Nodal 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.
In 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.
The transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems.
Combining 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.
