A hybrid method for two-dimensional crack reconstruction

Detalhes bibliográficos
Autor(a) principal: Kress, Rainer
Data de Publicação: 2005
Outros Autores: Serranho, Pedro
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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spelling 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
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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
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