Dr. Felix Schindler

Topics in Mathematics Münster

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

• 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
• 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
• 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, 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
• Leibner T, Milk R, Schindler F Extending DUNE: The dune-xt modules. Archive of Numerical Software Vol. 5 (1), 2017, pp 193-216 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
• 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, 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
• Albrecht F, Haasdonk B, Kaulmann S, Ohlberger M The Localized Reduced Basis Multiscale Method. , 2012, pp 393-403 online

Recent Publications of Dr. Felix Schindler

$\bullet$ 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.

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

$\bullet$ 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.

$\bullet$ 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.

$\bullet$ 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.

$\bullet$ 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.

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