Abstract
We consider point source approximation methods for the solution of inverse object reconstruction problems for the Laplace and the Helmholtz equation. We present a two-step algorithm to reconstruct the neighbourhood of the obstacle by a proper choice of approximation domains, first. Then we reconstruct the obstacle in the second step of the algorithm by varying the approximation domains adaptively. We formulate this two-step algorithm for the point source method, the singular sources method and the probe method. Moreover we show numerical examples both for the Laplace and the Helmholtz equation in two and three dimensions, respectively. Finally, we compare the point source approximation methods with the factorisation and the linear sampling method both for exact data and noisy data.
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