A convergence theory of multilevel additive Schwarz methods on unstructured meshes
Publication in refereed journal

香港中文大學研究人員

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摘要We develop a convergence theory for two level and multilevel additive Schwarz domain decomposition methods for elliptic and parabolic problems on general unstructured meshes in two and three dimensions. The coarse and fine grids are assumed only to be shape regular, and the domains formed by the coarse and fine grids need not be identical. In this general setting, our convergence theory leads to completely local bounds for the condition numbers of two level additive Schwarz methods, which imply that these condition numbers are optimal, or independent of fine and coarse mesh sizes and subdomain sizes if the overlap amount of a subdomain with its neighbors varies proportionally to the subdomain size. In particular, we will show that additive Schwarz algorithms are still very efficient for non-selfadjoint parabolic problems with only symmetric, positive definite solvers both for local subproblems and for the global coarse problem. These conclusions for elliptic and parabolic problems improve our earlier results in [12, 15, 16]. Finally, the convergence theory is applied to multilevel additive Schwarz algorithms. Under some very weak assumptions on the fine mesh and coarser meshes, e.g., no requirements oil the relation between neighboring coarse level meshes, we are able to derive a condition number bound of the order O(rho(2)L(2)), where rho=max,(1 less than or equal to l less than or equal to L)(h(l)+h(l-1))/delta(l), h(l) is the element size of the lth level mesh, delta(l) the overlap of subdomains on the lth level mesh, and L the number of mesh levels.
著者Chan TF, Zou J
期刊名稱Numerical Algorithms
出版年份1996
月份1
日期1
卷號13
期次3-4
出版社BALTZER SCI PUBL BV
頁次365 - 398
國際標準期刊號1017-1398
電子國際標準期刊號1572-9265
語言英式英語
關鍵詞convergence; multilevel additive methods; unstructured meshes
Web of Science 學科類別Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED

上次更新時間 2020-20-11 於 01:52