A New Coarse Grid Correction for RAS/AS
A New Coarse Grid Correction for RAS/AS
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DOI：
10.1007/978-3-319-05789-7_24
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发表时间：
2014
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影响因子：
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通讯作者：
M. Gander;L. Halpern;Kévin Santugini Repiquet
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文献类型：
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作者：
M. Gander;L. Halpern;Kévin Santugini Repiquet
椭圆问题的区域分解方法需要一个可伸缩的粗空间，而好的粗空间是目前研究的一个活跃领域。本文针对受限加性Schwarz方法(RAS)提出了一种新的粗空间。粗空间通过粗网格节点的特定放置来适应RAS迭代的不连续性质。我们首先解释了一维模型问题的概念，然后将二维分解的方法推广到矩形子区域。数值实验表明，这种新的粗网格比经典的加性Schwarz(AS)方法更有效。
Domain decomposition methods for elliptic problems need a coarse space in order to be scalable, and good coarse spaces are currently an active area of research. We propose here a new coarse space for the restricted additive Schwarz method (RAS). The coarse space is adapted to the discontinuous nature of the iterates of RAS, by specific placement of the coarse grid nodes. We explain the idea first for a one dimensional model problem, and then generalize the approach to two dimensional decompositions into rectangular subdomains. We show with numerical experiments that the new coarse grid is much more effective than classical ones, also for the more classical additive Schwarz (AS) method.