A numerical study of the probe method

Erhard, K. and Potthast, R. ORCID: https://orcid.org/0000-0001-6794-2500 (2006) A numerical study of the probe method. Siam Journal on Scientific Computing, 28 (5). pp. 1597-1612. ISSN 1064-8275

Abstract/Summary

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.