RI-IGABEM in inhomogeneous heat conduction problems

Abstract

The isogeometric analysis boundary element method (IGABEM) has great potential in the simulation of heat conduction problems due to its exact geometric representation and good approximation properties. In this paper, the radial integration IGABEM (RI-IGABEM) is proposed to solve isotropic heat conduction problems in inhomogeneous media with heat source. Similar to traditional BEM, the domain integrals cannot be avoided since the foundational solution for the Laplace equation is used to derive integral equation. In order to preserve the advantage of IGABEM, i.e. only boundary is discretized, the radial integration method (RIM) is applied to transform the domain integral into an equivalent boundary integral. In addition, using a simple transformation method, the uniform potential method is successfully applied to solve the strongly singular integrals, and the Telles scheme and the element sub-division method are used to solve the weakly singular integrals in RI-IGABEM respectively. In order to validate the accuracy and convergence of the RI-IGABEM in the analysis of the single or multiple boundary heat conduction problems, several 2D and 3D numerical examples are used to discuss the influence of some factors, such as the number of applied points, the order of basis functions, and the position of internal applied points.