A multigrid-like algorithm for probabilistic domain decomposition

Detalhes bibliográficos
Autor(a) principal: Bernal, F.
Data de Publicação: 2016
Outros Autores: Acebron, J. A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/13167
Resumo: 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.
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spelling A multigrid-like algorithm for probabilistic domain decompositionPDDDomain decompositionScalabilityHigh-performance supercomputingVariance reductionFeynman–Kac formulaWe 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.Pergamon/Elsevier2017-05-02T14:00:46Z2016-01-01T00:00:00Z20162019-04-23T11:54:23Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/13167eng0898-122110.1016/j.camwa.2016.07.030Bernal, F.Acebron, J. A.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-09T17:48:59Zoai:repositorio.iscte-iul.pt:10071/13167Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:23:58.752083Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A multigrid-like algorithm for probabilistic domain decomposition
title A multigrid-like algorithm for probabilistic domain decomposition
spellingShingle A multigrid-like algorithm for probabilistic domain decomposition
Bernal, F.
PDD
Domain decomposition
Scalability
High-performance supercomputing
Variance reduction
Feynman–Kac formula
title_short A multigrid-like algorithm for probabilistic domain decomposition
title_full A multigrid-like algorithm for probabilistic domain decomposition
title_fullStr A multigrid-like algorithm for probabilistic domain decomposition
title_full_unstemmed A multigrid-like algorithm for probabilistic domain decomposition
title_sort A multigrid-like algorithm for probabilistic domain decomposition
author Bernal, F.
author_facet Bernal, F.
Acebron, J. A.
author_role author
author2 Acebron, J. A.
author2_role author
dc.contributor.author.fl_str_mv Bernal, F.
Acebron, J. A.
dc.subject.por.fl_str_mv PDD
Domain decomposition
Scalability
High-performance supercomputing
Variance reduction
Feynman–Kac formula
topic PDD
Domain decomposition
Scalability
High-performance supercomputing
Variance reduction
Feynman–Kac formula
description 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.
publishDate 2016
dc.date.none.fl_str_mv 2016-01-01T00:00:00Z
2016
2017-05-02T14:00:46Z
2019-04-23T11:54:23Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10071/13167
url http://hdl.handle.net/10071/13167
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0898-1221
10.1016/j.camwa.2016.07.030
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Pergamon/Elsevier
publisher.none.fl_str_mv Pergamon/Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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