A NEW APPROACH AND ERROR ANALYSIS FOR RECONSTRUCTING THE SCATTERED WAVE BY THE POINT SOURCE METHOD  

作　　者：Jijun Liu Gen Nakamura Roland Potthast 

机构地区：[1]Department of Mathematics, Southeast University, Nanjing, 210096, China [2]Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan [3]Institute for Numerical and Applied Mathematics, University of Gottingen, Lotzestr, 16-18,37085, Gottingen, Germany

出　　处：《Journal of Computational Mathematics》2007年第2期113-130,共18页计算数学（英文）

基　　金：Supported NSFC(No.10371018).

摘　　要：Consider an inverse scattering problem by an obstacle D belong to R^2 with impedance boundary. We investigate the reconstruction of the scattered field u^s from its far field pattern u^∞ 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 reconstruc- tion of the scattered wave. Third, numerical implementations are given to test the validity and stability of the inversion method for the impedance obstacle.Consider an inverse scattering problem by an obstacle D belong to R^2 with impedance boundary. We investigate the reconstruction of the scattered field u^s from its far field pattern u^∞ 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 reconstruc- tion of the scattered wave. Third, numerical implementations are given to test the validity and stability of the inversion method for the impedance obstacle.

关 键 词：Inverse scattering REGULARIZATION Error estimate NUMERICS 

分 类 号：O241.1[理学—计算数学]