Efficient Variants of the Vertex Space Domain Decomposition Algorithm

Autor:	Jian-Ping Shao, Tarek P. Mathew, Tony F. Chan
Rok vydání:	1994
Předmět:	Discrete mathematics Computational Mathematics Elliptic curve Rate of convergence Preconditioner Applied Mathematics Schur complement Domain decomposition methods Decomposition method (constraint satisfaction) Algebraic number Edge space Mathematics
Zdroj:	SIAM Journal on Scientific Computing. 15:1349-1374
ISSN:	1095-7197 1064-8275
DOI:	10.1137/0915082
Popis:	Several variants of the vertex space algorithm of Smith for two-dimensional elliptic problems are described. The vertex space algorithm is a domain decomposition method based on nonoverlapping subregions, in which the reduced Schur complement system on the interface is solved using a generalized block Jacobi-type preconditioner, with the blocks corresponding to the vertex space, edges, and a coarse grid. Two kinds of approximations are considered for the edge and vertex space subblocks, one based on Fourier approximation, and another based on an algebraic probing technique in which sparse approximations to these subblocks are computed. Our motivation is to improve the efficiency of the algorithm without sacrificing the optimal convergence rate. Numerical and theoretical results on the performance of these algorithms, including variants of an algorithm of Bramble, Pasciak, and Schatz are presented.
Databáze:	OpenAIRE
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