Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems

doi:10.1088/1674-1056/22/5/050202

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 50202-050202.doi: 10.1088/1674-1056/22/5/050202

Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems

陈丽^{a b}, 马和平^a, 程玉民^c

a Department of Mathematics, Shanghai University, Shanghai 200072, China;
b Department of Engineering Mechanics, Chang'an University, Xi'an 710064, China;
c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2012-11-06 修回日期:2012-12-19 出版日期:2013-04-01 发布日期:2013-04-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Special Fund for Basic Scientific Research of Central Colleges of Chang'an University, China (Grant No. CHD2011JC080).

Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems

Chen Li (陈丽)^{a b}, Ma He-Ping (马和平)^a, Cheng Yu-Min (程玉民)^c

a Department of Mathematics, Shanghai University, Shanghai 200072, China;
b Department of Engineering Mechanics, Chang'an University, Xi'an 710064, China;
c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received:2012-11-06 Revised:2012-12-19 Online:2013-04-01 Published:2013-04-01
Contact: Cheng Yu-Min E-mail:ymcheng@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Special Fund for Basic Scientific Research of Central Colleges of Chang'an University, China (Grant No. CHD2011JC080).

摘要/Abstract

摘要： In this paper, the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

关键词: complex variable reproducing kernel particle method, finite element method, combined method, transient heat conduction

Abstract: In this paper, the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

Key words: complex variable reproducing kernel particle method, finite element method, combined method, transient heat conduction

中图分类号: (Several complex variables and analytic spaces)

02.30.Fn

02.30.Jr (Partial differential equations) 02.60.-x (Numerical approximation and analysis) 02.60.Cb (Numerical simulation; solution of equations)

陈丽, 马和平, 程玉民. Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems[J]. 中国物理B, 2013, 22(5): 50202-050202.

Chen Li (陈丽), Ma He-Ping (马和平), Cheng Yu-Min (程玉民). Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems[J]. Chin. Phys. B, 2013, 22(5): 50202-050202.

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Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems

Combine complex variable reproducing kernel particle method and finite element method for solving transient heat conduction problems

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