127 An Efficient Spectral Method for Bisection of Regular Finite Element Meshes

In this paper an efficient analytical method is presented for calculating the eigenvalues ofspecial matrices related to finite element meshes (FEMs) with regular topologies. In theproposed method, a skeleton graph is used as the model of a FEM. This graph is thenconsidered as the Cartesian product of its generators. The eigenvalues of the Laplacianmatrix of the entire graph are then easily calculated using the eigenvalues of its generators. An exceptionally fast method is also proposed for computing the second eigenvalue of the Laplacian of the graph model of a FEM, known as the Fiedler vector. After ordering the entries of the second eigenvector, the graph model is partitioned and the corresponding FEM is bisected.