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Extending the method of fundamental solutions to non-homogeneous elastic wave problems

2017-05Journal article Restricted access
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dc.contributor.authorAlves, Carlos J. S.
dc.contributor.authorMartins, Nuno F. M.
dc.contributor.authorValtchev, Svilen
dc.date.accessioned2025-07-17T08:44:43Z
dc.date.available2025-07-17T08:44:43Z
dc.date.issued2017-05
dc.description.abstractTwo meshfree methods are developed for the numerical solution of the non-homogeneous Cauchy–Navier equations of elastodynamics in an isotropic material. The two approaches differ upon the choice of the basis functions used for the approximation of the unknown wave amplitude. In the first case, the solution is approximated in terms of a linear combination of fundamental solutions of the Navier differential operator with different source points and test frequencies. In the second method the solution is approximated by superposition of acoustic waves, i.e. fundamental solutions of the Helmholtz operator, with different source points and test frequencies. The applicability of the two methods is justified in terms of density results and a convergence result is proven. The accuracy of the methods is illustrated through 2D numerical examples. Applications to interior elastic wave scattering problems are also presented.eng
dc.description.sponsorshipThe financial support from CEMAT and CMA through Fundação para a Ciência e a Tecnologia (FCT) projects PEst-OE/MAT/UI0822/2014 (first and third author) and EXCL/MAT-NAN/0114/2012 (first and second author) is gratefully acknowledged.
dc.identifier.citationCarlos J.S. Alves, Nuno F.M. Martins, Svilen S. Valtchev, Extending the method of fundamental solutions to non-homogeneous elastic wave problems, Applied Numerical Mathematics, Volume 115, 2017, Pages 299-313, ISSN 0168-9274, https://doi.org/10.1016/j.apnum.2016.06.002.
dc.identifier.doi10.1016/j.apnum.2016.06.002
dc.identifier.issn0168-9274
dc.identifier.urihttp://hdl.handle.net/10400.8/13682
dc.language.isoeng
dc.peerreviewedyes
dc.publisherElsevier BV
dc.relationPEst-OE/MAT/UI0822/2014
dc.relationEXCL/MAT-NAN/0114/2012
dc.relation.hasversionhttps://www.sciencedirect.com/science/article/pii/S0168927416300952
dc.relation.ispartofApplied Numerical Mathematics
dc.rights.uriN/A
dc.subjectElastic wave scattering
dc.subjectMeshfree method
dc.subjectMethod of fundamental solutions
dc.subjectNon-homogeneous problems
dc.titleExtending the method of fundamental solutions to non-homogeneous elastic wave problemseng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage313
oaire.citation.startPage299
oaire.citation.titleApplied Numerical Mathematics
oaire.citation.volume115
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
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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