Meshless reconstruction of the support of a source
, Bin-Mohsin, B. and Lesnic, D. . 2016
The meshless reconstruction of the support of a three-dimensional volumetric source from a single pair of exterior boundary Cauchy data is investigated. The underlying potential satisfying the Laplace equation is sought as a discretised single-layer boundary integral representation but with sources relocated outside the solution domain, as in the method of fundamental solutions (MFS). The unknown source domain is parametrised by the radial coordinate, as a function of the spherical angles. The resulting least-squares functional estimating the gap between the measured and the computed data is minimized using the 1 sqnonl in toolbox routine in Matlab. Numerical results are presented and discussed for both exact and noisy data.
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