Fourier and probe variants of the vertex space domain decomposition algorithm

Tony F. Chan*, Tarek P. Mathew, Jian Ping Shao

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

The vertex space algorithm of Smith is a domain decomposition method for two dimensional elliptic problems based on non-overlapping 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. In this paper, we describe several variants of this algorithm derived from using two kinds of approximations for the edge and vertex space sub-blocks, one based on Fourier approximation, and another based on an algebraic probing technique in which sparse approximations to these sub-blocks are computed. Our motivation is to improve efficiency of the algorithm without sacrificing the optimal convergence rate. Numerical and theoretical results on the performance of these algorithms are presented.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods for Partial Differential Equations
PublisherPubl by Soc for Industrial & Applied Mathematics Publ
Pages236-249
Number of pages14
ISBN (Print)0898712882
StatePublished - Dec 1 1992
Externally publishedYes
EventFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA
Duration: May 6 1991May 8 1991

Conference

ConferenceFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
CityNorfolk, VA, USA
Period05/6/9105/8/91

ASJC Scopus subject areas

  • Engineering(all)

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