Hybrid Method for Inverse Elastic Obstacle Scattering Problems

Inverse obstacle scattering for elastic waves

Uniqueness Theorems for Inverse Obstacle Scattering Problems in Lipschitz Domains

For the Neumann and Robin boundary conditions the uniqueness theorems for inverse obstacle scattering problems are proved in Lipschitz domains. The role of non-smoothness of the boundary is analyzed.

Multilevel Linear Sampling Method for Inverse Obstacle Scattering

In this talk, we will be mainly concerned with a novel multilevel linear sampling method (MLSM) for reconstructing the obstacle from its corresponding scattering amplitude. The new method is shown to possess asymptotically optimal computational complexity. For an n×n sampling mesh in R2 or an n×n×n sampling mesh in R3, the proposed algorithm requires to solve only O(nN−1) far-field equations fo...

The method of fundamental solutions for inverse obstacle acoustic scattering

In this paper we propose a simple method for detecting (shape, size and location) a scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered acoustic pressure in the vicinity (near-or far-field) of the obstacle. We develop a nonlinear constrained minimization regularized method of fundamental solutions for obtaining the numerical solution of the inverse ...

The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is generated by an initial data with compact support outside the surface. The method yields the distance from a given point outside the surface to obstacles and thus mo...