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

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 th...

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Bibliographic Details
Published inChinese physics B Vol. 22; no. 5; pp. 67 - 74
Main Author 陈丽 马和平 程玉民
Format Journal Article
LanguageEnglish
Published 01.05.2013
Subjects
Approximation
Complex variables
Computational efficiency
Discretization
Finite element method
Kernels
Mathematical analysis
Mathematical models
Transient heat conduction
时间离散
有限元方法
本质边界条件
热传导问题
瞬态
粒子
计算效率
边界值问题
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/22/5/050202

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Summary: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.
Bibliography:complex variable reproducing kernel particle method, finite element method, combined method,transient heat conduction
Chen Li, Ma He-Ping, and Cheng Yu-Min（ 1 Department of Mathematics, Shanghai University, Shanghai 200072, China 2 Department of Engineering Mechanics, Chang＇an University, Xi＇ an 710064, China 3 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China）
11-5639/O4
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.
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content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/5/050202