Research Interests

Research Interests

$\bullet$ Numerical analysis of partial differential equations.
$\bullet$ Error control and adaptivity for finite element, finite volume, and DG methods.
$\bullet$ Model reduction for parametrised evolution equations, Reduced Basis Methods.
$\bullet$ Development and analysis of numerical multiscale methods.
$\bullet$ Software development and scientific computing.
$\bullet$ Complex applications in life sciences, fluid mechanics and environmental sciences.

Selected Publications

Selected Publications of Prof. Dr. Mario Ohlberger

$\bullet$ A. Buhr, C. Engwer, M. Ohlberger, and S. Rave. Arbi Lo Mod, a simulation technique designed for arbitrary local modifications. SIAM J. Numer. Anal., 39(4):A1435–A1465, 2017.

$\bullet$ K. Smetana and M. Ohlberger. Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniques. ESAIM Math. Model. Numer. Anal., 51(2):641–677, 2017.

$\bullet$ P. Henning, M. Ohlberger, and B. Verfürth. A new heterogeneous multiscale method for time-harmonic Maxwell's equations. SIAM J. Numer. Anal., 54(6):3493–3522, 2016.

$\bullet$ M. Ohlberger and F. Schindler. Error control for the localized reduced basis multiscale method with adaptive on-line enrichment. SIAM J. Sci. Comput., 37(6):A2865–A2895, 2015.

$\bullet$ P. Henning, M. Ohlberger, and B. Schweizer. An adaptive multiscale finite element method. Multiscale Model. Simul., 12(3):1078–1107, 2014.

$\bullet$ M. Drohmann, B. Haasdonk, and M. Ohlberger. Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation. SIAM J. Sci. Comput., 34(2):A937–A969, 2012.

$\bullet$ B. Haasdonk and M. Ohlberger. Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM Math. Model. Numer. Anal., 42(2):277–302, 2008.

$\bullet$ P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A generic grid interface for parallel and adaptive scientific computing. {II}. Implementation and tests in DUNE. Computing, 82(2-3):121–138, 2008.

$\bullet$ M. Ohlberger. A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems. Multiscale Model. Simul., 4(1):88–114, 2005.

$\bullet$ M. Ohlberger. A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations. ESAIM Math. Model. Numer. Anal., 35(2):355–387, 2001.

Current Cluster Publications

Current Cluster Publications of Prof. Dr. Mario Ohlberger

$\bullet $ Tim Keil and Mario Ohlberger. A relaxed localized trust-region reduced basis approach for optimization of multiscale problems. ESAIM: Mathematical Modelling and Numerical Analysis, 58(1):79–105, January 2024. doi:10.1051/m2an/2023089.

$\bullet $ Lukas Renelt, Christian Engwer, and Mario Ohlberger. An optimally stable approximation of reactive transport using discrete test and infinite trial spaces. In Emmanuel Franck, Jürgen Fuhrmann, Victor Michel-Dansac, and Laurent Navoret, editors, Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, 289–298. Springer Nature Switzerland, October 2023. doi:10.1007/978-3-031-40860-1_30.

$\bullet $ Christian Engwer, Mario Ohlberger, and Lukas Renelt. Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems. arXiv e-prints, October 2023. arXiv:2310.19674.

$\bullet $ Michael Kartmann, Tim Keil, Mario Ohlberger, Stefan Volkwein, and Barbara Kaltenbacher. Adaptive reduced basis trust region methods for parameter identification problems. arXiv e-prints, September 2023. arXiv:2309.07627.

$\bullet $ Bernard Haasdonk, Hendrik Kleikamp, Mario Ohlberger, Felix Schindler, and Tizian Wenzel. A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. SIAM J. Sci. Comput., pages A1039–A1065, June 2023. doi:10.1137/22M1493318.

$\bullet $ Tim Keil, Mario Ohlberger, and Felix Schindler. Adaptive localized reduced basis methods for large scale parameterized systems. arXiv e-prints, March 2023. arXiv:2303.03074.

$\bullet $ Tizian Wenzel, Bernard Haasdonk, Hendrik Kleikamp, Mario Ohlberger, and Felix Schindler. Application of deep kernel models for certified and adaptive RB-ML-ROM surrogate modeling. arXiv e-prints, February 2023. arXiv:2302.14526.

$\bullet $ M.; Banholzer Ohlberger, S.; Haasdonk, B.; Keil, Kleikamp T., H.; Mechelli, L.; Oguntola, M, and Schindler andF.; Volkwein, S.; Wenzel, and T. Model reduction and learning for PDE constrained optimization. Oberwolfach Reports, 2023.

$\bullet $ Tim Keil, Hendrik Kleikamp, Rolf J. Lorentzen, Micheal B. Oguntola, and Mario Ohlberger. Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery. Advances in Computational Mathematics, 48(6):Paper No. 73, 35, November 2022. doi:10.1007/s10444-022-09981-z.

$\bullet $ Manuel Landstorfer, Mario. Ohlberger, Stephan Rave, and Marie-Christin Tacke. A modelling framework for efficient reduced order simulations of parametrised lithium-ion battery cells. European Journal of Applied Mathematics, pages 1–38, November 2022. doi:10.1017/S0956792522000353.

$\bullet $ Stefan Banholzer, Tim Keil, Mario Ohlberger, Luca Mechelli, Felix Schindler, and Stefan Volkwein. 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, October 2022. URL:

$\bullet $ Hendrik Kleikamp, Mario Ohlberger, and Stephan Rave. Nonlinear model order reduction using diffeomorphic transformations of a space-time domain. In ARGESIM Report 17, 57–58. July 2022. doi:10.11128/arep.17.a17129.

$\bullet $ Bernard Haasdonk, Mario Ohlberger, and Felix Schindler. An adaptive model hierarchy for data-augmented training of kernel models for reactive flow. In ARGESIM Report 17, 67–68. July 2022. doi:10.11128/arep.17.a17155.

$\bullet $ Pavel Gavrilenko, Bernard Haasdonk, Oleg Iliev, Mario Ohlberger, Felix Schindler, Pavel Toktaliev, Tizian Wenzel, and Maha Youssef. A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows. In Large-Scale Scientific Computing, 378–386. March 2022. doi:10.1007/978-3-030-97549-4_43.

$\bullet $ Tim Keil and Mario Ohlberger. Model reduction for large scale systems. In Large-Scale Scientific Computing, 16–28. March 2022. doi:10.1007/978-3-030-97549-4_2.

$\bullet $ Tobias Leibner and Mario Ohlberger. A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations. ESAIM: Math. Model. Numer. Anal., 55(6):2567–2608, November 2021. doi:10.1051/m2an/2021065.

$\bullet $ Tobias Leibner, Maja Matis, Mario Ohlberger, and Stephan Rave. Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD. arXiv e-prints, October 2021. arXiv:2111.00129.

$\bullet $ Tim Keil, Luca Mechelli, Mario Ohlberger, Felix Schindler, and Stefan Volkwein. A non-conforming dual approach for adaptive Trust-Region reduced basis approximation of PDE-constrained parameter optimization. ESAIM: M2AN, 55(3):1239–1269, May 2021. doi:10.1051/m2an/2021019.

$\bullet $ Tim Keil and Mario Ohlberger. Model reduction for large scale systems. arXiv e-prints, May 2021. arXiv:2105.01433.

$\bullet $ Andreas Buhr, Laura Iapichino, Mario Ohlberger, Stephan Rave, Felix Schindler, and Kathrin Smetana. Localized model reduction for parameterized problems. In Model order reduction. Volume 2: Snapshot-based methods and algorithms, pages 245–305. January 2021. doi:10.1515/9783110671490-006.

$\bullet $ Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, and Oliver Sander. The DUNE framework: Basic concepts and recent developments. Computers and Mathematics with Applications, 81:75–112, January 2021. doi:10.1016/j.camwa.2020.06.007.

$\bullet $ Peter Bastian, Mirco Altenbernd, Nils-Arne Dreier, Christian Engwer, Jorrit Fahlke, René Fritze, Markus Geveler, Dominik Göddeke, Oleg Iliev, Olaf Ippisch, Jan Mohring, Steffen Müthing, Mario Ohlberger, Dirk Ribbrock, Nikolay Shegunov, and Stefan Turek. Exa-duneflexible PDE solvers, numerical methods and applications. In Hans-Joachim Bungartz, Severin Reiz, Benjamin Uekermann, Philipp Neumann, and Wolfgang E. Nagel, editors, Software for Exascale Computing - SPPEXA 2016-2019, pages 225–269. Cham, July 2020. doi:10.1007/978-3-030-47956-5_9.

$\bullet $ Tobias Leibner and Mario Ohlberger. A new coordinate-transformed discretization method for minimum entropy moment approximations of linear kinetic equations. arXiv e-prints, July 2020. arXiv:2007.04467.

$\bullet $ Mario Ohlberger, Ben Schweizer, Maik Urban, and Barbara Verfürth. Mathematical analysis of transmission properties of electromagnetic meta-materials. Networks & Heterogeneous Media, 15(1):29–56, January 2020. doi:10.3934/nhm.2020002.

$\bullet $ Mario Ohlberger, Andreas Buhr, Dennis Eikhorn, Christian Engwer, and Stephan Rave. Advances in model order reduction for large scale or multi-scale problems. Oberwolfach Reports, 2019:38–40, September 2019.

$\bullet $ Stefan Hain, Mario Ohlberger, Mladjan Radic, and Karsten Urban. A hierarchical a posteriori error estimator for the Reduced Basis Method. Advances in Computational Mathematics, 45(5-6):2191–2214, February 2019. doi:10.1007/s10444-019-09675-z.

$\bullet $ Julian Feinauer, Simon Hein, Stephan Rave, Sebastian Schmidt, Daniel Westhoff, Jochen Zausch, Oleg Iliev, Arnulf Latz, Mario Ohlberger, and Volker Schmidt. 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, February 2019. doi:10.1016/j.jocs.2018.03.006.