Topology and graph products; eigenproblems in optimal structural analysis

Abstract

In this paper, a topological method is presented to obtain the eigensolution of a cylindrical-shaped grid from those of a plane grid. Similarly, the eigenproperty of a torus-shaped grid is calculated from those of a cylindrical-shaped grid. These transformations are performed using an identification approach employed in topology for the formation of different surfaces. The proven theorems simplify the evaluation of the eigenvectors to be employed in the ordering and graph partitioning of regular structures for optimal analysis. Copyright © 2007 John Wiley & Sons, Ltd.