Identification of the combination of monopolar and dipolar sources for elliptic equations

Abstract

In this paper, we propose an algorithm for detecting the combination of monopolar and multipolar point sources for elliptic partial differential equations in the two-dimensional domain from their Neumann and Dirichlet boundary data. We prove that the source locations are shown to be the solutions of some characteristic equation related to the inverse of a Hankel-type matrix derived from the boundary data. We then apply this fact to provide a detection algorithm.