@MISC{Potthast_apoint-source, author = {Roland Potthast}, title = {A Point-Source Method in Inverse Acoustic Scattering.}, year = {} }

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Abstract

We present a point-source method to solve inverse acoustic obstacle scattering problems. The point-source method gives a new and explicit procedure how to compute from the far field pattern u 1 of a scattered field an approximation for the total acoustic field u near the unknown obstacle. The point-source method then searches for the boundary of the obstacle as a zero-curve of u or @u @ , respectively, where is normal to the unknown domain D. A threedimensional example for the numerical reconstruction of a scatterer consisting of two separate components is provided. 1 Introduction. We consider the scattering of acoustic waves from a sound-soft or sound-hard scatterer D. We assume D to be bounded in IR 3 and the boundary @D sufficiently smooth. An incident time-harmonic acoustic wave u i satisfies the Helmholtz equation 4u + 2 u = 0 in IR 3 , where denotes the wave number. The direct scattering problem is to find a scattered field u s which solves the Helmholtz equati...