An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition

© 2024 Elsevier. This manuscript version is made available under the CC BY 4.0 DEED license https://creativecommons.org/licenses/by/4.0/

Bibliographic Details
Authors: Discacciati, Marco|||0000-0001-8343-8953, Evans, Ben J., Giacomini, Matteo|||0000-0001-6094-5944
Format: article
Publication Date:2024
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/406500
Online Access:https://hdl.handle.net/2117/406500
https://dx.doi.org/10.1016/j.cma.2023.116484
Access Level:Open access
Keyword:Arithmetical algebraic geometry
Computing Methodologies
Reduced order models
Proper generalized decomposition
Domain decomposition methods
Overlapping Schwarz method
Non-intrusiveness
Geometria algèbrica--Aritmètica
Informàtica
Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
Classificació AMS::68 Computer science::68U Computing methodologies and applications
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
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oai_identifier_str oai:upcommons.upc.edu:2117/406500
network_acronym_str ES
network_name_str España
repository_id_str
spelling An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decompositionDiscacciati, Marco|||0000-0001-8343-8953Evans, Ben J.Giacomini, Matteo|||0000-0001-6094-5944Arithmetical algebraic geometryComputing MethodologiesReduced order modelsProper generalized decompositionDomain decomposition methodsOverlapping Schwarz methodNon-intrusivenessGeometria algèbrica--AritmèticaInformàticaClassificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)Classificació AMS::68 Computer science::68U Computing methodologies and applicationsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombresÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències© 2024 Elsevier. This manuscript version is made available under the CC BY 4.0 DEED license https://creativecommons.org/licenses/by/4.0/A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an overlapping domain decomposition (DD) method, is proposed to efficiently construct surrogate models of parametric linear elliptic problems. A parametric multi-domain formulation is presented, with local subproblems featuring arbitrary Dirichlet interface conditions represented through the traces of the finite element functions used for spatial discretization at the subdomain level, with no need for additional auxiliary basis functions. The linearity of the operator is exploited to devise low-dimensional problems with only few active boundary parameters. An overlapping Schwarz method is used to glue the local surrogate models, solving a linear system for the nodal values of the parametric solution at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the overlapping region. The proposed DD-PGD methodology relies on a fully algebraic formulation allowing for real-time computation based on the efficient interpolation of the local surrogate models in the parametric space, with no additional problems to be solved during the execution of the Schwarz algorithm. Numerical results for parametric diffusion and convection–diffusion problems are presented to showcase the accuracy of the DD-PGD approach, its robustness in different regimes and its superior performance with respect to standard high-fidelity DD methods.The authors acknowledge funding as follows. MD: EPSRC, United Kingdom grant EP/V027603/1. BJE: EPSRC Doctoral Training Partnership grant EP/W523987/1. MG: Spanish Ministry of Science and Innovation and Spanish State Research Agency MCIN/AEI/10.13039/501100011033 (Grants No. PID2020-113463RB-C33 and CEX2018-000797-S). MG is Fellow of the Serra Húnter Programme of the Generalitat de Catalunya.Peer ReviewedElsevier20242024-01-0120242024-04-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/406500https://dx.doi.org/10.1016/j.cma.2023.116484reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113463RB-C33 MACHINE LEARNING FOR DATA-DRIVEN MODELINGopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4065002026-05-27T15:37:01Z
dc.title.none.fl_str_mv An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
title An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
spellingShingle An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
Discacciati, Marco|||0000-0001-8343-8953
Arithmetical algebraic geometry
Computing Methodologies
Reduced order models
Proper generalized decomposition
Domain decomposition methods
Overlapping Schwarz method
Non-intrusiveness
Geometria algèbrica--Aritmètica
Informàtica
Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
Classificació AMS::68 Computer science::68U Computing methodologies and applications
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
title_short An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
title_full An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
title_fullStr An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
title_full_unstemmed An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
title_sort An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
dc.creator.none.fl_str_mv Discacciati, Marco|||0000-0001-8343-8953
Evans, Ben J.
Giacomini, Matteo|||0000-0001-6094-5944
author Discacciati, Marco|||0000-0001-8343-8953
author_facet Discacciati, Marco|||0000-0001-8343-8953
Evans, Ben J.
Giacomini, Matteo|||0000-0001-6094-5944
author_role author
author2 Evans, Ben J.
Giacomini, Matteo|||0000-0001-6094-5944
author2_role author
author
dc.subject.none.fl_str_mv Arithmetical algebraic geometry
Computing Methodologies
Reduced order models
Proper generalized decomposition
Domain decomposition methods
Overlapping Schwarz method
Non-intrusiveness
Geometria algèbrica--Aritmètica
Informàtica
Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
Classificació AMS::68 Computer science::68U Computing methodologies and applications
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
topic Arithmetical algebraic geometry
Computing Methodologies
Reduced order models
Proper generalized decomposition
Domain decomposition methods
Overlapping Schwarz method
Non-intrusiveness
Geometria algèbrica--Aritmètica
Informàtica
Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
Classificació AMS::68 Computer science::68U Computing methodologies and applications
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
description © 2024 Elsevier. This manuscript version is made available under the CC BY 4.0 DEED license https://creativecommons.org/licenses/by/4.0/
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-01
2024
2024-04-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/406500
https://dx.doi.org/10.1016/j.cma.2023.116484
url https://hdl.handle.net/2117/406500
https://dx.doi.org/10.1016/j.cma.2023.116484
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113463RB-C33 MACHINE LEARNING FOR DATA-DRIVEN MODELING
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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