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, Mario Ohlberger, Felix Schindler, and Julia Schleuß. Local training and enrichment based on a residual localization strategy. arXiv e-prints, April 2024. arXiv:2404.16537.

$\bullet $ Christian Engwer, Mario Ohlberger, and Lukas Renelt. Construction of local reduced spaces for friedrichs' systems via randomized training. arXiv e-prints, April 2024. arXiv:2404.18839.

$\bullet $ Amrita Singh, Sameedha Thale, Tobias Leibner, Lucas Lamparter, Andrea Ricker, Harald Nüsse, Jürgen Klingauf, Milos Galic, Mario Ohlberger, and Maja Matis. Dynamic interplay of microtubule and actomyosin forces drive tissue extension. Nature Communications, April 2024. doi:10.1038/s41467-024-47596-8.

$\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: yokohamapublishers.jp/online2/oppafa/vol7/p1561.html.

$\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 $ 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 $ 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 $ 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-dune—flexible 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.