Universität zu Köln

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Widlund, Olof B. (2022). ADAPTIVE GDSW COARSE SPACES OF REDUCED DIMENSION FOR OVERLAPPING SCHWARZ METHODS. SIAM J. Sci. Comput., 44 (3). S. A1176 - 29. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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Abstract

A new reduced-dimension adaptive generalized Dryja-Smith-Widlund (GDSW) overlapping Schwarz method for linear second-order elliptic problems in three dimensions is introduced. It is robust with respect to large contrasts of the coefficients of the partial differential equations. The condition number bound of the new method is shown to be independent of the coefficient contrast and only dependent on a user-prescribed tolerance. The interface of the nonoverlapping domain decomposition is partitioned into nonoverlapping patches. The new coarse space is obtained by selecting a few eigenvectors of certain local eigenproblems which are defined on these patches. These eigenmodes are energy-minimally extended to the interior of the nonoverlapping subdomains and added to the coarse space. By using a new interface decomposition, the reduced-dimension adaptive GDSW overlapping Schwarz method usually has a smaller coarse space than existing GDSW and adaptive GDSW domain decomposition methods. A robust condition number estimate is proven for the new reduced-dimension adaptive GDSW method which is also valid for existing adaptive GDSW methods. Numerical results for the equations of isotropic linear elasticity in three dimensions confirming the theoretical findings are presented.

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 orcid.org/0000-0002-8769-2235 UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED Widlund, Olof B. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-675835
DOI:	10.1137/20M1364540
Journal or Publication Title:	SIAM J. Sci. Comput.
Volume:	44
Number:	3
Page Range:	S. A1176 - 29
Date:	2022
Publisher:	SIAM PUBLICATIONS
Place of Publication:	PHILADELPHIA
ISSN:	1095-7197
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DOMAIN DECOMPOSITION PRECONDITIONERS; PRIMAL FETI METHODS; ELLIPTIC PROBLEMS; PARALLEL IMPLEMENTATION; BDDC; DP; ALGORITHMS; TRANSFORMATION; SUBDOMAINS Multiple languages Mathematics, Applied Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67583