Source reconstruction for the Helmholtz equation

N. C. Roberty, D. M. de Sousa
The purpose of this paper is investigate the Helmholtz star-shaped characteristic sources reconstruction from a boundary data. Using a Green identity we establish a reciprocity functional mapping solutions of the Helmholtz equation to their integral in the unknown characteristic support. The restrict identifiability for an small frequency is investigated. An evaluation of the reciprocity functional based on the Fourier coefficients of the parametric curve representation of the source boundary is presented. Numerical simulations in a two dimensional model shows that after the first eigenvalue for the Helmholtz problem associated with the domain $\Omega$ we start to have poor reconstructions.
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