Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Kühn, Martin Joachim ORCID: 0000-0002-0906-6984 (2018). Local spectra of adaptive domain decomposition methods. Technical Report.


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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 Type: Preprints, Working Papers or Reports (Technical Report)
CreatorsEmailORCIDORCID Put Code
Heinlein, Alexanderalexander.heinlein@uni-koeln.deUNSPECIFIEDUNSPECIFIED
Klawonn, Axelaxel.klawonn@uni-koeln.deorcid.org/0000-0003-4765-7387UNSPECIFIED
Kühn, Martin Joachimmartin.kuehn@uni-koeln.deorcid.org/0000-0002-0906-6984UNSPECIFIED
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
Date: 16 November 2018
Language: English
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects: Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
adaptive coarse spacesEnglish
overlapping SchwarzEnglish
Refereed: No
URI: http://kups.ub.uni-koeln.de/id/eprint/9019


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