Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Kühn, Martin Joachim (2018). Local spectra of adaptive domain decomposition methods. Technical Report.

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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 {\color{blue}sophisticated but more expensive} harmonic extensions or deluxe-scaling can reduce the number of bad eigenvalues.

Item Type: Preprints, Working Papers or Reports (Technical Report)
Creators:
CreatorsEmailORCID
Heinlein, Alexanderalexander.heinlein@uni-koeln.deUNSPECIFIED
Klawonn, Axelaxel.klawonn@uni-koeln.deorcid.org/0000-0003-4765-7387
Kühn, Martin Joachimmartin.kuehn@uni-koeln.deUNSPECIFIED
URN: urn:nbn:de:hbz:38-90194
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2018,10
Subjects: Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
adaptive coarse spacesEnglish
GDSWEnglish
ACMSEnglish
overlapping SchwarzEnglish
FETI-1English
FETI-DPEnglish
BDDCEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Central Institutions / Interdisciplinary Research Centers > Center for Data and Simulation Science
Language: English
Date: 16 November 2018
URI: http://kups.ub.uni-koeln.de/id/eprint/9019

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