Determination of locations of point-like masses in an inverse source problem of the Poisson equation

AbstractAn inverse source problem of the Poisson equation is discussed with a boundary element approach and discrete Fourier transform. We consider the case that several point-like masses are placed in a disk domain, and consider the problem to determine the mass positions from the potential and flux on the boundary. Effective algorithms are presented for the determination of mass positions and for error estimations using the boundary element method and discrete Fourier transform of the logarithmic potential. The applicability of our algorithms is illustrated by numerical examples