A multigrid-like algorithm for probabilistic domain decomposition

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dc.contributor.author Bernal Martínez, Francisco Manuel
dc.contributor.author Acebrón, Juan Antonio
dc.date.accessioned 2021-03-11T09:03:37Z
dc.date.available 2021-03-11T09:03:37Z
dc.date.issued 2016-10
dc.identifier.bibliographicCitation Bernal, F., Acebrón, J. A. (2016). A multigrid-like algorithm for probabilistic domain decomposition. Computers & Mathematics with Applications, 72(7), 1790–1810.
dc.identifier.issn 0898-1221
dc.identifier.uri http://hdl.handle.net/10016/32096
dc.description.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.
dc.description.sponsorship This work was supported by Portuguese national funds through Fundação para a Ciência e a Tecnologia under grants UID/CEC/50021/2013 and PTDC/EIA-CCO/098910/2008. FB also acknowledges FCT funding under grant SFRH/BPD/79986/2011.
dc.format.extent 21
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2016 Elsevier Ltd.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other PDD
dc.subject.other Domain decomposition
dc.subject.other Scalability
dc.subject.other High-performance supercomputing
dc.subject.other Variance reduction
dc.subject.other Feynman-Kac formula
dc.title A multigrid-like algorithm for probabilistic domain decomposition
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.camwa.2016.07.030
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1790
dc.identifier.publicationissue 7
dc.identifier.publicationlastpage 1810
dc.identifier.publicationtitle Computers & Mathematics with Applications
dc.identifier.publicationvolume 72
dc.identifier.uxxi AR/0000026514
dc.affiliation.dpto UC3M. Departamento de Matemáticas
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