Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 268, Issue -, Pages 417-431Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.10.020
Keywords
Inverse potential problem; Kohn-Vogelius criterion; Total variation; Reconstruction method
Funding
- Uruguayan Research Council ANII
- Uruguayan Research Council CSIC
- Brazilian Research Council CNPq
- DFG Research Center Matheon Mathematics for key technologies
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The inverse potential problem consists in reconstructing an unknown measure with support in a geometrical domain from a single boundary measurement. In order to deal with this severely ill-posed inverse problem, we rewrite it as an optimization problem where a Kohn-Vogelius-type functional measuring the misfit between the solutions of two auxiliary problems is minimized. One auxiliary problem contains information on the boundary measurement while the other one corresponds to the boundary excitation. The solutions of the auxiliary problems coincide once the inverse problem is solved. In order to minimize the Kohn-Vogelius criterion, its total variation with respect to a set of ball-shaped perturbations on the measure is explicitly evaluated. Then, a new method for solving the inverse potential problem based on the expression obtained is devised. Finally, some numerical results are presented in order to show the effectiveness of the proposed reconstruction algorithm. (C) 2013 Elsevier Inc. All rights reserved.
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