Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuehn, Martin and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2018). ADAPTIVE FETI-DP AND BDDC METHODS WITH A GENERALIZED TRANSFORMATION OF BASIS FOR HETEROGENEOUS PROBLEMS. Electron. Trans. Numer. Anal., 49. S. 1 - 28. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

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Abstract

In FETI-DP (Finite Element Tearing and Interconnecting) and BDDC (Balancing Domain Decomposition by Constraints) domain decomposition methods, the transformation-of-basis approach is used to improve the convergence by combining the local assembly with a change of basis. Suitable basis vectors can be constructed by the recently introduced adaptive coarse space approaches. The resulting FETI-DP and BDDC methods fulfill a condition number bound independent of heterogeneities in the problem. The adaptive method with a transformation of basis presented here builds on a recently introduced adaptive FETI-DP approach for elliptic problems in three dimensions and uses a coarse space constructed from solving small, local eigenvalue problems on closed faces and on a small number of edges. In contrast to our earlier work on adaptive FETI-DP, the coarse space correction is not implemented by using balancing (or deflation), which requires the use of an exact coarse space solver, but by using local transformations. This will make it simpler to extend the method to a large number of subdomains and large supercomputers. The recently established theory of a generalized transformation-of-basis approach yields a condition number estimate for the preconditioned operator that is independent of jumps of the coefficients across and inside subdomains when using the local adaptive constraints. It is shown that all results are also valid for BDDC. Numerical results are presented in three dimensions for FETI-DP and BDDC. We also provide a comparison of different scalings, i.e., deluxe, rho, stiffness, and multiplicity for our adaptive coarse space in 3D.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED Kuehn, Martin UNSPECIFIED UNSPECIFIED UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-199466
DOI:	10.1553/etna_vol49s1
Journal or Publication Title:	Electron. Trans. Numer. Anal.
Volume:	49
Page Range:	S. 1 - 28
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 DOMAIN DECOMPOSITION PRECONDITIONERS; ITERATIVE SUBSTRUCTURING METHODS; 3-DIMENSIONAL ELLIPTIC PROBLEMS; COARSE SPACES; STRUCTURAL MECHANICS; PRIMAL CONSTRAINTS; MULTISCALE FLOWS; DEFLATION; CONNECTIONS; SELECTION Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19946