论文标题
关于径向对称结构域的逆散射问题
On the inverse scattering problem for radially-symmetric domains in two dimensions
论文作者
论文摘要
在本文中，我们描述了一种在给定多频数据的径向对称域中求解helmholtz方程的反问题的方法。我们的方法基于合适的痕量公式的构建，该公式将以多个频率的总场的阻抗与电势的衍生物相关联。使用此痕迹公式，我们获得了一个耦合微分方程的系统，该系统可以解决以稳定的方式获得电势。最后，用几个数值示例说明了重建算法的性能。
In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate the impedance of the total field at multiple frequencies to derivatives of the potential. Using this trace formula we obtain a system of coupled differential equations which can be solved to obtain the potential in a stable manner. Finally, the performance of the reconstruction algorithm is illustrated with several numerical examples.
