A Finite Element Nodal Ordering with Algebraic Graph Theory

Abstract:

A new methodology is proposed for construction of weighted element clique graph (WECG) based on nodal degrees of freedom.The Fiedler vector of the Laplacian Matrix of WECG is used for reduction of the bandwidth and profile of stiffness matrix in finite element analysis.The present method is not only suitable for common finite element models,but also for models including different nodal degrees of freedom of element in number and usually leads to better results for the latter models compared with common methodology of algebraic graph theory based on Laplacian Matrix of element clique graph.A pre-processing routine based on the present method is embedded in a finite element program,which can reduce the generation task of finite element model without consideration of nodal ordering.The numerical experiments show that the present method is efficient.