Projects in Mathematics Muenster

Research area C: Models and Approximations
Unit C2: Multi-scale phenomena and macroscopic structures
Unit C4: Geometry-based modelling, approximation, and reduction

Further Projects
• Lokalisierte Reduzierte Basis Methoden für Parameteroptimierung bei partiellen Differentialgleichungen online
• pyMOR - Nachhaltige Software zur Modell-Ordnungs-Reduktion online
• Modellbasierte Abschätzung der Lebensdauer von gealterten Li-Batterien für die 2nd Life Anwendung als stationärer Stromspeicher online

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 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 Publications

$\bullet $ M. Ohlberger, B. Schweizer, M. Urban, and B. 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 $ P. Bastian, M. Altenbernd, N.-A. Dreier, C. Engwer, J. Fahlke, R. Fritze, M. Geveler, D. Göddeke, O. Iliev, O. Ippisch, J. Mohring, S. Müthing, M. Ohlberger, D. Ribbrock, N. Shegunov, and S. Turek. Exa-Dune – flexible PDE solvers, numerical methods and applications. arXiv e-prints, November 2019.

$\bullet $ P. Bastian, M. Blatt, A. Dedner, N.-A. Dreier, C. Engwer, R. Fritze, C. Gräser, D. Kempf, R. Klöfkorn, M. Ohlberger, and O. Sander. The DUNE framework: Basic concepts and recent developments. arXiv e-prints, September 2019. arXiv:1909.13672.

$\bullet $ S. Hain, M. Ohlberger, M. Radic, and K. 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 $ J. Feinauer, S. Hein, S. Rave, S. Schmidt, D. Westhoff, J. Zausch, O. Iliev, A. Latz, M. Ohlberger, and V. 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. URL: https://authors.elsevier.com/c/1Yiix6gytGezRh, doi:10.1016/j.jocs.2018.03.006.

$\bullet $ A. Buhr, L. Iapichino, M. Ohlberger, S. Rave, F. Schindler, and K. Smetana. Localized model reduction for parameterized problems. arXiv e-prints, pages 51, February 2019. arXiv:1902.08300.

$\bullet $ M. Ohlberger, A. Buhr, D. Eikhorn, C. Engwer, and S. Rave. Advances in model order reduction for large scale or multi-scale problems. Oberwolfach Reports, 2019:38–40, 2019.