利用线性抽样方法重建Dirichlet边界条件声波散射区域

Linear Sampling Method for Reconstructing the Acoustic Scattering Region with Dirichlet Boundary

线性抽样方法是考虑一个第一类线性积分方程中的参数从区域内部趋近散射区域边界时,该方程的解趋近于无穷大。本文在此基础上就Dirichlet边界条件的声波反散射问题,利用积分方程理论严格证明了线性抽样方法对其的可用性,具体数值例子表明该方法是有效的。

The linear sampling method for the inverse scattering problem of acoustic waves is based on the fact that： a linear integral equation of first kind-far field equation including a parameter has an unbounded solution as the parameter approaches the scattering boundary from inside. However, this equation is not uniquely solvable, the convergence of the solution is thus necessary. Secondly, the equation is unsolved when the parameter lays outside the scattering region. We solved these two problems in this paper by relying on the inverse impendence boundary problem. Our numerical examples show that our theory is correct.