基于交互间隙法的内部Neumann反散射问题

Reciprocity gap method for an interior inverse scattering problem with a Neumann boundary condition

利用交互间隙法研究了具有Neumann边界条件的内部腔体反散射问题。首先,证明了由内部点源测量数据可以唯一确定具有Neumann边界条件的腔体的位置及其形状。然后,采用交互间隙法的思想,设计和分析快速有效的数值算法来反演未知腔体的位置及其形状。最后,利用若干数值例子加以验证。

An interior inverse scattering problem with a Neumann boundary condition is studied by using reciprocity gap method. First, the conclusion that the position and shape of a cavity with a Neumann boundary condition can be uniquely determined by providing measurments of point sources inside the cavity is proven. Next, by following the idea of reciprocity gap method, a numerical algorithm to effectively reconstruct position and shape of an unknown cavity from interior measurements is designed. Finally, some numerical examples to validate the method are presented.