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Local spectra of adaptive domain decomposition methods

Heinlein, Alexander and Klawonn, Axel and Kühn, Martin Joachim (2020) Local spectra of adaptive domain decomposition methods. In: Domain Decomposition Methods in Science and Engineering XXV. The twenty-fifth international domain decomposition conference, St. Johns, Newfoundland, Canada.

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Abstract

We compare the spectra of local generalized eigenvalue problems in different adaptive coarse spaces for overlapping and nonoverlapping domain decomposition methods. In particular, we compare the AGDSW (Adaptive Generalized Dryja--Smith--Widlund), the OS-ACMS (Overlapping Schwarz-Approximate Component Mode Synthesis), and the SHEM (Spectral Harmonically Enriched Multiscale) coarse spaces for overlapping Schwarz methods, the GenEO (Generalized Eigenproblems in the Overlaps) coarse space for FETI-1 and BDD methods, and two approaches based on estimates for the $P_D$ operator for FETI-DP and BDDC methods. Therefore, we consider eight different two-dimensional coefficient functions with jumps ranging from simple channels to a realistic microstructure of a dual-phase steel. We observe significant differences in the width of the gap between good and bad eigenvalues depending on the coefficient distribution. In addition to that, eigenvalue problems involving sophisticated but more expensive harmonic extensions or deluxe-scaling can reduce the number of bad eigenvalues.

Item URL in elib:https://elib.dlr.de/138644/
Document Type:Conference or Workshop Item (Speech)
Title:Local spectra of adaptive domain decomposition methods
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Heinlein, Alexanderalexander.heinlein (at) uni-koeln.dehttps://orcid.org/0000-0003-1578-8104
Klawonn, Axelaxel.klawonn (at) uni-koeln.deUNSPECIFIED
Kühn, Martin JoachimMartin.Kuehn (at) dlr.dehttps://orcid.org/0000-0002-0906-6984
Date:25 October 2020
Journal or Publication Title:Domain Decomposition Methods in Science and Engineering XXV
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:No
Status:Published
Keywords:Domain decomposition, linear systems, preconditioning, adaptive, solver
Event Title:The twenty-fifth international domain decomposition conference
Event Location:St. Johns, Newfoundland, Canada
Event Type:international Conference
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Vorhaben SISTEC (old)
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology
Institute for Software Technology > High-Performance Computing
Deposited By: Kühn, Martin Joachim
Deposited On:07 Dec 2020 09:50
Last Modified:11 Dec 2020 10:46

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