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.

通过一种新颖的无边界类型无元素方法，即无虚拟边界元素的Galerkin方法（VBEFGM），将具有可变热源的非均质介质中的3D热分析解决方案分为均匀解决方案和特殊解决方案。均质解可以通过虚拟边界自由法（VBEFM）获得。均质解的虚拟源函数和特定解的未知系数通过径向基函数插值（RBFI）构造。用于可变热源的非均匀介质中3D热分析的VBEFGM是真正无网格的，不需要背景积分元素。其方程式由加权残差法的Galerkin方法获得。ANSYS参数化设计语言（APDL）的演示可以极大地方便编程，以提取节点上的坐标信息和外部法线余弦。通过VBEFGM详细推导了在热源可变的非均质介质中进行3D热分析的计算方案和特定的加权系数。给出了数值计算步骤和流程图。计算了三个数值示例。将结果与其他数值方法和精确解进行比较。通过VBEFGM证明了该方法的稳定性和准确性，可用于热源不均匀的非均匀介质中的3D热分析。通过VBEFGM详细推导了在热源可变的非均质介质中进行3D热分析的计算方案和特定的加权系数。给出了数值计算步骤和流程图。计算了三个数值示例。将结果与其他数值方法和精确解进行比较。通过VBEFGM证明了该方法的稳定性和准确性，可用于热源不均匀的非均匀介质中的3D热分析。通过VBEFGM详细推导了在具有可变热源的非均匀介质中进行3D热分析的计算方案和特定的加权系数。给出了数值计算步骤和流程图。计算了三个数值示例。将结果与其他数值方法和精确解进行比较。通过VBEFGM证明了该方法的稳定性和准确性，可用于热源不均匀的非均匀介质中的3D热分析。