Domain Decomposition Methods for Problems with Partial Refinement

Autor:	Joseph E. Pasciak, Rossen R. Parashkevov, Richard E. Ewing, James H. Bramble
Rok vydání:	1992
Předmět:	Discrete system Algebraic equation Local mesh refinement Mathematical optimization Development (topology) Rate of convergence Applied mathematics Domain decomposition methods Boundary value problem Mathematics
Zdroj:	SIAM Journal on Scientific and Statistical Computing. 13:397-410
ISSN:	2168-3417 0196-5204
DOI:	10.1137/0913021
Popis:	In this paper, a flexible mesh refinement strategy for the approximation of solutions of elliptic boundary value problems is considered. The main purpose of the paper is the development of preconditioners for the resulting discrete system of algebraic equations. These techniques lead to efficient computational procedures in serial as well as parallel computing environments. The preconditioners are based on overlapping domain decomposition and involve solving (or preconditioning) subproblems on regular subregions. It is proven that the iteration schemes converge to the discrete solution at a rate which is independent of the mesh parameters in the case of two spatial dimensions. The estimates proved for the iterative convergence rate in three dimensions are somewhat weaker. The results of numerical experiments illustrating the theory are also presented.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::81ec11af6b77922d9e173483e4b9bc4e https://doi.org/10.1137/0913021 Zobrazit plný text záznamu