On the numerical solution of the three-dimensional inverse obstacle scattering problem
type: Item
instance of: scholarly article
title: On the numerical solution of the three-dimensional inverse obstacle scattering problem
zbMATH Open document ID: 0774.65092
DOI: 10.1016/0377-0427(92)90162-Q
author: Rainer Kress
author: Axel Zinn
published in: Journal of Computational and Applied Mathematics
publication date: 1992-10-26T00:00:00Z
review text: The authors examine numerical methods for the determination of the shape of an impenetrable sound-soft obstacle from the knowledge of a time- harmonic incident plane acoustic wave and far-field, or near-field measurements of the scattered wave. The nonlinear optimization formulation of \textit{A. Kirsch} and \textit{R. Kress} [An optimization method in inverse acoustic scattering, in: C. A. Brebbia et al., Eds., Boundary elements IX, Vol. 3. Fluid Flow and Potential Applications (Springer, Heidelberg, 3-18 (1987)], which stabilizes the underlying inverse problem, is used and analyzed. Numerical verification is presented.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 69584
zbMATH Keywords: inverse scattering
zbMATH Keywords: optimization
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: time-harmonic acoustic obstacle scattering
zbMATH Keywords: inverse problem
zbMATH Keywords: ill-posed problem
zbMATH Keywords: integral equation method
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: numerical examples
zbMATH Keywords: exterior boundary value problem
reviewed by: Robert S. Anderssen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 69584