Universität zu Köln

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2019). ADAPTIVE GDSW COARSE SPACES FOR OVERLAPPING SCHWARZ METHODS IN THREE DIMENSIONS. SIAM J. Sci. Comput., 41 (5). S. A3045 - 28. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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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. Indeed, the condition number only depends on a user-prescribed tolerance. The 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:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander UNSPECIFIED orcid.org/0000-0003-1578-8104 UNSPECIFIED Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED Knepper, Jascha UNSPECIFIED UNSPECIFIED UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-160407
DOI:	10.1137/18M1220613
Journal or Publication Title:	SIAM J. Sci. Comput.
Volume:	41
Number:	5
Page Range:	S. A3045 - 28
Date:	2019
Publisher:	SIAM PUBLICATIONS
Place of Publication:	PHILADELPHIA
ISSN:	1095-7197
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DOMAIN DECOMPOSITION PRECONDITIONERS; FINITE-ELEMENT-METHOD; PRIMAL FETI METHODS; ELLIPTIC PROBLEMS; PARALLEL IMPLEMENTATION; DP; BDDC; ALGORITHMS; TRANSFORMATION; SUBDOMAINS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/16040