Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology

In this paper we analyze in detail the spectral properties of the block-triangular preconditioner introduced by Gerardo-Giorda et al. [J. Comput. Phys., 228 (2009), pp. 3625-3639] for the Bidomain system in non-symmetric form. We show that the conditioning of the preconditioned problem is bounded in...

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Detalles Bibliográficos
Autores: Gerardo-Giorda, L., Mirabella, L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/403
Acceso en línea:http://hdl.handle.net/20.500.11824/403
Access Level:acceso abierto
Palabra clave:Bidomain system
Electrocardiology
Finite elements
Preconditioning
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spelling Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiologyGerardo-Giorda, L.Mirabella, L.Bidomain systemElectrocardiologyFinite elementsPreconditioningIn this paper we analyze in detail the spectral properties of the block-triangular preconditioner introduced by Gerardo-Giorda et al. [J. Comput. Phys., 228 (2009), pp. 3625-3639] for the Bidomain system in non-symmetric form. We show that the conditioning of the preconditioned problem is bounded in the Fourier space independently of the frequency variable, ensuring quasi-optimality with respect to the mesh size. We derive an explicit formula to optimize the preconditioner performance by identifying a parameter that depends only on the coefficients of the problem and is easy to compute. We provide numerical tests in three dimensions that confirm the optimality of the parameter and the substantial independence of the mesh size. Copyright201720172012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/403reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84870768896&partnerID=40&md5=b5a4c95b9ac4515028057eb621130615Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/4032026-06-19T12:47:47Z
dc.title.none.fl_str_mv Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
title Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
spellingShingle Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
Gerardo-Giorda, L.
Bidomain system
Electrocardiology
Finite elements
Preconditioning
title_short Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
title_full Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
title_fullStr Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
title_full_unstemmed Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
title_sort Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
dc.creator.none.fl_str_mv Gerardo-Giorda, L.
Mirabella, L.
author Gerardo-Giorda, L.
author_facet Gerardo-Giorda, L.
Mirabella, L.
author_role author
author2 Mirabella, L.
author2_role author
dc.subject.none.fl_str_mv Bidomain system
Electrocardiology
Finite elements
Preconditioning
topic Bidomain system
Electrocardiology
Finite elements
Preconditioning
description In this paper we analyze in detail the spectral properties of the block-triangular preconditioner introduced by Gerardo-Giorda et al. [J. Comput. Phys., 228 (2009), pp. 3625-3639] for the Bidomain system in non-symmetric form. We show that the conditioning of the preconditioned problem is bounded in the Fourier space independently of the frequency variable, ensuring quasi-optimality with respect to the mesh size. We derive an explicit formula to optimize the preconditioner performance by identifying a parameter that depends only on the coefficients of the problem and is easy to compute. We provide numerical tests in three dimensions that confirm the optimality of the parameter and the substantial independence of the mesh size. Copyright
publishDate 2012
dc.date.none.fl_str_mv 2012
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/403
url http://hdl.handle.net/20.500.11824/403
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
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
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instname_str Basque Center for Applied Mathematics (BCAM)
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