Volume 25, Issue 3
On Source Analysis by Wave Splitting with Applications in Inverse Scattering of Multiple Obstacles

J. Comp. Math., 25 (2007), pp. 266-281.

Published online: 2007-06

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• Abstract

We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise control. Splitting algorithms can be based on general boundary layer potential representation or Green's representation formula. We will prove the unique decomposition of scattered wave outside the specified reference domain $G$ and the unique decomposition of far-field pattern with respect to different reference domain $G$. Further, we employ the splitting technique for field reconstruction for a scatterer with two or more separate components, by combining it with the point source method for wave recovery. Using the decomposition of scattered wave as well as its far-field pattern, the wave splitting procedure proposed in this paper gives an efficient way to the computation of scattered wave near the obstacle, from which the multiple obstacles which cause the far-field pattern can be reconstructed separately. This considerably extends the range of the decomposition methods in the area of inverse scattering. Finally, we will provide numerical examples to demonstrate the feasibility of the splitting method.

• Keywords

Inverse scattering, Wave splitting, Potential theory, Near field, Regularization.

35P25, 47A52, 81U40, 78A40, 78A45, 74J20, 74J25.

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@Article{JCM-25-266, author = {}, title = {On Source Analysis by Wave Splitting with Applications in Inverse Scattering of Multiple Obstacles}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {3}, pages = {266--281}, abstract = {

We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise control. Splitting algorithms can be based on general boundary layer potential representation or Green's representation formula. We will prove the unique decomposition of scattered wave outside the specified reference domain $G$ and the unique decomposition of far-field pattern with respect to different reference domain $G$. Further, we employ the splitting technique for field reconstruction for a scatterer with two or more separate components, by combining it with the point source method for wave recovery. Using the decomposition of scattered wave as well as its far-field pattern, the wave splitting procedure proposed in this paper gives an efficient way to the computation of scattered wave near the obstacle, from which the multiple obstacles which cause the far-field pattern can be reconstructed separately. This considerably extends the range of the decomposition methods in the area of inverse scattering. Finally, we will provide numerical examples to demonstrate the feasibility of the splitting method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8692.html} }
TY - JOUR T1 - On Source Analysis by Wave Splitting with Applications in Inverse Scattering of Multiple Obstacles JO - Journal of Computational Mathematics VL - 3 SP - 266 EP - 281 PY - 2007 DA - 2007/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8692.html KW - Inverse scattering, Wave splitting, Potential theory, Near field, Regularization. AB -

We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise control. Splitting algorithms can be based on general boundary layer potential representation or Green's representation formula. We will prove the unique decomposition of scattered wave outside the specified reference domain $G$ and the unique decomposition of far-field pattern with respect to different reference domain $G$. Further, we employ the splitting technique for field reconstruction for a scatterer with two or more separate components, by combining it with the point source method for wave recovery. Using the decomposition of scattered wave as well as its far-field pattern, the wave splitting procedure proposed in this paper gives an efficient way to the computation of scattered wave near the obstacle, from which the multiple obstacles which cause the far-field pattern can be reconstructed separately. This considerably extends the range of the decomposition methods in the area of inverse scattering. Finally, we will provide numerical examples to demonstrate the feasibility of the splitting method.

Fahmi ben Hassen, Jijun Liu & Roland Potthast. (1970). On Source Analysis by Wave Splitting with Applications in Inverse Scattering of Multiple Obstacles. Journal of Computational Mathematics. 25 (3). 266-281. doi:
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