Analytically-integrated radial integration BEM for solving three-dimensional transient heat conduction problems

This paper presents a new strategy using radial integration boundary element method (RIBEM) to solve three-dimensional transient heat conduction problems. In this method, the radial integral, which is used to transform the domain integrals into equivalent boundary integrals, is analytically integrated by using some newly proposed analytical expressions. This analytical approach can improve the computational efficiency and computational accuracy considerably compared with traditional RIBEM in evaluating the domain integrals through using the radial integration method (RIM). The Green's function for the Laplace equation is utilized as the fundamental solution to derive the boundary-domain integral equation for transient heat conduction. RIM is used to convert the domain integrals associated with the time derivative of temperature into equivalent boundary integrals. The derivation process about the analytical radial integral expressions published before is further investigated, the adequate and simple expression for settling the special circumstances in which the newly derived analytical expressions become invalid, is deduced in this paper. Numerical examples are given to demonstrate the efficiency of the presented method.