A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces

The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the emb...

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Detalles Bibliográficos
Autores: Petras, A., Ling, L., Piret, C., Ruuth, S.J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/909
Acceso en línea:http://hdl.handle.net/20.500.11824/909
Access Level:acceso abierto
Palabra clave:partial differential equations on moving surfaces
closest point method
grid based particle method
radial basis functions finite differences (RBF-FD)
least-squares method
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spelling A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfacesPetras, A.Ling, L.Piret, C.Ruuth, S.J.partial differential equations on moving surfacesclosest point methodgrid based particle methodradial basis functions finite differences (RBF-FD)least-squares methodThe closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.NSERC Canada Grant (RGPIN 2016-04361), Hong Kong Research Grant Council GRF Grant, Hong Kong Baptist University FRG Grant201920192018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/909reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/pii/S002199911830322Xinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/MINECO//MTM2015-69992-Rinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/9092026-06-19T12:47:47Z
dc.title.none.fl_str_mv A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
title A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
spellingShingle A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
Petras, A.
partial differential equations on moving surfaces
closest point method
grid based particle method
radial basis functions finite differences (RBF-FD)
least-squares method
title_short A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
title_full A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
title_fullStr A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
title_full_unstemmed A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
title_sort A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
dc.creator.none.fl_str_mv Petras, A.
Ling, L.
Piret, C.
Ruuth, S.J.
author Petras, A.
author_facet Petras, A.
Ling, L.
Piret, C.
Ruuth, S.J.
author_role author
author2 Ling, L.
Piret, C.
Ruuth, S.J.
author2_role author
author
author
dc.subject.none.fl_str_mv partial differential equations on moving surfaces
closest point method
grid based particle method
radial basis functions finite differences (RBF-FD)
least-squares method
topic partial differential equations on moving surfaces
closest point method
grid based particle method
radial basis functions finite differences (RBF-FD)
least-squares method
description The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.
publishDate 2018
dc.date.none.fl_str_mv 2018
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/909
url http://hdl.handle.net/20.500.11824/909
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/pii/S002199911830322X
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/MINECO//MTM2015-69992-R
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
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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