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.
• Keil Tim, Ohlberger Mario A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 58, 2024 online
• Kartmann, Michael; Keil, Tim; Ohlberger, Mario; Volkwein, Stephan; Kaltenbacher, Barbara Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems. Computational Science and Engineering Vol. 1 (3), 2024 online
• Haasdonk B, Kleikamp H, Ohlberger M, Schindler F, Wenzel T A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. SIAM Journal on Scientific Computing Vol. 45 (3), 2023 online
• Keil T, Kleikamp H, Lorentzen R, Oguntola M, Ohlberger M Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery. Advances in Computational Mathematics Vol. 2022 (48), 2022 online
• Keil T, Mechelli L, Ohlberger M, Schindler F, Volkwein S A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 55, 2021, pp 1239–1269 online
• Bastian P, Blatt M, Dedner A, Dreier N, Engwer C, Fritze R, Gräser C, Kempf D, Klöfkorn R, Ohlberger M, Sander O The DUNE Framework: Basic Concepts and Recent Developments. Computers & Mathematics with Applications Vol. 81, 2021, pp 75-112 online
• Ohlberger M, Verfürth B A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast . arXivMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Vol. 16 (1), 2018, pp 385-411 online
• Drohmann M, Haasdonk B, Ohlberger M Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation. SIAM Journal on Scientific Computing Vol. 34, 2012, pp A937-A969 online
• Haasdonk B, Ohlberger M Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations. M2AN Math. Model. Numer. Anal. Vol. 42 (2), 2008, pp 277-302 online
• Ohlberger M A posterior error estimates for the heterogenoeous mulitscale finite element method for elliptic homogenization problems. SIAM Multiscale Mod. Simul. Vol. 4 (1), 2005, pp 88 - 114 online
Recent Publications of Prof. Dr. Mario Ohlberger
$\bullet $ Hendrik Kleikamp and Mario Ohlberger. Adaptive model hierarchies for multi-query scenarios. arXiv e-prints, November 2024. arXiv:2411.17252.
$\bullet $ Christian Engwer, Mario Ohlberger, and Lukas Renelt. 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, October 2024. doi:10.1137/23m1613402.
$\bullet $ Michael Kartmann, Tim Keil, Mario Ohlberger, Stefan Volkwein, and Barbara Kaltenbacher. Adaptive reduced basis trust region methods for parameter identification problems. Computational Science and Engineering, September 2024. doi:10.1007/s44207-024-00002-z.
$\bullet $ Martin J. Gander, Mario Ohlberger, and Stephan Rave. A Parareal algorithm without Coarse Propagator? arXiv e-prints, September 2024. arXiv:2409.02673.
$\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. In Ivan Lirkov and Svetozar Margenov, editors, Large-Scale Scientific Computations, 117–125. Springer Nature Switzerland, May 2024. doi:10.1007/978-3-031-56208-2_11.
$\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 $ 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 $ Manuel Landstorfer, Mario. Ohlberger, Stephan Rave, and Marie-Christin Tacke. A modelling framework for efficient reduced order simulations of parametrised lithium-ion battery cells. Eur. J. Appl. Math., pages 1–38, November 2022. doi:10.1017/S0956792522000353.
$\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 $ 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 Appl. Funct. Anal., 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 $ 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. Springer International Publishing, 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 $ 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 Rep., 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. Lect. Notes. Pure. Appl., 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. J. Comput. Sci., 31:172–184, February 2019. doi:10.1016/j.jocs.2018.03.006.