A boundary element and radial basis function approximation method for a second order elliptic partial differential equation with general variable coefficients

Abstract

A numerical method based on boundary integral equation and radial basis function approximation is presented for solving boundary value problems governed by a second‐order elliptic partial differential equation with variable coefficients. The equation arises in the analysis of steady‐state anisotropic heat or mass diffusion in nonhomogeneous media with properties that vary according to general smoothly varying functions of space. The method requires only the boundary of the solution domain to be discretized into elements. To check the validity and accuracy of the numerical solution, some specific problems with known solutions are solved.

Keywords

• anisotropic diffusion
• boundary element method
• elliptic partial differential equation
• radial basis functions
• variable coefficients