Research Interests

Research Interests

$\bullet$ Multiscale analysis of two-phase flow in porous media with complex heterogeneities
$\bullet$ Model reduction of parametric partial differential equations
$\bullet$ Numerical analysis of partial differential equations

Selected Publications

Ohlberger Mario, Schaefer Michael, Schindler Felix Localized Model Reduction in PDE Constrained Optimization. Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 International Series of Numerical Mathematics, 2018, pp 143-163 online
Ohlberger M, Schindler F Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment. SIAM J. Sci. Comput. Vol. 37 (6), 2015, pp A2865-A2895 online
Albrecht F, Ohlberger M The localized reduced basis multi-scale method with online enrichment. Oberwolfach Reports Vol. 7, 2013, pp 406-409 online
Ohlberger M, Schindler F Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization. Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, 2017, pp 357-365 online
Albrecht F, Haasdonk B, Kaulmann S, Ohlberger M The Localized Reduced Basis Multiscale Method. , 2012, pp 393-403 online
Leibner T, Milk R, Schindler F Extending DUNE: The dune-xt modules. Archive of Numerical Software Vol. 5 (1), 2017, pp 193-216 online
Milk R, Rave S, Schindler F pyMOR - Generic algorithms and interfaces for model order reduction. SIAM Journal on Scientific Computing Vol. 38 (5), 2016, pp 194-216 online
Ohlberger M, Rave S, Schindler F True Error Control for the Localized Reduced Basis Method for Parabolic Problems. Model Reduction of Parametrized SystemsMS&A (Modeling, Simulation and Applications) Vol. 2016 (1606.09216), 2017, pp 169-182 online
Rave Stephan, Schindler Felix A locally conservative reduced flux reconstruction for elliptic problems. Special Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)arXiv Vol. 1903.09082, 2019 online
Buhr Andreas, Iapichino Laura, Ohlberger Mario, Rave Stephan, Schindler Felix, Smetana Kathrin Localized model reduction for parameterized problems. Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, 2021, pp 245 - 306 online

Current Publications

Current Publications

$\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. arXiv e-prints, April 2022. arXiv:2204.13454.

$\bullet $ Daria Fokina, Oleg Iliev, Pavel Toktaliev, Ivan Oseledets, and Felix Schindler. On the performance of machine learning methods for breakthrough curve prediction. arXiv e-prints, April 2022. arXiv:2204.11719.

$\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 $ Bernard Haasdonk, Mario Ohlberger, and Felix Schindler. An adaptive model hierarchy for data-augmented training of kernel models for reactive flow. arXiv e-prints, October 2021. arXiv:2110.12388.

$\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 $ 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. arXiv e-prints, April 2021. arXiv:2104.02800.

$\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 $ Stephan Rave and Felix Schindler. A locally conservative reduced flux reconstruction for elliptic problems. PAMM, November 2019. doi:10.1002/pamm.201900026.