基于分裂法的内部Neumann反散射问题

The decomposition method for an interior inverse scattering problem with a Neumann boundary condition

通过分裂法研究了具有Neumann边界条件的内部声波反散射问题。首先,证明了在Neumann边界条件下散射体的位置、形状可由腔体内部的点源测量数据唯一确定。然后,用分裂法的思想来反演未知散射体的边界及其形状。最后,给出了2个数值例子来验证该方法的可行性和有效性。

An internal acoustic inverse scattering problem with a Neumann boundary condition is studied by using the decomposition method. First,it is proved that the position and shape of a scatterer can be uniquely determined by the measurement data of the point source inside the cavity with the Neumann boundary condition. Then,the boundary of the unknown scatter and its shape is reconstructed by using the idea of the decomposition method. Finally,two numerical examples are given to verify the feasibility and effectiveness of the method.