论文标题
反向散射steklov特征值和反光谱问题的近似
Approximation of the inverse scattering Steklov eigenvalues and the inverse spectral problem
论文作者
论文摘要
在本文中，我们考虑了在反声散射中产生的Steklov特征值问题的数值近似。潜在的散射问题是针对不均匀的各向同性培养基。这些特征值已被提议用作目标特征，因为可以从散射数据中恢复它们。研究了一种Galerkin方法，其中基础函数是拉普拉斯式的neumann征素函数。特征值和本征函数的错误估计是通过吸引魏尔定律来证明的。我们将测试此方法，以验证变量的分离，以验证理论收敛。我们还考虑了从Steklov特征值的知识中估算/恢复折射指数的反光谱问题。由于相对于实用值的折射指数，特征值是单调的，这意味着它们可用于非破坏性测试。为反光谱问题提供了一些数值示例。
In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been proposed to be used as a target signature since they can be recovered from the scattering data. A Galerkin method is studied where the basis functions are the Neumann eigenfunctions of the Laplacian. Error estimates for the eigenvalues and eigenfunctions are proven by appealing to Weyl's Law. We will test this method against separation of variables in order to validate the theoretical convergence. We also consider the inverse spectral problem of estimating/recovering the refractive index from the knowledge of the Steklov eigenvalues. Since the eigenvalues are monotone with respect to a real-valued refractive index implies that they can be used for non-destructive testing. Some numerical examples are provided for the inverse spectral problem.
