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Title: A multigrid-like algorithm for probabilistic domain decomposition
Authors: Bernal, F.
Acebron, J. A.
Keywords: PDD
Domain decomposition
High-performance supercomputing
Variance reduction
Feynman–Kac formula
Issue Date: 2016
Publisher: Pergamon/Elsevier
Abstract: 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.
Peer reviewed: yes
DOI: 10.1016/j.camwa.2016.07.030
ISSN: 0898-1221
Accession number: WOS:000384851700003
Appears in Collections:CTI-RI - Artigos em revistas científicas internacionais com arbitragem científica

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