Recovering the source term in a linear diffusion problem by the method of fundamental solutions

Abstract

This work considers the detection of the spatial source term distribution in a multidimensional linear diffusion problem with constant (and known) thermal conductivity. This work can be physically associated with the detection of non-homogeneities in a material that are inclusion sources in a heat conduction problem. The uniqueness of the inverse problem is discussed in terms of classes of identifiable sources. Numerically, we propose to solve these inverse source problems using fundamental solution-based methods, namely an extension of the method of fundamental solutions to domain problems. Several examples are presented and the numerical reconstructions are discussed.