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A new one‐shot pointwise source reconstruction method
Author(s) -
Machado Thiago J.,
Angelo Jaqueline S.,
Novotny Antonio A.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4059
Subject(s) - pointwise , mathematics , set (abstract data type) , boundary (topology) , algorithm , inverse problem , mathematical optimization , iterative method , mathematical analysis , computer science , programming language
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.