Michael Feischl Associate Professor for Computational PDEs

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

Research Interests

My research focuses on three main areas:

Recent publications (complete list below):
  1. Feischl, M. An extension of general quasi-orthogonality. In Technical Report, 2020.
  2. Feischl, M. and Peterseim, D. Sparse Compression of Expected Solution Operators. In SIAM J. Numer. Anal (to appear), 2020.
  3. Feischl, M. and Scaglioni, A. Convergence of adaptive stochastic collocation with finite elements. Preprint: arXiv:2008.12591, 2020.

Teaching

Workgroup

PhD Bachelor
  • Lorenz Fischl

Software

List of Publications and Preprints

  1. Feischl, M. An extension of general quasi-orthogonality. In Technical Report, 2020.
  2. Feischl, M. and Peterseim, D. Sparse Compression of Expected Solution Operators. In SIAM J. Numer. Anal (to appear), 2020.
  3. Feischl, M. and Scaglioni, A. Convergence of adaptive stochastic collocation with finite elements. Preprint: arXiv:2008.12591, 2020.
  4. Akrivis, G.; Feischl, M.; Kovács, B. and Lubich, C. Higher-order linearly implicit time discretization of the Landau--Lifshitz--Gilbert equation. In Math. Comp, to appear, 2020.
  5. Jan Bohn, M. F. and Kovacs, B. FEM-BEM coupling for Maxwell-Landau-Lifshitz-Gilbert equations via convolution quadrature: Weak form and numerical approximation. Preprint: CRC 1173 Preprint 2020/10, 2020.
  6. Dick, J. and Feischl, M. A quasi-Monte Carlo data compression algorithm for machine learning. Preprint: arXiv E-print, 2020.
  7. Feischl, M. Optimal adaptivity for a standard finite element method for the Stokes problem. Preprint: arXiv:1710.08289: To appear in SIAM J. Numer. Anal., 2019.
  8. Dick, J.; Feischl, M. and Schwab, C. Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification. In SIAM J. Numer. Anal., to appear, 2019.
  9. Bohn, J. and Feischl, M. Recurrent Neural Networks as optimal mesh refinement strategies. Preprint: arXiv:1909.04275, 2019.
  10. Feischl, M. and Schwab, C. Exponential convergence in $H^1$ of hp-FEM for Gevrey regularity with isotropic singularities. In Numer. Math., to appear, 2019.
  11. 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 
  12. Feischl, M. Optimal adaptivity for non-symmetric FEM/BEM coupling. Preprint: arXiv:1710.06082, 2017.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. Feischl, M; Gantner, G; Haberl, A and Praetorius, D Adaptive 2D IGA boundary element methods. In Eng. Anal. Bound. Elem., 62: 141-153, 2016.
  18. 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.
  19. 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.
  20. 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 
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. Carstensen, C; Feischl, M; Page, M and Praetorius, D Axioms of adaptivity. In Comput. Math. Appl., 67: 1195-1253, 2014.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. Aurada, M; Feischl, M; F├╝hrer, 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. 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.
  43. 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.
  44. 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.