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 (2018). MULTISCALE COARSE SPACES FOR OVERLAPPING SCHWARZ METHODS BASED ON THE ACMS SPACE IN 2D. Electron. Trans. Numer. Anal., 48. S. 156 - 183. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

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Abstract

Two-level overlapping Schwarz domain decomposition methods for second-order elliptic problems in two dimensions are proposed using coarse spaces constructed from the Approximate Component Mode Synthesis (ACMS) multiscale discretization approach. These coarse spaces are based on eigenvalue problems using Schur complements on subdomain edges. It is then shown that the convergence of the resulting preconditioned Krylov method can be controlled by a user-specified tolerance and thus can be made independent of heterogeneities in the coefficient of the partial differential equation. The relations of this new approach to other known adaptive coarse space approaches for overlapping Schwarz methods are also discussed. Compared to one of the competing adaptive approaches, the new coarse space can be significantly smaller. Compared to other competing approaches, the eigenvalue problems are significantly cheaper to solve, i.e., the dimension of the eigenvalue problems is minimal among the competing adaptive approaches under consideration. Our local eigenvalue problems can be solved using one iteration of LobPCG for essentially the same cost as a Cholesky-decomposition of a Schur complement on a subdomain edge.

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:38-199497
DOI:	10.1553/etna_vol48s156
Journal or Publication Title:	Electron. Trans. Numer. Anal.
Volume:	48
Page Range:	S. 156 - 183
Date:	2018
Publisher:	KENT STATE UNIVERSITY
Place of Publication:	KENT
ISSN:	1068-9613
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 FINITE-ELEMENT-METHOD; DOMAIN DECOMPOSITION PRECONDITIONERS; FETI-DP; PARALLEL IMPLEMENTATION; ELLIPTIC PROBLEMS; BDDC; ALGORITHMS; FRAMEWORK; FLOWS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19949