On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/8521 |
Resumo: | The method of fundamental solutions is broadly used in science and engineering to numerically solve the direct time-harmonic scattering problem. In 2D the choice of source points is usually made by considering an inner pseudo-boundary over which equidistant source points are placed. In 3D, however, this problem is much more challenging, since, in general, equidistant points over a closed surface do not exist. In this paper we discuss a method to obtain a quasi-equidistant point distribution over the unit sphere surface, giving rise to a Delaunay triangulation that might also be used for other boundary element methods. We give theoretical estimates for the expected distance between points and the expect area of each triangle. We illustrate the feasibility of the proposed method in terms of the comparison with the expected values for distance and area. We also provide numerical evidence that this point distribution leads to a good conditioning of the linear system associated with the direct scattering problem, being therefore an adequated choice of source points for the method of fundamental solutions. |
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On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutionsMethod of fundamental solutionsEquidistant pointsSource pointsTriangulationThe method of fundamental solutions is broadly used in science and engineering to numerically solve the direct time-harmonic scattering problem. In 2D the choice of source points is usually made by considering an inner pseudo-boundary over which equidistant source points are placed. In 3D, however, this problem is much more challenging, since, in general, equidistant points over a closed surface do not exist. In this paper we discuss a method to obtain a quasi-equidistant point distribution over the unit sphere surface, giving rise to a Delaunay triangulation that might also be used for other boundary element methods. We give theoretical estimates for the expected distance between points and the expect area of each triangle. We illustrate the feasibility of the proposed method in terms of the comparison with the expected values for distance and area. We also provide numerical evidence that this point distribution leads to a good conditioning of the linear system associated with the direct scattering problem, being therefore an adequated choice of source points for the method of fundamental solutions.The first author acknowledges his work is partially supported by National Funding from FCT (Portugal) UID/Multi/04019/2013 and UID/MAT/04561/2019. The second author acknowledges his work is partially supported by National Funding from FCT (Portugal) UID/Multi/04621/2013 and by National Funding from FCT (Portugal) under the project PTDC/EMD-EMD/32162/2017, co-funded by FEDER through COMPETE 2020.ElsevierRepositório AbertoAraújo, AntónioSerranho, Pedro2020-10-31T01:30:23Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/8521eng10.1016/j.cam.2019.03.019info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:30:21Zoai:repositorioaberto.uab.pt:10400.2/8521Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:48:33.483538Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
title |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
spellingShingle |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions Araújo, António Method of fundamental solutions Equidistant points Source points Triangulation |
title_short |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
title_full |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
title_fullStr |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
title_full_unstemmed |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
title_sort |
On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions |
author |
Araújo, António |
author_facet |
Araújo, António Serranho, Pedro |
author_role |
author |
author2 |
Serranho, Pedro |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Araújo, António Serranho, Pedro |
dc.subject.por.fl_str_mv |
Method of fundamental solutions Equidistant points Source points Triangulation |
topic |
Method of fundamental solutions Equidistant points Source points Triangulation |
description |
The method of fundamental solutions is broadly used in science and engineering to numerically solve the direct time-harmonic scattering problem. In 2D the choice of source points is usually made by considering an inner pseudo-boundary over which equidistant source points are placed. In 3D, however, this problem is much more challenging, since, in general, equidistant points over a closed surface do not exist. In this paper we discuss a method to obtain a quasi-equidistant point distribution over the unit sphere surface, giving rise to a Delaunay triangulation that might also be used for other boundary element methods. We give theoretical estimates for the expected distance between points and the expect area of each triangle. We illustrate the feasibility of the proposed method in terms of the comparison with the expected values for distance and area. We also provide numerical evidence that this point distribution leads to a good conditioning of the linear system associated with the direct scattering problem, being therefore an adequated choice of source points for the method of fundamental solutions. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019 2019-01-01T00:00:00Z 2020-10-31T01:30:23Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.2/8521 |
url |
http://hdl.handle.net/10400.2/8521 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1016/j.cam.2019.03.019 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799135066328137728 |