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

Abstract

Summary 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.

Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

“…By combining the dimension splitting method and meshless methods, the hybrid complex variable EFG method [27][28][29][30][31], the dimension split EFG method [32][33][34][35], and the dimension splitting reproducing kernel particle method [36] for 3D problems are proposed, respectively, and those new methods can improve the computational speed of traditional meshless methods for solving 3D problems greatly.…”

INverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation

“…The complex variable moving least-squares (CVMLS) [45] and the improved complex variable moving least-squares (ICVMLS) approximations, which are approximation of a vector function, have been developed. Therefore, based on these approximations, the complex variable element-free Galerkin (CVEFG) and the improved complex variable element-free Galerkin (ICVEFG) methods have been presented [10,14,15,37,38,44,54,55].…”

The dimension splitting reproducing kernel particle method for three‐dimensional potential problems

“…D'Souza et al presented the DSM for simplifying diffusion in lattice‐gas models . Cheng et al combined the DSM with improved complex variable EFG method to solve 3D potential problems, wave propagation problems, 3D transient heat conduction problems, and advection‐diffusion problems . Meng et al combined the DSM with IEFG method to solve 3D potential problems, wave propagation problems, and transient heat conduction problems …”