Repository logo
 
Publication

The MFS-SVD method for the laplace equation in three dimensions

2025-02-12Journal article Open access
Simple item page
datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorAntunes, Pedro
dc.contributor.authorSantos, Vinicius
dc.contributor.authorSerranho, Pedro
dc.date.accessioned2026-01-05T11:18:45Z
dc.date.available2026-01-05T11:18:45Z
dc.date.issued2025-02-12
dc.description.abstractThe method of fundamental solutions (MFS) has been widely used to numerically solve boundary value problems involving linear partial differential equations. This method is easy to implement computationally and can be very effective for smooth domains and boundary conditions. The main drawback of the MFS is the ill-conditioning of the associated matrices, which may deteriorate the method’s accuracy. We present three methods to reduce the ill-conditioning of the classical MFS for the Laplace equation defined in bounded star-shaped domains in 3D. The idea is to expand the MFS basis functions in terms of spherical harmonics, in order to use the reduced QR factorization and singular value decomposition to deal with the ill-conditioning, leading to a better function basis that spans the same approximation space as the classical MFS. The numerical results illustrate that these approaches significantly decrease the ill-conditioning, allowing higher accuracy when compared to the classical MFS.eng
dc.identifier.doi10.1137/24m1634928
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.urihttp://hdl.handle.net/10400.2/20621
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relationGroup of Mathematical Physics of the University of Lisbon
dc.relationCoimbra Institute for Biomedical Imaging and Translational Research
dc.relationCenter for Computational and Stochastic Mathematics
dc.relationUIDP/04621/2020
dc.relation.hasversionhttps://epubs.siam.org/doi/10.1137/24M1634928
dc.relation.ispartofSIAM Journal on Scientific Computing
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectMethod of fundamental solutions
dc.subjectIll-conditioning
dc.subjectLaplace equation
dc.titleThe MFS-SVD method for the laplace equation in three dimensionseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleGroup of Mathematical Physics of the University of Lisbon
oaire.awardTitleCoimbra Institute for Biomedical Imaging and Translational Research
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00208%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04950%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04621%2F2020/PT
oaire.citation.issue1
oaire.citation.titleSIAM Journal on Scientific Computing
oaire.citation.volume47
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_ab4af688f83e57aa
person.familyNameAntunes
person.familyNameSantos
person.familyNameSerranho
person.givenNamePedro
person.givenNameVinicius
person.givenNamePedro
person.identifier.ciencia-id6710-138C-A69D
person.identifier.ciencia-id031F-5D62-E6EC
person.identifier.orcid0000-0003-1969-1860
person.identifier.orcid0009-0008-5647-4519
person.identifier.orcid0000-0003-2176-3923
person.identifier.ridM-2406-2015
person.identifier.scopus-author-id55346859100
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
relation.isAuthorOfPublicationbef314d2-4a78-4fba-aecd-9f4e8e19e70c
relation.isAuthorOfPublication37e4b313-0c6b-4a16-9796-13f012a3eb7d
relation.isAuthorOfPublicationc7f6eb4c-c743-4b38-83f5-70796c0851ca
relation.isAuthorOfPublication.latestForDiscoveryc7f6eb4c-c743-4b38-83f5-70796c0851ca
relation.isProjectOfPublicationa79ad082-93a2-48af-acd1-6c5f0fb42899
relation.isProjectOfPublicationec375bb8-8117-49ab-9d14-4bca5449e893
relation.isProjectOfPublication3471b937-6390-4db2-873a-4c793b7d70ec
relation.isProjectOfPublication.latestForDiscoverya79ad082-93a2-48af-acd1-6c5f0fb42899

Files

Collections

Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals