Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Radtke, Patrick and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2016). A COMPARISON OF ADAPTIVE COARSE SPACES FOR ITERATIVE SUBSTRUCTURING IN TWO DIMENSIONS. Electron. Trans. Numer. Anal., 45. S. 75 - 107. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Full text not available from this repository.

Abstract

The convergence rate of iterative substructuring methods generally deteriorates when large discontinuities occur in the coefficients of the partial differential equations to be solved. In dual-primal Finite Element Tearing and Interconnecting (FETI-DP) and Balancing Domain Decomposition by Constraints (BDDC) methods, sophisticated scalings, e.g., deluxe scaling, can improve the convergence rate when large coefficient jumps occur along or across the interface. For more general cases, additional information has to be added to the coarse space. One possibility is to enhance the coarse space by local eigenvectors associated with subsets of the interface, e.g., edges. At the center of the condition number estimates for FETI-DP and BDDC methods is an estimate related to the P-D-operator which is defined by the product of the transpose of the scaled jump operator B-D(T) and the jump operator B of the FETI-DP algorithm. Some enhanced algorithms immediately bring the P-D-operator into focus using related local eigenvalue problems, and some replace a local extension theorem and local Poincare inequalities by appropriate local eigenvalue problems. Three different strategies, suggested by different authors, are discussed for adapting the coarse space together with suitable scalings. Proofs and numerical results comparing the methods are provided.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED Radtke, Patrick UNSPECIFIED UNSPECIFIED UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-288112
Journal or Publication Title:	Electron. Trans. Numer. Anal.
Volume:	45
Page Range:	S. 75 - 107
Date:	2016
Publisher:	KENT STATE UNIVERSITY
Place of Publication:	KENT
ISSN:	1068-9613
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DOMAIN DECOMPOSITION PRECONDITIONERS; PRIMAL FETI METHODS; LINEAR ELASTICITY; DP METHODS; BDDC; COEFFICIENTS; SUBDOMAINS; ALGORITHM; MATRICES Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28811