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首页> 美国政府科技报告 >Domain Decomposition Preconditioners for Elliptic Problems in Two and Three Dimensions: First Approach
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Domain Decomposition Preconditioners for Elliptic Problems in Two and Three Dimensions: First Approach

机译：二维和三维椭圆问题的区域分解预处理器：第一种方法

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In this talk, we shall describe some domain decomposition preconditioners for elliptic boundary value problems in two and three dimensions. We consider the case where more than two subdomains meet at an interior point of the original domain; this allows a subdivision into an arbitrary number of subdomains without the deterioration of the iterative convergence rates of the resulting algorithms. The described preconditioners (for both two and three dimensional applications) result in preconditioned systems whose condition number growth is bounded by c(1 + ln sup 2 (d/h)). Here h is the mesh size and d is roughly the size of the largest subdomain. We finally give a technique which utilizes the earlier described methods to derive even more efficient preconditioners. This technique leads to preconditioned systems whose condition number remains bounded independently of the number of unknowns. 11 refs.

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