A boundary element formulation for the heat equation with dissipative and heat generation terms

This article presents a formulation of the Boundary Element Method (BEM) for the study of heat diffusion in isotropic and homogeneous media. The proposed formulation has a time independent fundamental solution obtained from the two-dimensional Laplace equation. Consequently, the formulation is called D-BEM since it has domain integrals in the basic integral equation. The first order time derivative that appears in the integral equations is approximated by a backward finite difference scheme. Internal dissipative and heat generation terms are considered in the analyses. The results from the numerical model are compared with the available analytical solutions. The correlation estimator R2 is employed to validate the numerical model and to demonstrate the accuracy of the proposed formulation.