Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 2 : pp. 113–130
Abstract
Consider an inverse scattering problem by an obstacle $D \subset \mathcal{R}^2$ with impedance boundary. We investigate the reconstruction of the scattered field $u^s$ from its far field pattern $u^\infty$ using the point source method. First, by applying the boundary integral equation method, we provide a new approach to the point-source method of Potthast by classical potential theory. This extends the range of the point source method from plane waves to scattering of arbitrary waves. Second, by analyzing the behavior of the Hankel function, we obtain an improved strategy for the choice of the regularizing parameter from which an improved convergence rate (compared to the result of [15]) is achieved for the reconstruction of the scattered wave. Third, numerical implementations are given to test the validity and stability of the inversion method for the impedance obstacle.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8679
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 2 : pp. 113–130
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Inverse scattering Regularization Error estimate Numerics.