Simulation of heat conduction problems in layered materials using the meshless singular boundary method

Abstract

In this paper, we apply the novel singular boundary method for the simulation of heat conduction problems in layered materials. The singular boundary method is a recently developed boundary-type meshless collocation method. While inheriting the merits of conventional boundary-type methods, mesh and singularity of fundamental solutions are also circumvented. In the singular boundary method, the approximation is established via the linear combination of the fundamental solutions. Basic concept behind the methodology for the heat conduction problems in layered materials is the domain decomposition technique. For problems under consideration, the layered materials are divided into several sub-domains where the solutions are established separately by means of the singular boundary method. To form the final solution system, the interface continuity conditions are taken into account. Numerical experiments verify the accuracy and convergence of the present approach.