Universität zu Köln

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235 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:	Creators Email ORCID ORCID Put Code Heinlein, Alexander alexander.heinlein@uni-koeln.de UNSPECIFIED UNSPECIFIED Klawonn, Axel axel.klawonn@uni-koeln.de orcid.org/0000-0003-4765-7387 UNSPECIFIED Knepper, Jascha jascha.knepper@uni-koeln.de orcid.org/0000-0002-8769-2235 UNSPECIFIED Rheinbach, Oliver oliver.rheinbach@math.tu-freiberg.de UNSPECIFIED UNSPECIFIED
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
Date:	15 October 2018
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language domain decomposition English multiscale English GDSW English overlapping Schwarz English adaptive coarse spaces English
URI:	http://kups.ub.uni-koeln.de/id/eprint/8756