A note on the enclosure method for an inverse obstacle scattering problem with a single point source

Details A note on the enclosure method for an inverse obstacle scattering problem with a single point source A note on the enclosure method for an inverse obstacle scattering problem with a single point source

2010-02-24

arxiv.org/abs/1002.4457v3

Inverse Problems 26 (2010) 105006

Mathematics

Analysis of PDEs

20 pages

Scientific paper

10.1088/0266-5611/26/10/105006

This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown sound-hard polygonal obstacle from the trace of the total wave that was exerted by a single point source onto a known circle surrounding the obstacle provided the source is sufficiently far from the obstacle. The result contains a formula that extracts the value of the support function of the obstacle at a generic direction. Some other applications to thin obstacles, obstacles in a layered medium and the far-field equation in the linear sampling method are also included.

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