Computing, Vol. 13127 of Lecture Notes in Computer Science (LNCS), edited by Margenov Lirkov Ivan. Basel: Springer International Publishing. doi: 10.1007/978-3-030-97549-4_2.
- Gander Martin, Rave . . “Localized Reduced Basis Additive Schwarz Methods.” in Domain Decomposition Methods in Science and Engineering XXVI, edited by Susanne Brenner, Eric Chung, Axel Klawonn, Felix Kwok, Jinchao Xu and Jun Zou. Basel: Springer International Publishing. doi: 10.1007/978-3-030-95025-5_52.
- Banholzer, S, Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, and 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.
- Fokina, D, Iliev, O, Toktaliev, P, Oseledets, I, and 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.
- Hendrik, Kleikamp, Mario, Ohlberger, and Stephan, Rave. . “Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain.” in MATHMOD 2022 - Discussion Contribution Volume, Vol. 17 of ARGESIM Report, edited by Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi and 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, and 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, and Benner, P. . “Efficient Gas Network Simulations.” in German Success Stories in Industrial Mathematics, Vol. 35 of Mathematics in Industry, edited by HG Bock, KH Küfer, P Maass, A Milde and V Schulz. doi: 10.1007/978-3-030-81455-7_4.
- Haasdonk, B, Ohlberger, M, and Schindler, F. . “An adaptive model hierarchy for data-augmented training of kernel models for reactive flow.” in MATHMOD 2022 Discussion Contribution Volume, edited by Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi and Inge Troch. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17155.
- Benner, P., Burger, M., Göddeke, D., Himpe, C., Hintermüller, M., Heiland, J., Koprucki, T., Ohlberger, M., Rave, S., Reidelbach, M., Saak, J., Schöbel, A., and Tabelow, K. . “Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative).” GAMM Rundbrief, № 1/2022: 40–43.
- Singh, A, Thale, S, Leibner, T, Ricker, A, Nüsse, H, Klingauf, J, Ohlberger, M, and Matis, M. . “Dynamic interplay of protrusive microtubule and contractile actomyosin forces drives tissue extension.” eLife, № 2022 doi: 10.1101/2022.06.21.496930.
- Julia Schleuß, Kathrin . . “Optimal local approximation spaces for parabolic problems.” Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, № 20 (1) doi: 10.1137/20M1384294.
- Fritze, René, and Rave, Stephan. . “Specification and Validation of Numerical Algorithms with the Gradual Contracts Pattern.” in Testing Software and Systems, Lecture Notes in Computer Science, edited by David Clark, Hector Menendez and Ana Cavalli. Basel: Springer International Publishing.
- Himpe, Christian, Grundel, Sara, and Benner, Peter. . “Next-Gen Gas Network Simulation.” in Progress in Industrial Mathematics at ECMI 2021, Vol. 39 of Mathematics in Industry, edited by Matthias Ehrhardt and Michael Günther. Heidelberg: Springer. doi: 10.1007/978-3-031-11818-0_15.
- Keil, T, Kleikamp, H, Lorentzen, R, Oguntola, M, and 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.
- Leibner Tobias. . “Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition.” Dissertation thesis, Universität Münster.
- Bastian, P, Blatt, M, Dedner, A, Dreier, N, Engwer, C, Fritze, R, Gräser, C, Kempf, D, Klöfkorn, R, Ohlberger, M, and 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.
- Buhr Andreas, Iapichino , Ohlberger Mario, Rave , and Schindler Felix, Smetana . . “Localized model reduction for parameterized problems.” in Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by P Benner, S Grivet-Talocia, A Quarteroni, G Rozza, W Schilders and L Sileira. doi: 10.1515/9783110671490-006.
- Fehr, J, Himpe, C, Rave, S, and Saak, J. . “Sustainable Research Software Hand-Over.” Journal of Open Research Software, № 9 (1) doi: 10.5334/jors.307/.
- Leibner, T, and 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.
- Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, and 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.
- Leibner, T, Matis, M, Ohlberger, M, and Rave, S. . “Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD.” arXiv [math.NA], № 2111.00129
- Himpe, C. . “Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms.” in Model Reduction of Complex Dynamical Systems, Vol. 171 of International Series of Numerical Mathematics, edited by P Benner, T Breiten, H Faßbender, M Hinze, T Stykel and R Zimmermann. doi: 10.1007/978-3-030-72983-7_7.
- Himpe, C, Grundel, S, and 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, and Wirsen, A. . “MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.” in Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, Vol. 34 of Mathematics in Industry, edited by S Göttlich, M Herty and A Milde. doi: 10.1007/978-3-030-62732-4_11.
- Brunken, Julia. . “Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations.” Dissertation thesis, Universität Münster.
- 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, and Turek, S. . “Exa-Dune -- Flexible PDE Solvers, Numerical Methods and Applications.” in Software for Exascale Computing - SPPEXA 2016-2019, Vol. 136 of LNCSE, edited by Reiz Bungartz Hans-Joachim and Nagel Neumann Philipp. Basel: Springer International Publishing. doi: 10.1007/978-3-030-47956-5_9.
- Ohlberger Mario, Schweizer , and Urban Maik, Verfürth . . “Mathematical analysis of transmission properties of electromagnetic meta-materials.” Networks and Heterogeneous Media, № 15 (1): 29–56. doi: 10.3934/nhm.2020002.
- Brunken Julia Smetana Kathrin. . “Stable and efficient Petrov-Galerkin methods for a kinetic Fokker-Planck equation.” arXiv, № 2020
- Buchfink, P, Haasdonk, B, and Rave, S. . “PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems.” contribution to the ALGORITMY 2020, Vysoké Tatry
- 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, and 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.
- Bansal, H, Rave, S, Iapichino, L, Schilders, WHA, and van de, Wouw N. . “Model order reduction framework for problems with moving discontinuities.” contribution to the Proceedings of ENUMATH 2019, Egmond aan Zee
- Rave, S, and Saak, J. Forthcoming. “A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction.” contribution to the ENUMATH 2019, Graz Heidelberg: Springer.
- Mlinarić, P, Rave, S, and Saak, J. Forthcoming. “Parametric model order reduction using pyMOR.” contribution to the MODRED 2019, Graz Heidelberg: Springer.
- Schneider Florian, Leibner . . “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.
- Fredrik, Hellman, Tim, Keil, and Axel, Målqvist. . “Numerical Upscaling of Perturbed Diffusion Problems.” SIAM Journal on Scientific Computing, № 2020 (Volume 42, Issue 4): A2014–A2036. doi: 10.1137/19M1278211.
- Lehrenfeld Christoph, Rave . . “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.
- Julia, Brunken, Kathrin, Smetana, and Karsten, Urban. . “(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods.” SIAM Journal on Scientific Computing, № 41 (1) doi: 10.1137/18M1176269.
- Hain, S, Ohlberger, M, Radic, M, and 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.
- Balicki, L, Mlinarić, P, Rave, S, and Saak, J. . “System-theoretic model order reduction with pyMOR.” PAMM, № 19 doi: 10.1002/pamm.201900459.
- Ohlberger, M, Buhr, A, Eikhorn, D, Engwer, C, and 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.
- Fredrik, Hellman, Tim, Keil, and Axel, Målqvist. . “Multiscale methods for perturbed diffusion problems.” Oberwolfach Reports, № 16: 2099–2181. doi: 10.4171/OWR/2019/35.
- Julia Schleuß. . Master's thesis, Optimal local approximation spaces for parabolic problems (Master's thesis),
- Rave Stephan, Schindler . . “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), Vol. 19 , edited by J Eberhardsteiner and M Schöberl. New York City: John Wiley & Sons. doi: 10.1002/pamm.201900026.
- Schneider Florian, Leibner . . “First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis.” arXiv, № 2019
- Benner, P, and 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, and Saak, J. . “On Empirical System Gramians.” in Vol. 19 of Proceedings in Applied Mathematics and Mechanics (PAMM) doi: 10.1002/pamm.201900006.
- Feinauer, J, Hein, S, Rave, S, Schmidt, S, Westhoff, D, Zausch, J, Iliev, O, Latz, A, Ohlberger, M, and 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.
- Verfürth, B. . “Numerical multiscale methods for Maxwell's equations in heterogeneous media.” Dissertation thesis, Universität Münster.
- Dennis Eickhorn. . Randomisierte lokalisierte Modellreduktion mit Robin-Transferoperator (Masterarbeit),
- Ohlberger Mario, Rave , and Schindler Felix, Wedemeier . . “Model reduction for parameterized systems and inverse problems.” Oberwolfach Reports, № 2018 (39): 2454–2457. doi: 10.4171/OWR/2018/39.
- Benner, P, Himpe, C, and 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, and Tischendorf, C. . “Gas Network Benchmark Models.” in Applications of Differential-Algebraic Equations: Examples and Benchmarks, Differential-Algebraic Equations Forum, edited by S Campbell, A Ilchmann, V Mehrmann and 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, and Himpe, C. . “Parametric Model Order Reduction for Gas Flow Models.” in Vol. MoRePaS 4 of ScienceOpen Posters ScienceOpen. doi: 10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1.
- Himpe, C, Leibner, T, and Rave, S. . “HAPOD - Fast, Simple and Reliable Distributed POD Computation.” in Vol. 55 of ARGESIM Report doi: 10.11128/arep.55.a55283.
- Kottke, Kathrin, Deninger, Christopher, and Ohlberger, Mario. . “Mathematik Münster: Dynamik – Geometrie – Struktur.” Mitteilungen der Deutschen Mathematiker-Vereinigung, № 26 (4): 189–193. doi: 10.1515/dmvm-2018-0058.
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- Henning, P, and 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.
- Ohlberger, M, and 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, edited by Aubry D. et al. Barcelona: CIMNE.
- Drohmann, M, Haasdonk, B, and Ohlberger, M. . “Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations.” in Finite Volumes for Complex Applications VI - Problems & Perspectives, Vol. 4 (1) of Springer Proceedings in Mathematics, edited by Fort J. et al. Heidelberg: Springer. doi: 10.1007/978-3-642-20671-9_39.
- Haasdonk, B, and 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, and Ohlberger, M. . “Inflow-Implicit/Outflow-Explicit scheme for solving advection equations.” in Finite Volumes for Complex Applications VI - Problems & Perspectives, Vol. 4(1) of Springer Proceedings in Mathematics, edited by Fort J. et al. Heidelberg: Springer. doi: 10.1007/978-3-642-20671-9_72.
- Lehrenfeld Christoph. . “Nitsche-XFEM for a Transport Problem in Two- Phase Incompressible Flows.” in Proc. Appl. Math. Mech., Vol. 11 New York City: John Wiley & Sons. doi: 10.1002/pamm.201110296.
- Dedner, A, Klöfkorn, R, Nolte, M, and 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.
- Mikula, K, and 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.
- Henning, P, and 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.
- Mikula, K, and Ohlberger, M. . “A New Inflow-Implicit/Outflow-Explicit Finite Volume Method for Solving Variable Velocity Advection Equations.”
- Ohlberger, M, and Smetana, K. . “A new problem adapted hierarchical model reduction technique based on reduced basis methods and dimensional splitting.”
- Drohmann, M, Haasdonk, B, and Ohlberger, M. . “Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation.”
- Lehrenfeld Christoph. . Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems,
- 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, and 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.”
- Haasdonk, B, and Ohlberger, M. . “Efficient reduced models for parametrized dynamical systems by offline/online decomposition.”
- Albrecht, F. . Local Discontinuous Galerkin Verfahren für die Stokes Gleichungen und Homogenisierung in porösen Medien (Diplomarbeit),
- Drohmann, M, Haasdonk, B, and Ohlberger, M. . “Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries.” contribution to the Proceedings of ALGORITMY 2009
- Haasdonk, B, and Ohlberger, M. . “Space-adaptive reduced basis simulation for time-dependent problems.”
- Haasdonk, B, and Ohlberger, M. . “Reduced Basis Method for Explicit Finite Volume Approximations of Nonlinear Conservation Laws.” in Hyperbolic problems: theory, numerics and applications, Vol. 67 of Proc. Sympos. Appl. Math. Providence, RI: American Mathematical Society.
- Henning, P, and 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.
- Goldsmith, F, Ohlberger, M, Schumacher, J, Steinkamp, K, and 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.
- Haasdonk, B, and Ohlberger, M. . “Adaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes.” contribution to the Finite Volumes for Complex Applications VI Problems & Perspectives: FVCA 6, Prague
- Klöfkorn, R, Kröner, D, and Ohlberger, M. . “Parallel adaptive simulation of PEM fuel cells.” in Mathematics – Key Technology for the Future, edited by Jäger Krebs.
- Haasdonk, B, and 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.
- Haasdonk, B, Ohlberger, M, and Rozza, G. . “A reduced basis method for evolution schemes with parameter-dependent explicit operators.” Electronic transactions on numerical analysis, № 32: 145–161.
- Dedner, A, and Ohlberger, M. . “A new $hp$-adaptive DG scheme for conservation laws based on error control.” in Hyperbolic Problems: Theory, Numerics, Applications, edited by Serre Benzoni-Gavage. Berlin. doi: 10.1007/978-3-540-75712-2_15.
- Haasdonk, B, Ohlberger, M, and 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, and Ohlberger, M. . “Parallel and adaptive simulation of fuel cells in 3d.” in Computational science and high performance computing III, Vol. 101 of Notes Numer. Fluid Mech. Multidiscip. Des. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-540-69010-8_7.
- Haasdonk, B, and Ohlberger, M. . “Basis Construction for Reduced Basis Methods by Adaptive Parameter Grids.”
- Henning, P. . Die Heterogene Mehrskalenmethode f\�r elliptische Differentialgleichungen in perforierten Gebieten,
- Fuhrmann, J, Haasdonk, B, Holzbecher, E, and 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)
- Klöfkorn, R, Kröner, D, and Ohlberger, M. . “Parallel and adaptive simulaiton of fuel cells in 3D.”
- Dedner, A, Makridakis, C, and Ohlberger, M. . “Error control for a class of Runge-Kutta discontinuous Galerkin methods for nonlinear conservation laws.” SIAM J. Numer. Anal., № 45: 514–538.
- Ohlberger, M, and Schweizer, B. . “Modelling of interfaces in unsaturated porous media.” Discrete Contin. Dyn. Syst.(Dynamical Systems and Differential Equations. Proceedings of the 6th AIMSInternational Conference, suppl.): 794–803.
- Rave, S. . Über die Entscheidbarkeit gewisser Prädikate in der Theorie der C*-Algebren, Münster.
- Burri, A, Dedner, A, Diehl, D, Klöfkorn, R, and Ohlberger, M. . “A general object oriented framework for discretizing nonlinear evolution equations.”
- Burri, A, Dedner, A, Klöfkorn, R, and Ohlberger, M. . “An efficient implementation of an adaptive and parallel grid in DUNE.”
- Haasdonk, B, and Ohlberger, M. . “Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations.”
- Ohlberger, M, and Vovelle, J. . “Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method.” Math. Comp., № 75: 113–150.
- Dedner, A, Makridakis, C, and 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.
- Ohlberger, M. . “Error control for approximations of non-linear conservation laws.”
- Bastian, P, Droske, M, Engwer, C, Klöfkorn, R, Neubauer, T, Ohlberger, M, and Rumpf, M. . “Towards a unified framework for scientific computing.”
- Ohlberger, M. . “A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems.” Multiscale Model. Simul., № 4: 88–114.
- Barth, T, and Ohlberger, M. . “Finite volume methods: foundation and analysis.”
- 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.
- Kröner, D, Küther, M, Ohlberger, M, and Rohde, C. . “A posteriori error estimates and adaptive methods for hyperbolic and convection dominates parabolic conservation laws.”
- Küther, M, and Ohlberger, M. . “Adaptive second order central schemes on unstructured staggered grids.”
- Haasdonk, B, Ohlberger, M, Rumpf, M, Schmidt, A, and Siebert, K. . “Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations.” Computing, № 70 (Computing): 181–204.
- Herbin, R, and Ohlberger, M. . “A posteriori error estimate for finite volume approximations of convection diffusion problems.”
- Ohlberger, M, and Rohde, C. . “Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems.” IMA J. Numer. Anal., № 22 (2): 253–280.
- Bürkle, D, and Ohlberger, M. . “Adaptive finite volume methods for displacement problems in porous media.” Comp. Vis. Sci., № 5 (2): 95–106.
- Klöfkorn, R, Kröner, D, and Ohlberger, M. . “Local adaptive methods for convection dominated problems.” International Journal for Numerical Methods in Fluids, № 40 (1-2): 79–91.
- Karlsen, KH, and Ohlberger, M. . “A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.” J. Math. Anal. Appl., № 275: 439–458.
- 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,
- Haasdonk, B, Ohlberger, M, Rumpf, M, Schmidt, A, and Siebert, K. . “h-p-Multiresolution Visualization of Adaptive Finite Element Simulations.”
- 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.
- Kröner, D, and Ohlberger, M. . “A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multidimensions.” Math. Comp., № 69: 25–39.
- Geßner, T, Haasdonk, B, Kende, R, Lenz, M, Metscher, M, Neubauer, R, Ohlberger, M, Rosenbaum, W, Rumpf, M, Schwörer, R, Spielberg, M, and 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, and Rumpf, M. . “Adaptive protection operators in multiresolution scientific visualizations.” IEEE Transactions on Visualization and Computer Graphics, № 5 (1): 74–94.
- Ohlberger, M. . “Mixed finite element-finte volume methods for two-phase flow in porous media.”
- Grüne, L, Metscher, M, and Ohlberger, M. . “On numerical algorithm and interactive visualization for optimal control problems.” Comp. Visual. Sci., № 1 (4): 221–229.
- Ohlberger, M, and Schwörer, R. . Challenges in Fluid Dynamics,
- 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, and Schwörer, R. . “Efficient visualization of large-scale data on hierarchical meshes.”
- Ohlberger, M, and Rumpf, M. . “Hierarchical and adaptive visualization on nested grids.” Computing, № 59 (Computing): 365–385.