A multigrid-like algorithm for probabilistic domain decomposition

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• 作者：Francisco Bernal^a ; ^c ; ^{francisco.bernal@ist.utl.pt" class="auth_mail" title="E-mail the corresponding author} ; Juan A. Acebró ; n^b ; ^a ; ^{juan.acebron@ist.utl.pt" class="auth_mail" title="E-mail the corresponding author}
• 关键词：PDD ; Domain decomposition ; Scalability ; High-performance supercomputing ; Variance reduction ; Feynman&ndash ; Kac formula
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：72
• 期：7
• 页码：1790-1810
• 全文大小：1379 K

文摘

We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control variates in order to reduce the Monte Carlo error of the following iterates—resulting in an overall acceleration of PDD for a given error tolerance. The key feature of the proposed algorithm is the ability to approximately predict the speedup with little computational overhead and in parallel. Besides, the theoretical framework allows to explore other aspects of PDD, such as stability. One numerical example is worked out, yielding an improvement between one and two orders of magnitude over the previous version of PDD.