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Improving the conditioning of the method of fundamental solutions for the Helmholtz equation on domains in polar or elliptic coordinates

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dc.contributor.authorAntunes, Pedro R. S.
dc.contributor.authorCalunga, Hernani
dc.contributor.authorSerranho, Pedro
dc.date.accessioned2024-09-05T15:18:28Z
dc.date.embargo2026-08-31
dc.date.issued2024
dc.description.abstractA new approach to overcome the ill-conditioning of the Method of Fundamental Solutions (MFS) combining Singular Value Decomposition (SVD) and an adequate change of basis was introduced in [1] as MFS-SVD. The original formulation considered polar coordinates and harmonic polynomials as basis functions and is restricted to the Laplace equation in 2D. In this work, we start by adapting the approach to the Helmholtz equation in 2D and later extending it to elliptic coordinates. As in the Laplace case, the approach in polar coordinates has very good numerical results both in terms of conditioning and accuracy for domains close to a disk but does not perform so well for other domains, such as an eccentric ellipse. We therefore consider the MFS-SVD approach in elliptic coordinates with Mathieu functions as basis functions for the latter. We illustrate the feasibility of the approach by numerical examples in both cases.pt_PT
dc.description.versioninfo:eu-repo/semantics/acceptedVersionpt_PT
dc.identifier.doi10.1016/j.amc.2024.128969pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.2/16527
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relationGroup of Mathematical Physics of the University of Lisbon
dc.relationCoimbra Institute for Biomedical Imaging and Translational Research
dc.relationCoimbra Institute for Biomedical Imaging and Translational Research
dc.relationCenter for Computational and Stochastic Mathematics
dc.relationCenter for Computational and Stochastic Mathematics
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/pt_PT
dc.subjectMethod of fundamental solutionspt_PT
dc.subjectHelmholtz equationpt_PT
dc.subjectMFS-SVDpt_PT
dc.subjectAddition theorempt_PT
dc.subjectIll-conditioningpt_PT
dc.subjectMathieu functionspt_PT
dc.titleImproving the conditioning of the method of fundamental solutions for the Helmholtz equation on domains in polar or elliptic coordinatespt_PT
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.awardTitleCoimbra Institute for Biomedical Imaging and Translational Research
oaire.awardTitleCenter for Computational and Stochastic Mathematics
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/UIDP%2F04950%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04621%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04621%2F2020/PT
oaire.citation.startPage128969pt_PT
oaire.citation.titleApplied Mathematics and Computationpt_PT
oaire.citation.volume482pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
person.familyNameAntunes
person.familyNameCalunga
person.familyNameSerranho
person.givenNamePedro
person.givenNameHernani
person.givenNamePedro
person.identifier.ciencia-id6710-138C-A69D
person.identifier.ciencia-id031F-5D62-E6EC
person.identifier.orcid0000-0003-1969-1860
person.identifier.orcid0009-0007-5315-6251
person.identifier.orcid0000-0003-2176-3923
person.identifier.ridM-2406-2015
person.identifier.scopus-author-id55346859100
project.funder.identifierhttp://doi.org/10.13039/501100001871
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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
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.embargofctJournal policy.pt_PT
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