Boundary corrections on multi-dimensional PDEs

Two new boundary correction techniques are proposed in order to mitigate the order reduction phenomenon associated to the numerical solution of initial boundary value problems for parabolic Partial Differential Equations in arbitrary spatial dimensions with time dependent Dirichlet boundary conditio...

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Detalles Bibliográficos
Autores: Hernández Abreu, Domingo, González Pinto, Severiano, Pérez Rodríguez, María Soledad
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad de La Laguna (ULL)
Repositorio:RIULL. Repositorio Institucional de la Universidad de La Laguna
OAI Identifier:oai:riull.ull.es:915/39061
Acceso en línea:http://riull.ull.es/xmlui/handle/915/39061
Access Level:acceso abierto
Palabra clave:High-dimensional PDEs
Approximate matrix factorization
W-methods
Finite differences
Order reduction
Boundary correction technique
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spelling Boundary corrections on multi-dimensional PDEsHernández Abreu, DomingoGonzález Pinto, SeverianoPérez Rodríguez, María SoledadHigh-dimensional PDEsApproximate matrix factorizationW-methodsFinite differencesOrder reductionBoundary correction techniqueTwo new boundary correction techniques are proposed in order to mitigate the order reduction phenomenon associated to the numerical solution of initial boundary value problems for parabolic Partial Differential Equations in arbitrary spatial dimensions with time dependent Dirichlet boundary conditions. The new techniques are based on the idea of discretizing the PDE problem at the boundary points as similar as possible to that of the interior points of the domain. These new techniques are considered for the time integration with W-methods based on Approximate Matrix Factorization. By suitably modifying the internal stages of the methods on the boundary points, it is illustrated by numerical testing with time dependent boundary conditions that the new boundary correction techniques are able to keep the same accuracy and order of convergence that the method reaches in the case of homogeneous boundary conditions.Análisis MatemáticoGrupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/202420242024info:eu-repo/semantics/articleapplication/pdfhttp://riull.ull.es/xmlui/handle/915/39061reponame:RIULL. Repositorio Institucional de la Universidad de La Lagunainstname:Universidad de La Laguna (ULL)Numerical Algorithms (2024) 96:507–535Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ESoai:riull.ull.es:915/390612026-06-22T13:13:57Z
dc.title.none.fl_str_mv Boundary corrections on multi-dimensional PDEs
title Boundary corrections on multi-dimensional PDEs
spellingShingle Boundary corrections on multi-dimensional PDEs
Hernández Abreu, Domingo
High-dimensional PDEs
Approximate matrix factorization
W-methods
Finite differences
Order reduction
Boundary correction technique
title_short Boundary corrections on multi-dimensional PDEs
title_full Boundary corrections on multi-dimensional PDEs
title_fullStr Boundary corrections on multi-dimensional PDEs
title_full_unstemmed Boundary corrections on multi-dimensional PDEs
title_sort Boundary corrections on multi-dimensional PDEs
dc.creator.none.fl_str_mv Hernández Abreu, Domingo
González Pinto, Severiano
Pérez Rodríguez, María Soledad
author Hernández Abreu, Domingo
author_facet Hernández Abreu, Domingo
González Pinto, Severiano
Pérez Rodríguez, María Soledad
author_role author
author2 González Pinto, Severiano
Pérez Rodríguez, María Soledad
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
Grupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/
dc.subject.none.fl_str_mv High-dimensional PDEs
Approximate matrix factorization
W-methods
Finite differences
Order reduction
Boundary correction technique
topic High-dimensional PDEs
Approximate matrix factorization
W-methods
Finite differences
Order reduction
Boundary correction technique
description Two new boundary correction techniques are proposed in order to mitigate the order reduction phenomenon associated to the numerical solution of initial boundary value problems for parabolic Partial Differential Equations in arbitrary spatial dimensions with time dependent Dirichlet boundary conditions. The new techniques are based on the idea of discretizing the PDE problem at the boundary points as similar as possible to that of the interior points of the domain. These new techniques are considered for the time integration with W-methods based on Approximate Matrix Factorization. By suitably modifying the internal stages of the methods on the boundary points, it is illustrated by numerical testing with time dependent boundary conditions that the new boundary correction techniques are able to keep the same accuracy and order of convergence that the method reaches in the case of homogeneous boundary conditions.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://riull.ull.es/xmlui/handle/915/39061
url http://riull.ull.es/xmlui/handle/915/39061
dc.language.none.fl_str_mv
language_invalid_str_mv
dc.relation.none.fl_str_mv Numerical Algorithms (2024) 96:507–535
dc.rights.none.fl_str_mv Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES
rights_invalid_str_mv Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIULL. Repositorio Institucional de la Universidad de La Laguna
instname:Universidad de La Laguna (ULL)
instname_str Universidad de La Laguna (ULL)
reponame_str RIULL. Repositorio Institucional de la Universidad de La Laguna
collection RIULL. Repositorio Institucional de la Universidad de La Laguna
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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