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.

Keywords:

• inverse problems
• meshfree methods
• fundamental solutions
• heat source detection
• characteristic sources

AMS Subject Classifications:

• MSC 65N35
• 35J25
• 80A23

Acknowledgements

This work results from a cooperation between the Engineering and Mathematics departments of UFRJ and IST. The work was partially funded by CNPq, CAPES (agencies for the fostering of science from the Brazilian Ministry of Science and Education, respectively) and FCT, GRICES (agencies for the fostering of science from the Portugal Ministry of Science and Higher Education) and projects POCI MAT/60863/2004, ECM/58940/2004.