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A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks

2009-11-27Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorAntunes, Pedro R. S.
dc.contributor.authorValtchev, Svilen S.
dc.date.accessioned2025-11-10T17:49:41Z
dc.date.available2025-11-10T17:49:41Z
dc.date.issued2009-11-27
dc.descriptionFonte: https://www.researchgate.net/publication/222298491_A_meshfree_numerical_method_for_acoustic_wave_propagation_problems_in_planar_domains_with_corners_and_cracks
dc.description.abstractThe numerical solution of acoustic wave propagation problems in planar domains with corners and cracks is considered. Since the exact solution of such problems is singular in the neighborhood of the geometric singularities the standard meshfree methods, based on global interpolation by analytic functions, show low accuracy. In order to circumvent this issue, a meshfree modification of the method of fundamental solutions is developed, where the approximation basis is enriched by an extra span of corner adapted non-smooth shape functions. The high accuracy of the new method is illustrated by solving several boundary value problems for the Helmholtz equation, modelling physical phenomena from the fields of room acoustics and acoustic resonance.eng
dc.description.sponsorshipThe authors would like to thank Dr. Carlos J. S. Alves for his valuable ideas and many critical discussions concerning the Method os Fundamental Solutions and its variants. The financial support received from the Fundação para a Ciência e a Tecnologia through the scholarship SFRH/BPD/47595/2008 (first author) and the scientific projects PTDC/MAT/101007/2008 (first author) and PPCDT/MAT/60863/2004, POCTI/MAT/45700/2002 (second author) is also gratefully acknowledged.
dc.identifier.citationAntunes, Pedro & Valtchev, Svilen. (2010). A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks. Journal of Computational and Applied Mathematics. 2646-2662. DOI: https://doi.org/10.1016/j.cam.2010.01.031.
dc.identifier.doi10.1016/j.cam.2010.01.031
dc.identifier.issn0377-0427
dc.identifier.urihttp://hdl.handle.net/10400.8/14578
dc.language.isoeng
dc.peerreviewedyes
dc.publisherElsevier
dc.relation.hasversionhttps://www.sciencedirect.com/science/article/pii/S037704271000035X?via%3Dihub
dc.relation.ispartofJournal of Computational and Applied Mathematics
dc.rights.uriN/A
dc.subjectMeshfree methods
dc.subjectMethod of Fundamental Solutions
dc.subjectSingular problems
dc.subjectAcoustic wave propagation
dc.subjectRoom acoustics
dc.subjectAcoustic resonance
dc.titleA meshfree numerical method for acoustic wave propagation problems in planar domains with corners and crackseng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage22
oaire.citation.startPage1
oaire.citation.titleJournal of Computational and Applied Mathematics
oaire.versionhttp://purl.org/coar/version/c_b1a7d7d4d402bcce
person.familyNameValtchev
person.givenNameSvilen
person.identifier.ciencia-idAF1E-BD9D-A8D7
person.identifier.gsidhttps://scholar.google.com/citations?user=MtxwhiUAAAAJ&hl=en
person.identifier.orcid0000-0002-3474-2788
person.identifier.scopus-author-id8361079200
relation.isAuthorOfPublicationb6302c21-a0e4-4419-967b-0a1bac949132
relation.isAuthorOfPublication.latestForDiscoveryb6302c21-a0e4-4419-967b-0a1bac949132

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The numerical solution of acoustic wave propagation problems in planar domains with corners and cracks is considered. Since the exact solution of such problems is singular in the neighborhood of the geometric singularities the standard meshfree methods, based on global interpolation by analytic functions, show low accuracy. In order to circumvent this issue, a meshfree modification of the method of fundamental solutions is developed, where the approximation basis is enriched by an extra span of corner adapted non-smooth shape functions. The high accuracy of the new method is illustrated by solving several boundary value problems for the Helmholtz equation, modelling physical phenomena from the fields of room acoustics and acoustic resonance.
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