Author:
Kaveh A.,Zahedi M.,Laknegadi K.
Abstract
PurposeNodal ordering for the formation of well‐structures stiffness matrices are often performed using graph theory and algebraic graph theory. The purpose of this paper is to present a new method for nodal ordering for profile optimization of finite element models.Design/methodology/approachIn the present method, a combination of graph theory and differential equations is employed. The proposed method transforms the eigenvalue problem involved in optimal ordering of algebraic graph method into a specific initial value problem of an ordinary differential equation.FindingsThe transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems.Originality/valueCombining two different tools, namely graph theory and differential equations, results in a more efficient and accurate method for nodal ordering problem, which is a combinatorial optimization problem. Examples are included to illustrate the efficiency of the present method.
Subject
Computational Theory and Mathematics,Computer Science Applications,General Engineering,Software
Reference14 articles.
1. Chandrupatla, T.R. and Belegundu, A. (1997), Introduction to Finite Elements in Engineering, Prentice‐Hall, Englewood Cliffs, NJ.
2. Cuthill, E. and McKee, J. (1969), “Reducing the bandwidth of sparse symmetric matrices”, Proceedings of the 24th National Conference ACM, Bardon System Press, New Jersey, pp. 157‐72.
3. Fiedler, M. (1973), “Algebraic connectivity of graphs”, Czechoslovak Mathematical Journal, Vol. 23, pp. 298‐305.
4. Gupta, K.K. (1973), “Eigenproblem solution by a combined sturm sequence and inverse iteration technique”, International Journal for Numerical Methods in Engineering, Vol. 7, pp. 17‐42.
5. Kaveh, A. (2004), Structural Mechanics: Graph and Matrix Methods, 3rd ed., Research Studies Press (Wiley), Taunton.
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