A new boundary meshfree method for calculating the multi-domain constant coefficient heat conduction with a heat source problem

A new high-precision boundary meshfree method, namely virtual boundary meshfree Galerkin method (VBMGM), for calculating the multi-domain constant coefficient heat conduction with a heat source problem is given. In the paper, the radial basis function interpolation is used to solve the virtual source function of virtual boundary and the heat source within each subdomain. Simultaneously, the equation of VBMGM for multi-domain constant coefficient heat conduction with a heat source problem is obtained by the Galerkin method. Therefore, the proposed method has common advantages of the boundary element method, meshfree method, and Galerkin method. Coefficient matrix of this specific expression is symmetrical and the specific expression of VBMGM for the multi-domain constant coefficient heat conduction with a heat source problem is given. Two numerical examples are given. The numerical results are also compared with other numerical methods. The accuracy and feasibility of the method for the multi-domain constant coefficient heat conduction with a heat source problem are proved.