Inverse Problems for Obstacles in a Waveguide ∗
نویسنده
چکیده
In this paper we prove that a particular entry in the scattering matrix, if known for all energies, determines certain rotationally symmetric obstacles in a generalized waveguide. The generalized waveguide X can be of any dimension and we allow either Dirichlet or Neumann boundary conditions on the boundary of the obstacle and on ∂X. In the case of a two-dimensional waveguide, two particular entries of the scattering matrix suffice to determine the obstacle, without the requirement of symmetry.
منابع مشابه
An Adaptive Inverse Iteration Fem for the Inhomogeneous Dielectric Waveguides
We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse iteration method. The problem is formulated as a generalized eigenvalue problems. By modifying the exact inverse iteration algorithm for the eigenvalue problem, we design a new adaptive inverse iterat...
متن کاملLinear Sampling and Reciprocity Gap Methods for an Inverse Acoustic Problem in a Waveguide
We consider the problem of detecting bounded inhomogeneous obstacles in an infinite tubular waveguide. We have in mind the application of acoustic techniques to inspect underground pipes such as sewers: In this application a loud-speaker and microphone are lowered into a man-hole. Sound pulses are created in the pipe, and the acoustic field reflected by obstructions in the pipe is measured. Fro...
متن کاملConvex Meshfree Solutions for Arbitrary Waveguide Analysis in Electromagnetic Problems
This paper presents a convex meshfree framework for solving the scalar Helmholtz equation in the waveguide analysis of electromagnetic problems. The generalized meshfree approximation (GMF) method using inverse tangent basis functions and cubic spline weight functions is employed to construct the first-order convex approximation which exhibits a weak Kronecker-delta property at the waveguide bo...
متن کاملDirect and Inverse Medium Scattering in a 3d Homogeneous Planar Waveguide
Time-harmonic acoustic waves in an ocean of finite height are modeled by the Helmholtz equation inside a layer with suitable boundary conditions. Scattering in this geometry features phenomena unknown in free space: resonances might occur at special frequencies and wave fields consist of partly evanescent modes. Inverse scattering in waveguides hence needs to cope with energy loss and limited a...
متن کاملIll-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کامل