Michael Feischl Professor for Computational PDEs

michael.feischl@tuwien.ac.at Institute for Analysis and Scientific Computing (E 101) TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna Office: DA 04 L14 Phone: +43 (1) 58801 10154

Research Interests

My research focuses on three main areas (see also online talks ):

• Partial differential equations with random coefficients, fast random field generation, and machine learning
• Computational micromagnetism as well as numerics and theory of the Landau-Lifshitz-Gilbert equation
• Optimal adaptive mesh refinement and a posteriori error estimators

Recent publications (complete list below):

1. Bohn, J.; Dörfler, W.; Feischl, M. and Karch, S. Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation. In arXiv E-print, 2023.
2. An, X.; Dick, J.; Feischl, M.; Scaglioni, A. and Tran, T. Sparse grid approximation of the stochastic Landau-Lifshitz-Gilbert equation. In arXiv E-print, 2023.
3. Feischl, M. and Hackl, H. Adaptive Image Compression via Optimal Mesh Refinement. In arXiv E-print, 2023.

Teaching

• Numerik auf Quantencomputern (Sommer 2023)
• Einführung ins Programmieren für TM (Winter 2022/23)
• Seminar AKANA-AKNUM: Von Schauderbasen bis Wavelets (Winter 2021/22)
• Einführung ins Programmieren für TM (Sommer 2021, Winter 2021/22)
• Numerics of high-dimensional problems (Winter 2020/21)
more teaching
Numerik Partieller Differentialgleichungen: instationäre Probleme (Sommer 2020)
Numerik Partieller Differentialgleichungen: stationäre Probleme (Winter 2019/20)
Numerical Methods for Uncertainty Quantification (Summer 2019)

Workgroup

PhD	MSc
Hubert Hackl, M.Sc. Amanda Huber, M.Sc. Andrea Scaglioni, M.Sc. Fabian Zehetgruber, M.Sc.	Johannes Reicher

Software

• Fast generation of random fields: This Matlab program uses $H^2$-matrices to efficiently evaluate Gaussian random fields on arbitrary pointsets.
• Matlab $H^2$-matrix library: This is a simple, and very limited implementation of the $H^2$-matrix approach in Matlab.

List of Publications and Preprints

1. Bohn, J.; Dörfler, W.; Feischl, M. and Karch, S. Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation. In arXiv E-print, 2023.
2. An, X.; Dick, J.; Feischl, M.; Scaglioni, A. and Tran, T. Sparse grid approximation of the stochastic Landau-Lifshitz-Gilbert equation. In arXiv E-print, 2023.
3. Feischl, M. and Hackl, H. Adaptive Image Compression via Optimal Mesh Refinement. In arXiv E-print, 2023.
4. Bohn, J.; Feischl, M. and Kovács, B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. In Computational Methods in Applied Mathematics, 2022. doi 
5. Feischl, M. Inf-sup stability implies quasi-orthogonality. In Math. Comp., 91 (337): 2059-2094, 2022. doi 
6. Doppler, C.; Feischl, M.; Ganhör, C.; Puh, S.; Müller, M.; Kotnik, M.; Mimler, T.; Sonnleitner, M.; Bernhard, D. and Wechselberger, C. Low-entry-barrier point-of-care testing of anti-SARS-CoV-2 IgG in the population of Upper Austria from December 2020 until April 2021 - a feasible surveillance strategy for post-pandemic monitoring?. In Analytical and Bioanalytical Chemistry, 2022.
7. Feischl, M. and Scaglioni, A. Convergence of adaptive stochastic collocation with finite elements. In Computers & Mathematics with Applications, 98: 139-156, 2021. doi 
8. Akrivis, G.; Feischl, M.; Kovács, B. and Lubich, C. Higher-order linearly implicit full discretization of the Landau-Lifshitz-Gilbert equation. In Math. Comp., 90 (329): 995-1038, 2021. doi 
9. Bohn, J. and Feischl, M. Recurrent neural networks as optimal mesh refinement strategies. In Comput. Math. Appl., 97: 61-76, 2021. doi 
10. Dick, J. and Feischl, M. A quasi-Monte Carlo data compression algorithm for machine learning. In Journal of Complexity: 101587, 2021. doi 
11. Feischl, M. and Schwab, Ch. Exponential convergence in $H^1$ of $hp$-FEM for Gevrey regularity with isotropic singularities. In Numer. Math., 144 (2): 323-346, 2020. doi 
12. Feischl, M. and Peterseim, D. Sparse compression of expected solution operators. In SIAM J. Numer. Anal., 58 (6): 3144-3164, 2020. doi 
13. Feischl, M. Optimality of a standard adaptive finite element method for the Stokes problem. In SIAM J. Numer. Anal., 57 (3): 1124-1157, 2019. doi 
14. Dick, J.; Feischl, M. and Schwab, C. Improved efficiency of a multi-index FEM for computational uncertainty quantification. In SIAM J. Numer. Anal., 57 (4): 1744-1769, 2019. doi 
15. Feischl, M.; Kuo, F. Y. and Sloan, I. H. Fast random field generation with $H$-matrices. In Numer. Math., 140 (3): 639-676, 2018. doi 
16. Feischl, M. Optimal adaptivity for non-symmetric FEM/BEM coupling. Preprint: arXiv:1710.06082, 2017.
17. Feischl, M; Gantner, G; Haberl, A and Praetorius, D Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. In Numer. Math., 136: 147-182, 2017.
18. Aurada, M; Feischl, M; Führer, T; Karkulik, M; Melenk, J. M and Praetorius, D Local inverse estimates for non-local boundary integral operators. In Math. Comp., 86 (308): 2651-2686, 2017.
19. Feischl, M and Tran, T The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error Estimates. In SIAM J. Numer. Anal., 55 (4): 1786-1819, 2017.
20. Feischl, M and Tran, T Existence of arbitrarily regular solutions of the LLG equation in 3D with natural boundary conditions. In SIAM J. Math. Anal., 49 (6): 4470-4490, 2017.
21. Feischl, M; Gantner, G; Haberl, A and Praetorius, D Adaptive 2D IGA boundary element methods. In Eng. Anal. Bound. Elem., 62: 141-153, 2016.
22. Feischl, M; Praetorius, D and Van der Zee, K An abstract analysis of optimal goal-oriented adaptivity. In SIAM J. Numer. Anal., 54: 1423-1448, 2016.
23. Feischl, M; Führer, T; Niederer, M; Strommer, S; Steinboeck, A and Praetorius, D Efficient numerical computation of direct exchange areas in thermal radiation analysis. In Numerical Heat Transfer, Part B: Fundamentals, 69 (6): 511-533, 2016.
24. Feischl, M; Führer, T; Praetorius, D and Stephan, E. P Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations. In Calcolo, 2016. doi 
25. Aurada, M; Feischl, M; Führer, T; Karkulik, M and Praetorius, D Energy norm based error estimators for adaptive BEM for hypersingular integral equations. In Appl. Numer. Math., 95: 15-35, 2015.
26. Feischl, M; Gantner, G; Haberl, A; Praetorius, D and Führer, T Adaptive boundary element methods for optimal convergence of point errors. In Numer. Math., 2015.
27. Feischl, M; Führer, T; Praetorius, D and Stephan, E. P Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. In Numer. Methods Partial Differential Equations, 2015.
28. Feischl, M; Führer, T; Karkulik, M; Melenk, J. M and Praetorius, D Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. Part II: Hyper-singular integral equation. In Electron. Trans. Numer. Anal., 44: 153-176, 2015.
29. Feischl, M; Gantner, G and Praetorius, D Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations. In Comput. Methods Appl. Mech. Engrg., 290: 362-386, 2015.
30. Feischl, M; Führer, T; Karkulik, M and Praetorius, D Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. In Numer. Math., 130: 199-223, 2015.
31. Bruckner, F; Süss, D; Feischl, M; Führer, T; Goldenits, P; Page, M; Praetorius, D and Ruggeri, M Multiscale modeling in micromagnetics: Existence of solutions and numerical integration. In Math. Models Methods Appl. Sci., 24: 2627-2662, 2014.
32. Carstensen, C; Feischl, M; Page, M and Praetorius, D Axioms of adaptivity. In Comput. Math. Appl., 67: 1195-1253, 2014.
33. Feischl, M; Führer, T; Heuer, N; Karkulik, M and Praetorius, D Adaptive Boundary Element Methods: A Posteriori Error Estimators, Adaptivity, Convergence, and Implementation. In Arch. Comput. Methods Eng., 22: 309-389, 2014.
34. Feischl, M; Führer, T and Praetorius, D Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems. In SIAM J. Numer. Anal., 52: 601-625, 2014.
35. Feischl, M; Page, M and Praetorius, D Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. In J. Comput. Appl. Math., 255: 481-501, 2014.
36. Feischl, M; Page, M and Praetorius, D Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data. In Int. J. Numer. Anal. Model., 11: 230-254, 2014.
37. Feischl, M; Führer, T; Mitscha-Eibl, G; Praetorius, D and Stephan, E. P Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor. In Comput. Methods Appl. Math., 14: 485-508, 2014.
38. Feischl, M; Führer, T; Karkulik, M and Praetorius, D ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve. In Eng. Anal. Bound. Elem., 38: 49-60, 2014.
39. Aurada, M; Feischl, M; Führer, T; Karkulik, M; Melenk, J.M and Praetorius, D Classical FEM-BEM coupling methods: Nonlinearities, well-posedness, and adaptivity. In Comput. Mech., 51 (4): 399-419, 2013.
40. Aurada, M; Feischl, M; Kemetmüller, J; Page, M and Praetorius, D Each $H^{{1/2}}$-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in $\mathbb{R}^d$. In ESAIM Math. Model. Numer. Anal., 47: 1207-1235, 2013.
41. Aurada, M; Feischl, M; Führer, T; Karkulik, M and Praetorius, D Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods. In Comput. Methods Appl. Math., 13: 305-332, 2013.
42. Aurada, M; Ebner, M; Feischl, M; Ferraz-Leite, S; Führer, T; Goldenits, P; Karkulik, M; Mayr, M and Praetorius, D HILBERT - a MATLAB implementation of adaptive 2D-BEM. In Numer. Algorithms, 2013.
43. Bruckner, F; Vogler, C; Bergmair, B; Huber, T; Fuger, M; Süss, D; Feischl, M; Führer, T; Page, M and Praetorius, D Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations. In J. Magn. Magn. Mater., 343: 163-168, 2013.
44. Feischl, M; Führer, T; Karkulik, M; Melenk, J. M and Praetorius, D Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part I: weakly-singular integral equation. In Calcolo: 1-32, 2013.
45. Feischl, M; Karkulik, M; Melenk, J. M and Praetorius, D Quasi-optimal convergence rate for an adaptive boundary element method. In SIAM J. Numer. Anal., 51: 1327-1348, 2013.
46. Aurada, M; Feischl, M; Karkulik, M and Praetorius, D A posteriori error estimates for the Johnson-N\'ed\'elec FEM-BEM coupling. In Eng. Anal. Bound. Elem., 36: 255-266, 2012.
47. Aurada, M; Feischl, M and Praetorius, D Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. In ESAIM Math. Model. Numer. Anal., 46: 1147-1173, 2012.
48. Bruckner, F; Vogler, C; Feischl, M; Praetorius, D; Bergmair, B; Huber, T; Fuger, M and Süss, D 3D FEM-BEM-coupling method to solve magnetostatic Maxwell equations. In J. Magn. Magn. Mater., 324: 1862-1866, 2012.

Short CV

since 2022	Professor for Computational PDEs (TU Wien)
2019-2022	Associate Professor (TU Wien)
2018-2019	Professor (W2) (University of Bonn)
2017-2018	Junior Research Group Leader (KIT Karlsruhe)
2015-2017	Postdoc (UNSW Sydney)