A hybrid method for two-dimensional crack reconstruction
Autor(a) principal: | |
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Data de Publicação: | 2005 |
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/10400.2/1933 |
Resumo: | We present a new method for solving the time-harmonic inverse scattering problem for sound-soft or perfectly conducting cracks in two dimensions. Our approach extends a method that was recently suggested by one of us for inverse obstacle scattering. It can be viewed as a hybrid between a regularized Newton iterationmethod applied to a nonlinear operator equation involving the operator that, for a fixed incident wave, maps the crack onto the far-field pattern of the scattered wave and a decomposition method due to Kirsch and Kress. As an important feature, in contrast to the traditional Newton iterations for solving inverse scattering problems, our method does not require a forward solver for each iteration step. The theoretical background of the method is based on the minimization of a cost function containing an additional penalty term to deal with reconstructing the full crack. Numerical examples illustrate the feasibility of the method and its stability with respect to noisy data. We expect that the method can also be extended to sound-hard cracks. |
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A hybrid method for two-dimensional crack reconstructionInverse scattering problemCrackHybrid methodWe present a new method for solving the time-harmonic inverse scattering problem for sound-soft or perfectly conducting cracks in two dimensions. Our approach extends a method that was recently suggested by one of us for inverse obstacle scattering. It can be viewed as a hybrid between a regularized Newton iterationmethod applied to a nonlinear operator equation involving the operator that, for a fixed incident wave, maps the crack onto the far-field pattern of the scattered wave and a decomposition method due to Kirsch and Kress. As an important feature, in contrast to the traditional Newton iterations for solving inverse scattering problems, our method does not require a forward solver for each iteration step. The theoretical background of the method is based on the minimization of a cost function containing an additional penalty term to deal with reconstructing the full crack. Numerical examples illustrate the feasibility of the method and its stability with respect to noisy data. We expect that the method can also be extended to sound-hard cracks.Fundação para a Ciência e Tecnologia através da Bolsa de Doutoramento SFRH/BD/14248/2003.IOPScieceRepositório AbertoKress, RainerSerranho, Pedro2011-10-31T11:54:59Z20052005-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/1933engKress, Rainer; Serranho, Pedro - A hybrid method for two-dimensional crack reconstruction. "Inverse Problems" [Em linha]. ISSN 0266-5611 (Print) 1361-6420 (Online). Vol. 21, nº 2 (2005), p. 1-120266-5611info: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:RCAAP2023-11-16T15:15:04Zoai:repositorioaberto.uab.pt:10400.2/1933Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:34.200960Repositório 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 |
A hybrid method for two-dimensional crack reconstruction |
title |
A hybrid method for two-dimensional crack reconstruction |
spellingShingle |
A hybrid method for two-dimensional crack reconstruction Kress, Rainer Inverse scattering problem Crack Hybrid method |
title_short |
A hybrid method for two-dimensional crack reconstruction |
title_full |
A hybrid method for two-dimensional crack reconstruction |
title_fullStr |
A hybrid method for two-dimensional crack reconstruction |
title_full_unstemmed |
A hybrid method for two-dimensional crack reconstruction |
title_sort |
A hybrid method for two-dimensional crack reconstruction |
author |
Kress, Rainer |
author_facet |
Kress, Rainer 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 |
Kress, Rainer Serranho, Pedro |
dc.subject.por.fl_str_mv |
Inverse scattering problem Crack Hybrid method |
topic |
Inverse scattering problem Crack Hybrid method |
description |
We present a new method for solving the time-harmonic inverse scattering problem for sound-soft or perfectly conducting cracks in two dimensions. Our approach extends a method that was recently suggested by one of us for inverse obstacle scattering. It can be viewed as a hybrid between a regularized Newton iterationmethod applied to a nonlinear operator equation involving the operator that, for a fixed incident wave, maps the crack onto the far-field pattern of the scattered wave and a decomposition method due to Kirsch and Kress. As an important feature, in contrast to the traditional Newton iterations for solving inverse scattering problems, our method does not require a forward solver for each iteration step. The theoretical background of the method is based on the minimization of a cost function containing an additional penalty term to deal with reconstructing the full crack. Numerical examples illustrate the feasibility of the method and its stability with respect to noisy data. We expect that the method can also be extended to sound-hard cracks. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005 2005-01-01T00:00:00Z 2011-10-31T11:54:59Z |
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/10400.2/1933 |
url |
http://hdl.handle.net/10400.2/1933 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Kress, Rainer; Serranho, Pedro - A hybrid method for two-dimensional crack reconstruction. "Inverse Problems" [Em linha]. ISSN 0266-5611 (Print) 1361-6420 (Online). Vol. 21, nº 2 (2005), p. 1-12 0266-5611 |
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 |
IOPSciece |
publisher.none.fl_str_mv |
IOPSciece |
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 |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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1799135003549892608 |