The method of fundamental solutions for heat conduction in layered materials

In this paper, we investigate the application of the Method of Fundamental Solutions (MFS) to two-dimensional problems of steady-state heat conduction in isotropic and anisotropic bimaterials. Two approaches are used: a domain decomposition technique and a single-domain approach in which modified fundamental solutions are employed. The modified fundamental solutions satisfy the interface continuity conditions automatically for planar interfaces. The two approaches are tested and compared on several test problems and their relative merits and disadvantages discussed. Finally, we use the domain decomposition approach to investigate bimaterial problems where the interface is non-planar and the modified fundamental solutions cannot be used.