Coupled complex boundary method for a geometric inverse source problem

This work deals with a geometric inverse source problem. It consists in recovering the characteristic function of an unknown inclusion based on boundary measurements. We propose new reconstruction method CCBM and shape gradient method, problem is formulated as optimization one, corresponding to coupled complex state Well posedness existence results are presented. A computed expression for used implement algorithm. The efficiency accuracy algorithm illustrated by some numerical results, comparison between CCBM, Least-squares Kohn-Vogeluis methods