Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha and Rheinbach, Oliver (2018). Adaptive GDSW coarse spaces for overlapping Schwarz methods in three dimensions. Technical Report.

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Abstract

A robust two-level overlapping Schwarz method for scalar elliptic model problems with highly varying coefficient functions is introduced. While the convergence of standard coarse spaces may depend strongly on the contrast of the coefficient function, the condition number bound of the new method is independent of the coefficient function. Its coarse space is based on discrete harmonic extensions of vertex, edge, and face interface functions, which are computed from the solutions of corresponding local generalized edge and face eigenvalue problems. The local eigenvalue problems are of the size of the edges and faces of the decomposition, and the eigenvalue problems can be constructed solely from the local subdomain stiffness matrices and the fully assembled global stiffness matrix. The new AGDSW (Adaptive Generalized Dryja-Smith-Widlund) coarse space always contains the classical GDSW coarse space by construction of the generalized eigenvalue problems. Numerical results supporting the theory are presented for several model problems in three dimensions using structured as well as unstructured meshes and unstructured decompositions.

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
Knepper, Jaschajascha.knepper@uni-koeln.deUNSPECIFIED
Rheinbach, Oliveroliver.rheinbach@math.tu-freiberg.deUNSPECIFIED
URN: urn:nbn:de:hbz:38-87560
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2018,5
Subjects: Data processing Computer science
Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
domain decompositionEnglish
multiscaleEnglish
GDSWEnglish
overlapping SchwarzEnglish
adaptive coarse spacesEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Language: English
Date: 15 October 2018
URI: http://kups.ub.uni-koeln.de/id/eprint/8756

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