The inverse problem of dipolar source identification from incomplete boundary measurements

Abstract

We consider and combine two methods to solve the inverse problem of locating dipolar sources in a restricted domain from measurements of the Cauchy data on a part of the boundary for the Laplace equation. We begin by extending the boundary measurements, which are accessible only on a part of the boundary by solving an extremal bounded problem in an annulus. The inverse problem of source identification is then solved using the reciprocity gap concept applied to the completed data. In order to evaluate the effectiveness of source detection with regard to the expansion of the data, some numerical tests are provided.