| Abstract | In this work, we address the reconstruction of characteristic source functions in a potential problem, from the knowledge of full and partial boundary data. The inverse problem is formulated as an inverse obstacle problem and two iterative methods are applied. A decomposition method based on the Kirsch-Kress method (requires Cauchy data reconstruction) and a Newton-type of method based on the domain derivative (requires the resolution of direct transmission problems). For the reconstruction of Cauchy data we use the method of fundamental solutions (MFS) and we show that, for partial data, we can consider only one exterior artificial boundary. We test the domain derivative method using the MFS (for transmission problems) and present theoretical results that justifies this numerical approximation. The feasibility of these methods will be illustrated by numerical simulations for both full and partial data. |
