The dimension splitting and improved complex variable element‐free Galerkin method for 3‐dimensional transient heat conduction problems. (2nd February 2018)

• Record Type: Journal Article
• Authors: Cheng, H.; Peng, M.J.; Cheng, Y.M.
• Is Part Of: International journal for numerical methods in engineering. Volume 114:Number 3(2018)
• Page Start: 321
• Page End: 345
• Publication Date: 2018-02-02
• Subjects: dimension splitting and improved complex variable element‐free Galerkin method -- dimension splitting method -- finite difference method -- improved complex variable element‐free Galerkin method -- improved complex variable moving least‐square approximation; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5745
• Languages: English
• ISSNs: 0029-5981

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.