A novel boundary-type element-free method for 3D thermal analysis in inhomogeneous media with variable thermal source

Abstract Solutions of 3D thermal analysis in inhomogeneous media with variable thermal source are divided into homogeneous and particular solutions by a novel boundary-type element-free method, namely virtual boundary element-free Galerkin method (VBEFGM). The homogeneous solution can be obtained by the virtual boundary element-free method (VBEFM). The virtual source function of the homogeneous solution and the unknown coefficient of the particular solution are constructed by the radial basis function interpolation (RBFI). And VBEFGM for 3D thermal analysis in inhomogeneous media with variable thermal source is real meshfree and does not require the background integral element. Its equation is obtained the Galerkin method of the weighted residual methods. The demonstration of ANSYS Parametric Design Language (APDL) can greatly facilitate the programming for the extraction of the coordinate information and the outer normal cosines on nodes. The calculation scheme and the specific weighted coefficients are deducted in detail for 3D thermal analysis in inhomogeneous media with variable thermal source by VBEFGM. The numerical calculational steps and flow chart are given. Three numerical examples are computed. The results are compared with other numerical methods and the exact solutions. The stability and the accuracy of the proposed method is proved by VBEFGM for 3D thermal analysis in inhomogeneous media with variable thermal source.