Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.2/1930
Título: Huygens’ principle and iterative methods in inverse obstacle scattering
Autor: Ivanyshyn, Olha
Kress, Rainer
Serranho, Pedro
Palavras-chave: Inverse scattering problem
Huygen's principle
Sound-soft obstacle
Nonlinear integral equations
Inverse scattering
Data: 2010
Editora: Springer
Citação: Ivanyshyn,Olha; Kress, Rainer; Serranho, Pedro - Huygens’ principle and iterative methods in inverse obstacle scattering. "Advances in Computational Mathematics" [Em linha]. ISSN 1019-7168 (Print) 1572-9044 (Online). Vol. 33, nº 4 (Nov. 2010), p. 1-20
Relatório da Série N.º: 33
Resumo: The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scattering from a sound-soft obstacle, we will interpret Huygens’ principle as a system of two integral equations, named data and field equation, for the unknown boundary of the scatterer and the induced surface flux, i.e., the unknown normal derivative of the total field on the boundary. Reflecting the ill-posedness of the inverse obstacle scattering problem these integral equations are ill-posed. They are linear with respect to the unknown flux and nonlinear with respect to the unknown boundary and offer, in principle, three immediate possibilities for their iterative solution via linearization and regularization. In addition to presenting new results on injectivity and dense range for the linearized operators, the main purpose of this paper is to establish and illuminate relations between these three solution methods based on Huygens’ principle in inverse obstacle scattering. Furthermore, we will exhibit connections and differences to the traditional regularized Newton type iterations as applied to the boundary to far field map, including alternatives for the implementation of these Newton iterations.
Peer review: yes
URI: http://hdl.handle.net/10400.2/1930
ISSN: 1019-7168
1572-9044
Versão do Editor: DOI: 10.1007/s10444-009-9135-6
Aparece nas colecções:Matemática e Estatística - Artigos em revistas internacionais / Papers in international journals

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