Michael Feischl Professor for Computational PDEs
michael.feischl@tuwien.ac.at |


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
- Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation. In arXiv E-print, 2023.
- Adaptive Image Compression via Optimal Mesh Refinement. In arXiv E-print, 2023.
- 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
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)
- Numerik Partieller Differentialgleichungen: instationäre Probleme (Sommer 2020)
- Numerik Partieller Differentialgleichungen: stationäre Probleme (Winter 2019/20)
- Numerical Methods for Uncertainty Quantification (Summer 2019)
more teaching
Workgroup
PhD | MSc |
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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
- Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation. In arXiv E-print, 2023.
- Adaptive Image Compression via Optimal Mesh Refinement. In arXiv E-print, 2023.
- 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
- Inf-sup stability implies quasi-orthogonality. In Math. Comp., 91 (337): 2059-2094, 2022. doi
- 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.
- Convergence of adaptive stochastic collocation with finite elements. In Computers & Mathematics with Applications, 98: 139-156, 2021. doi
- Higher-order linearly implicit full discretization of the Landau-Lifshitz-Gilbert equation. In Math. Comp., 90 (329): 995-1038, 2021. doi
- Recurrent neural networks as optimal mesh refinement strategies. In Comput. Math. Appl., 97: 61-76, 2021. doi
- A quasi-Monte Carlo data compression algorithm for machine learning. In Journal of Complexity: 101587, 2021. doi
- Exponential convergence in $H^1$ of $hp$-FEM for Gevrey regularity with isotropic singularities. In Numer. Math., 144 (2): 323-346, 2020. doi
- Sparse compression of expected solution operators. In SIAM J. Numer. Anal., 58 (6): 3144-3164, 2020. doi
- Optimality of a standard adaptive finite element method for the Stokes problem. In SIAM J. Numer. Anal., 57 (3): 1124-1157, 2019. doi
- Improved efficiency of a multi-index FEM for computational uncertainty quantification. In SIAM J. Numer. Anal., 57 (4): 1744-1769, 2019. doi
- Fast random field generation with $H$-matrices. In Numer. Math., 140 (3): 639-676, 2018. doi
- Optimal adaptivity for non-symmetric FEM/BEM coupling. Preprint: arXiv:1710.06082, 2017.
- Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. In Numer. Math., 136: 147-182, 2017.
- Local inverse estimates for non-local boundary integral operators. In Math. Comp., 86 (308): 2651-2686, 2017.
- The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error Estimates. In SIAM J. Numer. Anal., 55 (4): 1786-1819, 2017.
- 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.
- Adaptive 2D IGA boundary element methods. In Eng. Anal. Bound. Elem., 62: 141-153, 2016.
- An abstract analysis of optimal goal-oriented adaptivity. In SIAM J. Numer. Anal., 54: 1423-1448, 2016.
- Efficient numerical computation of direct exchange areas in thermal radiation analysis. In Numerical Heat Transfer, Part B: Fundamentals, 69 (6): 511-533, 2016.
- Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations. In Calcolo, 2016. doi
- Energy norm based error estimators for adaptive BEM for hypersingular integral equations. In Appl. Numer. Math., 95: 15-35, 2015.
- Adaptive boundary element methods for optimal convergence of point errors. In Numer. Math., 2015.
- Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. In Numer. Methods Partial Differential Equations, 2015.
- 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.
- 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.
- Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. In Numer. Math., 130: 199-223, 2015.
- Multiscale modeling in micromagnetics: Existence of solutions and numerical integration. In Math. Models Methods Appl. Sci., 24: 2627-2662, 2014.
- Axioms of adaptivity. In Comput. Math. Appl., 67: 1195-1253, 2014.
- Adaptive Boundary Element Methods: A Posteriori Error Estimators, Adaptivity, Convergence, and Implementation. In Arch. Comput. Methods Eng., 22: 309-389, 2014.
- 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.
- Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. In J. Comput. Appl. Math., 255: 481-501, 2014.
- Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data. In Int. J. Numer. Anal. Model., 11: 230-254, 2014.
- Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor. In Comput. Methods Appl. Math., 14: 485-508, 2014.
- ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve. In Eng. Anal. Bound. Elem., 38: 49-60, 2014.
- Classical FEM-BEM coupling methods: Nonlinearities, well-posedness, and adaptivity. In Comput. Mech., 51 (4): 399-419, 2013.
- 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.
- Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods. In Comput. Methods Appl. Math., 13: 305-332, 2013.
- HILBERT - a MATLAB implementation of adaptive 2D-BEM. In Numer. Algorithms, 2013.
- Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations. In J. Magn. Magn. Mater., 343: 163-168, 2013.
- Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part I: weakly-singular integral equation. In Calcolo: 1-32, 2013.
- Quasi-optimal convergence rate for an adaptive boundary element method. In SIAM J. Numer. Anal., 51: 1327-1348, 2013.
- A posteriori error estimates for the Johnson-N\'ed\'elec FEM-BEM coupling. In Eng. Anal. Bound. Elem., 36: 255-266, 2012.
- Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. In ESAIM Math. Model. Numer. Anal., 46: 1147-1173, 2012.
- 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) |