Optimized schwarz methods for the bidomain system in electrocardiology

The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solu...

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Detalles Bibliográficos
Autores: Gerardo-Giorda, L., Perego, M.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/402
Acceso en línea:http://hdl.handle.net/20.500.11824/402
Access Level:acceso abierto
Palabra clave:Computational electrocardiology
Domain decomposition
Optimized schwarz methods
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spelling Optimized schwarz methods for the bidomain system in electrocardiologyGerardo-Giorda, L.Perego, M.Computational electrocardiologyDomain decompositionOptimized schwarz methodsThe propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in accelerating the convergence of such algorithms. The latter are based on interface matching conditions more efficient than the classical Dirichlet or Neumann ones. In this paper we analyze an Optimized Schwarz approach for the numerical solution of the Bidomain problem. We assess the convergence of the iterative method by means of Fourier analysis, and we investigate the parameter optimization in the interface conditions. Numerical results in 2D and 3D are given to show the effectiveness of the method.201720172013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/402reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84996128889&doi=10.1051%2fm2an%2f2012040&partnerID=40&md5=dfc1e43e1451a0a0a70b69a6586933b7Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/4022026-06-19T12:47:47Z
dc.title.none.fl_str_mv Optimized schwarz methods for the bidomain system in electrocardiology
title Optimized schwarz methods for the bidomain system in electrocardiology
spellingShingle Optimized schwarz methods for the bidomain system in electrocardiology
Gerardo-Giorda, L.
Computational electrocardiology
Domain decomposition
Optimized schwarz methods
title_short Optimized schwarz methods for the bidomain system in electrocardiology
title_full Optimized schwarz methods for the bidomain system in electrocardiology
title_fullStr Optimized schwarz methods for the bidomain system in electrocardiology
title_full_unstemmed Optimized schwarz methods for the bidomain system in electrocardiology
title_sort Optimized schwarz methods for the bidomain system in electrocardiology
dc.creator.none.fl_str_mv Gerardo-Giorda, L.
Perego, M.
author Gerardo-Giorda, L.
author_facet Gerardo-Giorda, L.
Perego, M.
author_role author
author2 Perego, M.
author2_role author
dc.subject.none.fl_str_mv Computational electrocardiology
Domain decomposition
Optimized schwarz methods
topic Computational electrocardiology
Domain decomposition
Optimized schwarz methods
description The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in accelerating the convergence of such algorithms. The latter are based on interface matching conditions more efficient than the classical Dirichlet or Neumann ones. In this paper we analyze an Optimized Schwarz approach for the numerical solution of the Bidomain problem. We assess the convergence of the iterative method by means of Fourier analysis, and we investigate the parameter optimization in the interface conditions. Numerical results in 2D and 3D are given to show the effectiveness of the method.
publishDate 2013
dc.date.none.fl_str_mv 2013
2017
2017
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url http://hdl.handle.net/20.500.11824/402
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
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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
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