Multilevel spectral domain decomposition

• Verfasst von: Bastian, Peter [VerfasserIn]
• Verfasst von: Scheichl, Robert [VerfasserIn]
• Verfasst von: Seelinger, Linus [VerfasserIn]
• Verfasst von: Strehlow, Arne [VerfasserIn]
• Titel: Multilevel spectral domain decomposition
• Verf.angabe: Peter Bastian, Robert Scheichl, Linus Seelinger, and Arne Strehlow
• E-Jahr: 2023
• Jahr: Jun 2023
• Umfang: 26 S.
• Illustrationen: Illustrationen
• Fussnoten: Online veröffentlicht: 31. January 2022 ; Gesehen am 20.11.2023
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on scientific computing
• Ort Quelle: Philadelphia, Pa. : SIAM, 1993
• Jahr Quelle: 2023
• Band/Heft Quelle: 45(2023), 3 vom: Juni, Seite S1-S26
• ISSN Quelle: 1095-7197
• DOI: doi:10.1137/21M1427231
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1870638581

Abstract

Highly heterogeneous, anisotropic coefficients, e.g., in the simulation of carbon-Fiber composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer from severe memory requirements and limited parallel scalability, while iterative solvers in general lack robustness. Two-level spectral domain decomposition methods can provide such robustness for symmetric positive definite linear systems by using coarse spaces based on independent generalized eigenproblems in the subdomains. Rigorous condition number bounds are independent of mesh size, number of subdomains, and coefficient contrast. However, their parallel scalability is still limited by the fact that (in order to guarantee robustness) the coarse problem is solved via a direct method. In this paper, we introduce a multilevel variant in the context of subspace correction methods and provide a general convergence theory for its robust convergence for abstract, elliptic variational problems. Assumptions of the theory are verified for conforming as well as for discontinuous Galerkin methods applied to a scalar diffusion problem. Numerical results illustrate the performance of the method for two- and three-dimensional problems and for various discretization schemes, in the context of scalar diffusion and linear elasticity.