On the Reconstruction of Characteristic Sources in Helmholtz equations using the Method of Fundamental Solutions.

Resumen

In we considered the inverse problem that consists in the determination of the support of characteristic sources in physical phenomena described by the modified and classical Helmholtz equations, from boundary measurements. There we identified the location of the barycenter of a star shaped support establishing a simple formula, and this allows to consider a minimization algorithm to recover the original shape, based on simulations by the method of fundamental solutions. Further numerical experiments that validate the barycenter results and the minimization algorithm are presented.