A well conditioned method of fundamental solutions for laplace equation

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorAntunes, Pedro R. S.-
Data de aceite: dc.date.accessioned2022-09-01T13:01:10Z-
Data de disponibilização: dc.date.available2022-09-01T13:01:10Z-
Data de envio: dc.date.issued2022-03-24-
Data de envio: dc.date.issued2021-
Data de envio: dc.date.issued2023-03-23-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/11856-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/11856-
Descrição: dc.descriptionThe method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and boundary conditions. The main drawback of the MFS is that the matrices involved typically are ill-conditioned and this may prevent to achieve high accuracy. In this work, we propose a new algorithm to remove the ill conditioning of the classical MFS in the context of Laplace equation defined in planar domains. The main idea is to expand the MFS basis functions in terms of harmonic polynomials. Then, using the singular value decomposition and Arnoldi orthogonalization we define well conditioned basis functions spanning the same functional space as the MFS's. Several numerical examples show that this approach is much superior to previous approaches, such as the classical MFS or the MFS-QR.-
Descrição: dc.descriptionThe research was partially supported by FCT, Portugal, through the scientific project UIDB/00208/2020.-
Descrição: dc.descriptioninfo:eu-repo/semantics/acceptedVersion-
Idioma: dc.languageen-
Publicador: dc.publisherSpringer-
Relação: dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00208%2F2020/PT-
Direitos: dc.rightsembargoedAccess-
Título: dc.titleA well conditioned method of fundamental solutions for laplace equation-
Tipo de arquivo: dc.typeaula digital-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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