Dr. Felix Schindler
Postdoc
Group Numerical Analysis and Scientific ComputingT: 0049 251 83 35130
F: 0049 251 83 32729
felix.schindler@wwu.de
F: 0049 251 83 32729
felix.schindler@wwu.de
Publications
Selection
- Buhr Andreas, Iapichino Laura, Ohlberger Mario, Rave Stephan, and Schindler Felix, Smetana Kathrin. . “Localized model reduction for parameterized problems.” in Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by P Benner, S Grivet-Talocia, A Quarteroni, G Rozza, W Schilders and L Sileira. doi: 10.1515/9783110671490-006.
- Rave, Stephan, and Schindler, Felix. . “A locally conservative reduced flux reconstruction for elliptic problems.” in Special Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Vol. 19 , edited by J Eberhardsteiner and M Schöberl. New York City: John Wiley & Sons. doi: 10.1002/pamm.201900026.
- Ohlberger, Mario, Schaefer, Michael, and Schindler, Felix. . “Localized Model Reduction in PDE Constrained Optimization.” in Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 , Vol. 169 of International Series of Numerical Mathematics, edited by V Schulz and D Seck. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-90469-6_8.
- Ohlberger, M, and Schindler, F. . “Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization.” in Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, edited by C Cancès and P Omnes. Basel: Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- Leibner, T, Milk, R, and Schindler, F. . “Extending DUNE: The dune-xt modules.” Archive of Numerical Software, № 5 (1): 193–216. doi: 10.11588/ans.2017.1.27720.
- Ohlberger, M, Rave, S, and Schindler, F. . “True Error Control for the Localized Reduced Basis Method for Parabolic Problems.” in Model Reduction of Parametrized Systems, Vol. 17 of MS&A (Modeling, Simulation and Applications), edited by P. Benner, M. Ohlberger, A. Patera, G. Rozza and K. Urban. Basel: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- Milk, R, Rave, S, and Schindler, F. . “pyMOR - Generic algorithms and interfaces for model order reduction.” SIAM Journal on Scientific Computing, № 38 (5): S194–S216. doi: 10.1137/15M1026614.
- Ohlberger, M, and Schindler, F. . “Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment.” SIAM J. Sci. Comput., № 37 (6): A2865–A2895. doi: 10.1137/151003660.
- Albrecht, F, and Ohlberger, M. . “The localized reduced basis multi-scale method with online enrichment.” Oberwolfach Reports, № 7: 406–409. doi: 10.4171/OWR/2013/07.
- Albrecht, F, Haasdonk, B, Kaulmann, S, and Ohlberger, M. . “The Localized Reduced Basis Multiscale Method.” contribution to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske Bratislava: Publishing House of Slovak University of Technology.
Complete List
- Wenzel, Tizian, Haasdonk, Bernard, Kleikamp, Hendrik, Ohlberger, Mario, and Schindler, Felix. . “Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.” in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I. Lirkov and S. Margenov. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- Keil, Tim, Ohlberger, Mario, and Schindler, Felix. . “Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.” in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I Lirkov and S Margenov. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
- Tim Keil, Mario Ohlberger, and Felix Schindler, Julia Schleuß. . “Local training and enrichment based on a residual localization strategy.” in Proceedings of the Conference Algoritmy 2024, Vol. 8 of Proceedings of the Conference Algoritmy, edited by P Frolkovič, K Mikula and D Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
- Haasdonk, B, Kleikamp, H, Ohlberger, M, Schindler, F, and Wenzel, T. . “A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.” SIAM Journal on Scientific Computing, № 45 (3): A1039–1065. doi: 10.1137/22M1493318.
- Gavrilenko Pavel, Haasdonk Bernard, Iliev Oleg, Ohlberger Mario, Schindler Felix, Toktaliev Pavel, and Wenzel Tizian, Youssef Maha. . “A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows.” in Large-Scale Scientific Computing, Vol. 13127 of Lecture Notes in Computer Science (LNCS), edited by Margenov Svetozar Lirkov Ivan. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-030-97549-4_43.
- Banholzer, S, Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, and Volkwein, S. . “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.
- Fokina, D, Iliev, O, Toktaliev, P, Oseledets, I, and Schindler, F. . “On the Performance of Machine Learning Methods for Breakthrough Curve Prediction.” arXiv [physics.flu-dyn], № 2204.11719 doi: 10.48550/arXiv.2204.11719.
- Haasdonk, B, Ohlberger, M, and Schindler, F. . “An adaptive model hierarchy for data-augmented training of kernel models for reactive flow.” in MATHMOD 2022 Discussion Contribution Volume, edited by Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi and Inge Troch. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17155.
- Buhr Andreas, Iapichino Laura, Ohlberger Mario, Rave Stephan, and Schindler Felix, Smetana Kathrin. . “Localized model reduction for parameterized problems.” in Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by P Benner, S Grivet-Talocia, A Quarteroni, G Rozza, W Schilders and L Sileira. doi: 10.1515/9783110671490-006.
- Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, and Volkwein, S. . “A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization.” ESAIM: Mathematical Modelling and Numerical Analysis, № 55: 1239–1269. doi: 10.1051/m2an/2021019.
- Rave, Stephan, and Schindler, Felix. . “A locally conservative reduced flux reconstruction for elliptic problems.” in Special Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Vol. 19 , edited by J Eberhardsteiner and M Schöberl. New York City: John Wiley & Sons. doi: 10.1002/pamm.201900026.
- Ohlberger, Mario, Schaefer, Michael, and Schindler, Felix. . “Localized Model Reduction in PDE Constrained Optimization.” in Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 , Vol. 169 of International Series of Numerical Mathematics, edited by V Schulz and D Seck. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-90469-6_8.
- Ohlberger, Mario, Rave, Stephan, Schindler, Felix, and Wedemeier, Tobias. . “Model reduction for parameterized systems and inverse problems.” Oberwolfach Reports, № 2018 (39): 2454–2457. doi: 10.4171/OWR/2018/39.
- Ohlberger, M, and Schindler, F. . “Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization.” in Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, edited by C Cancès and P Omnes. Basel: Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- Leibner, T, Milk, R, and Schindler, F. . “Extending DUNE: The dune-xt modules.” Archive of Numerical Software, № 5 (1): 193–216. doi: 10.11588/ans.2017.1.27720.
- Ohlberger, M, Rave, S, and Schindler, F. . “True Error Control for the Localized Reduced Basis Method for Parabolic Problems.” in Model Reduction of Parametrized Systems, Vol. 17 of MS&A (Modeling, Simulation and Applications), edited by P. Benner, M. Ohlberger, A. Patera, G. Rozza and K. Urban. Basel: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- Ohlberger, M, Rave, S, and Schindler, F. . “Model Reduction for Multiscale Lithium-Ion Battery Simulation.” in Numerical Mathematics and Advanced Applications ENUMATH 2015, Vol. 112 of Lecture Notes in Computational Science and Engineering, edited by B Karasözen, M Manguoğlu, M Teuer-Sezgin, S Göktepe and Ö Uğur. Heidelberg: Springer. doi: 10.1007/978-3-319-39929-4_31.
- Schindler, and F. . “Model reduction for parametric multi-scale problems.” Dissertation thesis, Westfälische Wilhelms-Universität Münster.
- Milk, R, Rave, S, and Schindler, F. . “pyMOR - Generic algorithms and interfaces for model order reduction.” SIAM Journal on Scientific Computing, № 38 (5): S194–S216. doi: 10.1137/15M1026614.
- Ohlberger, M, Rave, S, and Schindler, F. . “Adaptive Localized Model Reduction.” Oberwolfach Reports, № 13 (3): 2406–2409. doi: 10.4171/OWR/2016/42.
- Ohlberger, M, and Schindler, F. . “Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment.” SIAM J. Sci. Comput., № 37 (6): A2865–A2895. doi: 10.1137/151003660.
- Ohlberger, M, and Schindler, F. . “A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method.” in Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, Vol. 77 of Springer Proceedings in Mathematics & Statistics, edited by Rohde C and ,. Basel: Springer International Publishing. doi: 10.1007/978-3-319-05684-5_41.
- Albrecht, F, and Ohlberger, M. . “The localized reduced basis multi-scale method with online enrichment.” Oberwolfach Reports, № 7: 406–409. doi: 10.4171/OWR/2013/07.
- Ohlberger, M, Albrecht, F, Drohmann, M, Henning, P, Kaulmann, S, and Schweizer, B. . “Model reduction for multiscale problems.” Oberwolfach Reports, № 39: 2228–2230. doi: 10.4171/OWR/2013/39.
- Albrecht, F, Haasdonk, B, Kaulmann, S, and Ohlberger, M. . “The Localized Reduced Basis Multiscale Method.” contribution to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske Bratislava: Publishing House of Slovak University of Technology.
- Albrecht, F. . Local Discontinuous Galerkin Verfahren für die Stokes Gleichungen und Homogenisierung in porösen Medien (Diplomarbeit),
Selected research, projects, ...
The following is an extremely incomplete list of my activities. I just started collecting them and they should grow over time ...
- I recently started looking into discontinuous Galerkin (DG) and Finite Volume (FV) methods for hyperbolic equations, such as approximating the solution \(u\) of: $$\partial_t u + \nabla_x \cdot f(u) = 0$$ I was particularly interested in how to support the implementation of both FV and DG methods in our software library.
Preliminary findings aredocumented here.This is now part of our library dune-gdt (FV is joint work with T. Leiber), see for instance the advection operators here or these tests on linear transport and inviscid compressible flow.
- I recently started looking into discontinuous Galerkin (DG) and Finite Volume (FV) methods for hyperbolic equations, such as approximating the solution \(u\) of: $$\partial_t u + \nabla_x \cdot f(u) = 0$$ I was particularly interested in how to support the implementation of both FV and DG methods in our software library.
Software
dune-gdt
Joint work with: Rene Milk, Tobias Leibner
dune-gdt is a DUNE module which provides a generic discretization toolbox for grid-based numerical methods. It contains building blocks - like local operators, local integrands, local assemblers - for discretization methods and suitable discrete function spaces. For more information visit the official homepage.
\(\color{#00568a}{\huge{\text{py}}}\color{#e88e3f}{\huge{\text{MOR}}}\)
Joint work with: Stephan Rave, Rene Milk
pyMOR - Model Order Reduction with Python - is a software library for building model order reduction applications with the Python programming language. Its main focus lies on the application of reduced basis methods to parameterized partial differential equations. All algorithms in pyMOR are formulated in terms of abstract interfaces for seamless integration with external high-dimensional PDE solvers. Moreover, pure Python implementations of finite element and finite volume discretizations using the NumPy/SciPy scientific computing stack are provided for getting started quickly. For more information visit the official homepage.
Publications:
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, Nr. 5: 194-216. doi: 10.1137/15M1026614.
Scientific Talks
- Schindler, Felix : “Locally conservative Reduced Basis methods”. 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics GAMM 2019, Universität Wien, Wien, Österreich, .
- Ohlberger M, Rave S, Schindler F : “Fully certified and adaptive localized model reduction for elliptic and parabolic problems”. Recent developments in numerical methods for model reduction, Institute Henri Poincaré, Paris, France, .
The list of talks is not yet complete.
Teaching
- Seminar: Master Seminar Applied Mathematics [100391]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Seminar: Bachelorseminar: Innovative numerical methods [100388]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Praktikum: Lab Course Numerical Analysis of Partial Differential Equations I [108418]
(in cooperation with Prof. Dr. Mario Ohlberger) - Tutorial Numerics of Partial Differential Equations I [100387]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Masterseminar for Efficient numerical methods [106383]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Tutorial Modellreduction of Parameterized systems [106382]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Master Seminar Applied Mathematics [104435]
(in cooperation with Dr. Stephan Rave) - Seminar: Bachelor Seminar: A posteriori Error Estimations and their Applications [104438]
(in cooperation with Dr. Stephan Rave) - Praktikum: Introduction to Programming with C++ [104437]
(in cooperation with Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Numerical Programming with Python [100434]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Seminar: PhD in English and American Studies [102385]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Seminar: Bachelor Seminar: A posteriori Error Estimations and their Applications [102383]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Programming with C++ [102386]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Master Seminar Applied Mathematics [100386]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Seminar: Bachelor Seminar: A posteriori Error Estimations and their Applications [100385]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Praktikum: Non-linear modelling in the natural sciences [100387]
(in cooperation with Prof. Dr. Andreas Heuer, Liesel Sommer, Prof. Dr. Christian Engwer, apl. Prof. Svetlana Gurevich, Prof. Dr. Mario Ohlberger, Jun.-Prof. Arndt Telschow) - Praktikum: Introduction to Numerical Programming with Python [108048]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Numerical Programming with Python [108012]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Praktikum: Non-linear modelling in the natural sciences [108047]
(in cooperation with Prof. Dr. Andreas Heuer, Prof. Dr. Christian Engwer, apl. Prof. Svetlana Gurevich, Prof. Dr. Mario Ohlberger, Jun.-Prof. Arndt Telschow) - Vorlesung: Scientific Computing [106232]
(in cooperation with Dr. Stephan Rave) - Tutorial Scientific Computing [106233]
(in cooperation with Dr. Stephan Rave, Julia Brunken) - Praktikum: Introduction to Programming with C++ [104226]
(in cooperation with Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Numerical Programming with Python [104225]
(in cooperation with Julia Brunken, Prof. Dr. Mario Ohlberger) - Praktikum: Advanced Module Heritage of the Classical Age [104222]
(in cooperation with Prof. Dr. Mario Ohlberger) - Vorlesung: MGeL Module [102397]
(in cooperation with ) - Praktikum: Lab Course Numerical Analysis of Partial Differential Equations I [102274]
(in cooperation with Prof. Dr. Mario Ohlberger) - Tutorial Numerical Analysis of Partial Differential Equations I [102398]
(in cooperation with Dr. Christian Himpe) - Seminar: Biomedical Modellling and Model Reduction [104860]
(in cooperation with Prof. Dr. Mario Ohlberger) - Praktikum: Scientific Computing [103870]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Praktikum: Scientific Computing [103760]
(in cooperation with Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Programming with C++ [102906]
(in cooperation with Dr. Christian Himpe, Prof. Dr. Mario Ohlberger) - Praktikum: Scientific Computing [102868]
(in cooperation with Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Programming with C++ [100914]
(in cooperation with Dr. Christian Himpe, Prof. Dr. Mario Ohlberger) - Model Reduction for Parametrised Partial Differential Equations [100952]
(in cooperation with Dr. Stephan Rave) - Praktikum: Intermediate Module Communication and Media [102680]
(in cooperation with Prof. Dr. Andreas Heuer, Rudolf Friedrich, Prof. Dr. Mario Ohlberger)