A hybrid method for sound-hard obstacle reconstruction

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:204

Article; Proceedings Paper

Kress, Rainer ; Serranho, Pedro

关键词: inverse scattering problems;   

DOI  :  10.1016/j.cam.2006.02.047

来源: Elsevier

【 摘 要 】

We are interested in solving the inverse problem of acoustic wave scattering to reconstruct the position and the shape of sound-hard obstacles from a given incident field and the corresponding far field pattern of the scattered field. The method we suggest is an extension of the hybrid method for the reconstruction of sound-soft cracks as presented in [R. Kress, P. Serranho, A hybrid method for two-dimensional crack reconstruction, Inverse Problems 21 (2005) 773-784] to the case of sound-hard obstacles. The designation of the method is justified by the fact that it can be interpreted as a hybrid between a regularized Newton method applied to a nonlinear operator equation with the operator that maps the unknown boundary onto the solution of the direct scattering problem and a decomposition method in the spirit of the potential method as described in [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Cannon, Hornung (Eds.), Inverse Problems, ISNM, vol. 77, 1986, pp. 93-102. Since the method does not require a forward solver for each Newton step its computational costs are reduced. By some numerical examples we illustrate the feasibility of the method. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

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