New analytical expressions in radial integration BEM for solving heat conduction problems with variable coefficients

In this paper, a new approach using analytical expressions in the radial integration boundary element method (RIBEM) is presented for solving three kinds of representative variable coefficient heat conduction problems. This approach can improve the computational efficiency considerably and can overcome the time-consuming deficiency of RIBEM in computing involved radial integrals. Also, because it can solve any kinds of variable coefficient heat conduction problems, this approach has a very wide applicability. The fourth-order spline RBF is employed to approximate the unknowns appearing in domain integrals arising from the varying heat conductivity. The radial integration method is utilized to convert domain integrals to the boundary, which results in a pure boundary discretization algorithm. Numerical examples are given to demonstrate the efficiency of the presented approach.