A hybrid method for finite element ordering

Nodal ordering for the formation of suitable sparsity patterns for stiffness matrices of finite element meshes are often performed using graph theory and algebraic graph theory. In this paper a hybrid method is presented employing the main features of each theory. In this method, vectors containing certain properties of graphs are taken as Ritz vectors, and using methods for constructing a complementary Laplacian, a reduced eigenproblem is formed. The solution of this problem results in coefficients of the Ritz vectors, indicating the significance of each considered vector. The present method uses the global properties of graphs in ordering, and the local properties are incorporated using algebraic graph theory. The main feature of this method is its capability of transforming a general eigenproblem into an efficient approach incorporating graph theory. Examples are included to illustrate the efficiency of the presented method.