Finite element mesh decomposition using complementary Laplacian matrix

Abstract

In this paper an efficient method is developed for decomposition of finite element meshes. The present method is based on concepts from algebraic graph theory and consists of an efficient algorithm to calculate the Fiedler vector of the Laplacian matrix of a graph. The problem of finding the second eigenvalue of the Laplacian matrix is converted into that of evaluating the maximal eigenvalue of the complementary Laplacian matrix. The corresponding eigenvector is constructed by a simple iterative method and applied to graph partitioning. An appropriate transformation maps the graph partitioning into that of domain decomposition of the corresponding finite element mesh. Copyright © 2000 John Wiley & Sons, Ltd.