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A new one‐shot pointwise source reconstruction method
Authors:Thiago J Machado  Jaqueline S Angelo  Antonio A Novotny
Institution:Laboratório Nacional de Computa??o Científica LNCC/MCT, Coordena??o de Matemática Aplicada e Computacional, Petrópolis ‐ RJ, Brasil
Abstract:In this work, a new pointwise source reconstruction method is proposed. From a single pair of boundary measurements, we want to completely characterize the unknown set of pointwise sources, namely, the number of sources and their locations and intensities. The idea is to rewrite the inverse source problem as an optimization problem, where a Kohn‐Vogelius type functional is minimized with respect to a set of admissible pointwise sources. The resulting second‐order reconstruction algorithm is non‐iterative and thus very robust with respect to noisy data. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments into two spatial dimensions are presented. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:pointwise source reconstruction  non‐iterative second‐order algorithm  Kohn‐Vogelius criterion  sensitivity analysis
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