A new boundary element-free Galerkin method using dual CSRBFI for 2D inhomogeneous heat conduction problems

It is established that the new boundary element-free Galerkin method, namely the virtual boundary element-free Galerkin method (VBEFGM), using dual compactly supported radial basis function interpolation (CSRBFI) for 2D inhomogeneous heat conduction problems with variable heat sources, whose solutions are divided into homogeneous and particular solutions. The virtual loads of the homogeneous solutions and undetermined coefficients of particular solutions are interpolated by CSRBFI. Its formula is established by the Galerkin method. The homogeneous solutions are obtained by the virtual boundary element-free method (VBEFM). The recommended method for 2D inhomogeneous heat conduction problems is real meshfree without background integration elements and exhibits the merits of the meshfree method, Galerkin method, and boundary element method. Its calculation scheme is deduced in detail and easily programmed. The coefficient matrix has symmetrical characteristics. The implementation steps and implementation flow-chart are also shown in detail. Seven numerical examples, such as exponential functionally graded material, are calculated and contrasted with other numerical methods. The precision and stableness of the proposed method for 2D inhomogeneous heat conduction problems are verified.