Parallelizing the Kolmogorov-Fokker-Planck Equation

We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker-Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR p...

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Detalles Bibliográficos
Autores: Gerardo-Giorda, L., Tran, M.-B.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/277
Acceso en línea:http://hdl.handle.net/20.500.11824/277
Access Level:acceso abierto
Palabra clave:Domain decomposition
Schwarz waveform relaxation methods
optimized Schwarz
Kolmogorov equation
Fokker–Plank equation
kinetic equations
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spelling Parallelizing the Kolmogorov-Fokker-Planck EquationGerardo-Giorda, L.Tran, M.-B.Domain decompositionSchwarz waveform relaxation methodsoptimized SchwarzKolmogorov equationFokker–Plank equationkinetic equationsWe design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker-Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR procedures decompose the spatio- temporal computational domain into subdomains and solve (in parallel) subproblems, that are coupled through suitable conditions at the interfaces to recover the solution of the global problem. We consider coupling conditions of both Dirichlet (Classical SWR) and Robin (Optimized SWR) types. We prove well-posedeness of the schemes subproblems and convergence for the proposed algorithms. We corroborate our findings with some numerical tests.201620162015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/277reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttp://www.esaim-m2an.org/articles/m2an/abs/2015/02/m2an140038-s/m2an140038-s.htmlinfo:eu-repo/grantAgreement/EC/FP7/246775info:eu-repo/grantAgreement/MICINN//MTM2011-29306-C02-01Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/2772026-06-19T12:47:47Z
dc.title.none.fl_str_mv Parallelizing the Kolmogorov-Fokker-Planck Equation
title Parallelizing the Kolmogorov-Fokker-Planck Equation
spellingShingle Parallelizing the Kolmogorov-Fokker-Planck Equation
Gerardo-Giorda, L.
Domain decomposition
Schwarz waveform relaxation methods
optimized Schwarz
Kolmogorov equation
Fokker–Plank equation
kinetic equations
title_short Parallelizing the Kolmogorov-Fokker-Planck Equation
title_full Parallelizing the Kolmogorov-Fokker-Planck Equation
title_fullStr Parallelizing the Kolmogorov-Fokker-Planck Equation
title_full_unstemmed Parallelizing the Kolmogorov-Fokker-Planck Equation
title_sort Parallelizing the Kolmogorov-Fokker-Planck Equation
dc.creator.none.fl_str_mv Gerardo-Giorda, L.
Tran, M.-B.
author Gerardo-Giorda, L.
author_facet Gerardo-Giorda, L.
Tran, M.-B.
author_role author
author2 Tran, M.-B.
author2_role author
dc.subject.none.fl_str_mv Domain decomposition
Schwarz waveform relaxation methods
optimized Schwarz
Kolmogorov equation
Fokker–Plank equation
kinetic equations
topic Domain decomposition
Schwarz waveform relaxation methods
optimized Schwarz
Kolmogorov equation
Fokker–Plank equation
kinetic equations
description We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker-Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR procedures decompose the spatio- temporal computational domain into subdomains and solve (in parallel) subproblems, that are coupled through suitable conditions at the interfaces to recover the solution of the global problem. We consider coupling conditions of both Dirichlet (Classical SWR) and Robin (Optimized SWR) types. We prove well-posedeness of the schemes subproblems and convergence for the proposed algorithms. We corroborate our findings with some numerical tests.
publishDate 2015
dc.date.none.fl_str_mv 2015
2016
2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/277
url http://hdl.handle.net/20.500.11824/277
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://www.esaim-m2an.org/articles/m2an/abs/2015/02/m2an140038-s/m2an140038-s.html
info:eu-repo/grantAgreement/EC/FP7/246775
info:eu-repo/grantAgreement/MICINN//MTM2011-29306-C02-01
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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repository.mail.fl_str_mv
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