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

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorAntunes, Pedro R. S.-
Autor(es): dc.creatorCalunga, Hernani-
Autor(es): dc.creatorSerranho, Pedro-
Data de aceite: dc.date.accessioned2025-08-22T11:49:20Z-
Data de disponibilização: dc.date.available2025-08-22T11:49:20Z-
Data de envio: dc.date.issued2024-09-05-
Data de envio: dc.date.issued2023-
Data de envio: dc.date.issued2026-08-31-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/16527-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/16527-
Descrição: dc.descriptionA 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.-
Descrição: dc.descriptioninfo:eu-repo/semantics/acceptedVersion-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Publicador: dc.publisherElsevier-
Relação: dc.relationGroup of Mathematical Physics of the University of Lisbon-
Relação: dc.relationCoimbra Institute for Biomedical Imaging and Translational Research-
Relação: dc.relationCoimbra Institute for Biomedical Imaging and Translational Research-
Relação: dc.relationCenter for Computational and Stochastic Mathematics-
Relação: dc.relationCenter for Computational and Stochastic Mathematics-
Direitos: dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/-
Palavras-chave: dc.subjectMethod of fundamental solutions-
Palavras-chave: dc.subjectHelmholtz equation-
Palavras-chave: dc.subjectMFS-SVD-
Palavras-chave: dc.subjectAddition theorem-
Palavras-chave: dc.subjectIll-conditioning-
Palavras-chave: dc.subjectMathieu functions-
Título: dc.titleImproving the conditioning of the method of fundamental solutions for the Helmholtz equation on domains in polar or elliptic coordinates-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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