Acoustic Obstacle Scattering and the Factorization Method

Abstract

Scattering is a physical phenomenon which can be modeled with a boundary value problem for a partial differential equation. This boundary value problem gives rise to two kind of problems: direct scattering problem and inverse scattering problem. In the former one tries to find the solution of the boundary value problem while in the latter the aim is to determine the boundary (of the scatterer) given information about the solution of the boundary value problem. The main goal of this thesis is to analyze the direct scattering problem to an extent that is necessary in order to study the inverse scattering problem both theoretically and numerically.

This thesis establishes that the boundary value problem arising from two-dimen\-sional acoustic obstacle scattering of time-harmonic plane waves has a unique solution. In particular, the so-called far field pattern for the solution is derived; the far field pattern is a central concept in view of the corresponding inverse problem. The inverse problem is briefly considered together with the factorization method for solving the inverse problem. Computational methods both for solving the direct problem and the inverse problem are developed and illustrated with numerical examples. /Kir10