A level-set approach for inverse problems involving obstacles Fadil SANTOSA

A Level-set Approach for Inverse Problems Involving Obstacles

An approach for solving inverse problems involving obstacles is proposed. The approach uses a level-set method which has been shown to be eeective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear time-dependent partial diierential equation for...

A Level - Set Approach for Inverse Problems Involving

An approach for solving inverse problems involving obstacles is proposed. The approach uses a level-set method which has been shown to be eeective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear time-dependent partial diierential equation for...

A Level Set Method for Inverse Problems

Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypass...

Inverse Problems for Obstacles in a Waveguide ∗

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 en...