Using fundamental solutions in inverse scattering

被引:80
作者
Colton, David [1 ]
Kress, Rainer
机构
[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
[2] Univ Gottingen, Inst Numer & Angew Math, D-37083 Gottingen, Germany
关键词
D O I
10.1088/0266-5611/22/3/R01
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We provide a brief description of recent results in inverse scattering theory having as a common mathematical framework the exploitation of the behaviour of the fundamental solution to the Helmholtz equation, in particular the fact that for the source point on the boundary partial derivative D of the scattering object such a solution is not in the Sobolev space H-1/2(partial derivative D). Included in our discussion are uniqueness theorems, decomposition methods (including the point-source method), the method of singular sources, the linear sampling method and the factorization method.
引用
收藏
页码:R49 / R66
页数:18
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