A Meshless Boundary Element Method Formulation for Transient Heat Conduction Problems with Heat Sources

In the boundary element formulation of heat conduction, the heat source effect imposes an additional domain integral term on the system of integral equations. With this term, an important advantage of the boundary element method as a boundary-only formulation will be lost. This paper presents an accurate method for the evaluation of heat source domain integrals, with no need of domain discretization. Transformation of the domain integral into the corresponding boundary integral is carried out using Green s theorem. Both time-dependent and time-independent fundamental solutions are considered. The methodology can be implemented in general and for similar situations. Numerical examples will be presented to demonstrate the accuracy and efficiency of the presented method.