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Equivalent operator preconditioning for elliptic problems
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SYSNO ASEP 0328616 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Equivalent operator preconditioning for elliptic problems Author(s) Axelsson, Owe (UGN-S) RID
Karátson, J. (HU)Number of authors 2 Source Title Numerical Algorithms. - : Springer - ISSN 1017-1398
Roč. 50, č. 3 (2009), s. 297-380Number of pages 84 s. Publication form www - www Language eng - English Country NL - Netherlands Keywords Elliptic problem ; Conjugate gradient method ; preconditioning ; equivalent operators ; compact operators Subject RIV BA - General Mathematics CEZ AV0Z30860518 - UGN-S (2005-2011) UT WOS 000264495700005 DOI 10.1007/s11075-008-9233-4 Annotation The numerial solution of linear elliptic partial differential equations most often involves a finite element or finite difference discretization. To preserve sparsity, the arising system is normally solved using an iterative solution method, commonly a preconditioned conjugate gradient method.Preconditioning is a crucial part of such a solution process. In order to enable the solution of very large-scale systems, it is desirable that the total computational cost will be of optimal order, i.e. proportional to the degrees of freedom of the paaroximation used, which also induces mesh independent convergence of the iteration. This paper surveys the equivalent operator approach, which has proven to provide an efficient general framework to construct such preconditioners. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2010
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