A new radial integration polygonal boundary element method for solving heat conduction problems

Abstract

A new approach, radial integration polygonal boundary element method (RIPBEM), for solving heat conduction problems is presented in this paper. The proposed RIPBEM is a new concept in boundary element method (BEM), which would be of great flexibility in mesh generation of complex 3D geometries. Due to the characteristic of arbitrary shapes of polygonal elements, conventional shape functions are insufficient. Moreover, the resulted surface boundary integrals cannot be directly evaluated by the standard Gauss quadrature. To solve these problems, general shape functions for polygonal elements with arbitrary number of nodes are given. To generally and numerically calculate the resulted surface integrals, the radial integration method (RIM) is employed to convert the surface boundary integrals into equivalent contour line integrals of the polygonal elements. As for 3D domain integrals, they are transformed to equivalent line integrals using RIM twice. This methodology can explicitly eliminate strong singularities. Several numerical examples are given to show the effectiveness and the accuracy of the proposed polygonal boundary element method for solving heat conduction problems.