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The virtual boundary meshfree Galerkin method (VBMGM) is given to calculate the multi-domain transient heat conduction with heat source problem. The radial basis function interpolation is used to obtain the virtual source function on the virtual boundary, the heat source, the particular solutions of the temperature, and the heat flux in the computational domain. The formula of the proposed method is gotten by the Galerkin method and the control equations of the multi-domain transient heat conduction with heat source. Therefore, there are the advantages of the Galerkin method, the boundary element method, and the meshfree method for the multi-domain transient heat conduction with heat source problem by VBMGM. The numerical meaning of the weighted values are definite for the multi-domain transient heat conduction with heat source problem through VBMGM, such as the partial derivatives of the temperature, the heat flux, the heat source, and the continuity conditions on the public boundary at time. The detailed calculation scheme of VBMGM is deducted for the multi-domain transient heat conduction with heat source problem. Two numerical examples, four subdomains with the time-dependent heat source problem and two subdomains with the constant heat source and mixed boundary condition problem, are computed. The accuracy and the stability of VBMGM for the multi-domain transient heat conduction with heat source problem are verified. [ABSTRACT FROM AUTHOR]

This article presents a virtual boundary meshless with Trefftz method for calculation of the two-dimensional steady-state heat conduction crack problem, which is based on the idea of multidomain combination. The virtual source function is constructed by the radial basis functions approximation in the subdomain not containing the crack. The temperature or heat flux is calculated by crack special solution of Trefftz function in the crack subdomain. Thus, the proposed method has the advantages of both the boundary-type meshless method and the Trefftz method. No nodes or elements are distributed on the crack, because the boundary condition of the crack is automatically satisfied by employing the crack special solution of the Trefftz function. The heat stress intensity factor is simply and directly calculated. [ABSTRACT FROM PUBLISHER]