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A new algorithm for domain decomposition of finite element models

A new algorithm for domain decomposition of finite element models Purpose – Domain decomposition of finite element models (FEM) for parallel computing are often performed using graph theory and algebraic graph theory. This paper aims to present a new method for such decomposition, where a combination of algebraic graph theory and differential equations is employed. Design/methodology/approach – In the present method, a combination of graph theory and differential equations is employed. The proposed method transforms the eigenvalue problem involved in decomposing FEM by the algebraic graph method, into a specific initial value problem of an ordinary differential equation. Findings – The transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems. Originality/value – Combining two different tools, namely algebraic graph theory and differential equations, results in an efficient and accurate method for decomposing the FEM which is a combinatorial optimization problem. Examples are included to illustrate the efficiency of the present method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations: International Journal for Computer-Aided Engineering and Software Emerald Publishing

A new algorithm for domain decomposition of finite element models

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References (29)

Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0264-4401
DOI
10.1108/02644400810881392
Publisher site
See Article on Publisher Site

Abstract

Purpose – Domain decomposition of finite element models (FEM) for parallel computing are often performed using graph theory and algebraic graph theory. This paper aims to present a new method for such decomposition, where a combination of algebraic graph theory and differential equations is employed. Design/methodology/approach – In the present method, a combination of graph theory and differential equations is employed. The proposed method transforms the eigenvalue problem involved in decomposing FEM by the algebraic graph method, into a specific initial value problem of an ordinary differential equation. Findings – The transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems. Originality/value – Combining two different tools, namely algebraic graph theory and differential equations, results in an efficient and accurate method for decomposing the FEM which is a combinatorial optimization problem. Examples are included to illustrate the efficiency of the present method.

Journal

Engineering Computations: International Journal for Computer-Aided Engineering and Software – Emerald Publishing

Published: Jul 18, 2008

Keywords: Finite element analysis; Differential equations; Graph theory; Parallel programming

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