The dimension splitting and improved complex variable element-free Galerkin method for 3-dimensional transient heat conduction problems

In this paper, by combining the dimension splitting method and the improved complex variable element-free Galerkin method, the dimension splitting and improved complex variable element-free Galerkin (DS-ICVEFG) method is presented for 3-dimensional (3D) transient heat conduction problems. Using the dimension splitting method, a 3D transient heat conduction problem is translated into a series of 2-dimensional ones, which can be solved with the improved complex variable element-free Galerkin (ICVEFG) method. In the ICVEFG method for each 2-dimensional problem, the improved complex variable moving least-square approximation is used to obtain the shape functions, and the penalty method is used to apply the essential boundary conditions. Finite difference method is used in the 1-dimensional direction, and the Galerkin weak form of 3D transient heat conduction problem is used to obtain the final discretized equations. Then, the DS-ICVEFG method for 3D transient heat conduction problems is presented. Four numerical examples are given to show that the new method has higher computational precision and efficiency.