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Recovering the Source Term in a Linear Diffusion Problem by the Method of Fundamental Solutions

Alves, Carlos J. S.; Colaco, Marcelo J.; Leitao, Vitor M. A.; Martins, Nuno F. M.; Orlande, Helcio R. B.; Roberty, Nilson C.

Inverse Problems in Science and Engineering, 16(8) (2008), PII 905240936

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.