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
- . . ‘Localized model reduction for parameterized problems.’ In Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by , 245–306. doi: 10.1515/9783110671490-006.
- . . ‘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), edited by . New York City: John Wiley & Sons. doi: 10.1002/pamm.201900026.
- . . ‘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 , edited by , 143–163. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-90469-6_8.
- . . ‘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 , 357–365. Basel : Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- . . ‘Extending DUNE: The dune-xt modules.’ Archive of Numerical Software 5, № 1: 193–216. doi: 10.11588/ans.2017.1.27720.
- . . ‘True Error Control for the Localized Reduced Basis Method for Parabolic Problems.’ In Model Reduction of Parametrized Systems, edited by , 169–182. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, № 5: S194–S216. doi: 10.1137/15M1026614.
- . . ‘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.
- . . ‘The localized reduced basis multi-scale method with online enrichment.’ Oberwolfach Reports 7: 406–409. doi: 10.4171/OWR/2013/07.
- . . ‘The Localized Reduced Basis Multiscale Method.’ Contributed to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske.
Complete List
- . . ‘Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.’ In Large-Scale Scientific Computations, edited by , 117–125. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- . . ‘Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.’ In Large-Scale Scientific Computations, edited by , 108–116. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
- . . ‘Local training and enrichment based on a residual localization strategy.’ In Proceedings of the Conference Algoritmy 2024, edited by , 76–84. Bratislava: Jednota slovenských matematikov a fyzikov.
- . . ‘A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.’ SIAM Journal on Scientific Computing 45, № 3: A1039. doi: 10.1137/22M1493318.
- . . ‘A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows.’ In Large-Scale Scientific Computing, edited by , 378–386. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-030-97549-4_43.
- . . ‘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.
- . . ‘On the Performance of Machine Learning Methods for Breakthrough Curve Prediction.’ arXiv [physics.flu-dyn] 2204.11719. doi: 10.48550/arXiv.2204.11719. [submitted / under review]
- . . ‘An adaptive model hierarchy for data-augmented training of kernel models for reactive flow.’ In MATHMOD 2022 Discussion Contribution Volume, edited by , 67–68. 17th Ed. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17155.
- . . ‘Localized model reduction for parameterized problems.’ In Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by , 245–306. doi: 10.1515/9783110671490-006.
- . . ‘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.
- . . ‘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), edited by . New York City: John Wiley & Sons. doi: 10.1002/pamm.201900026.
- . . ‘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 , edited by , 143–163. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-90469-6_8.
- . . ‘Model reduction for parameterized systems and inverse problems.’ Oberwolfach Reports 2018, № 39: 2454–2457. doi: 10.4171/OWR/2018/39.
- . . ‘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 , 357–365. Basel : Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- . . ‘Extending DUNE: The dune-xt modules.’ Archive of Numerical Software 5, № 1: 193–216. doi: 10.11588/ans.2017.1.27720.
- . . ‘True Error Control for the Localized Reduced Basis Method for Parabolic Problems.’ In Model Reduction of Parametrized Systems, edited by , 169–182. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- . . ‘Model Reduction for Multiscale Lithium-Ion Battery Simulation.’ In Numerical Mathematics and Advanced Applications ENUMATH 2015, edited by , 317–331. Heidelberg: Springer. doi: 10.1007/978-3-319-39929-4_31.
- . . Model reduction for parametric multi-scale problems Dissertation thesis, Westfälische Wilhelms-Universität Münster.
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, № 5: S194–S216. doi: 10.1137/15M1026614.
- . . ‘Adaptive Localized Model Reduction.’ Oberwolfach Reports 13, № 3: 2406–2409. doi: 10.4171/OWR/2016/42.
- . . ‘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.
- . . ‘A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method.’ In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, edited by , 421–429. Basel : Springer International Publishing. doi: 10.1007/978-3-319-05684-5_41.
- . . ‘The localized reduced basis multi-scale method with online enrichment.’ Oberwolfach Reports 7: 406–409. doi: 10.4171/OWR/2013/07.
- . . ‘Model reduction for multiscale problems.’ Oberwolfach Reports 39: 2228–2230. doi: 10.4171/OWR/2013/39.
- . . ‘The Localized Reduced Basis Multiscale Method.’ Contributed to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske.
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)