Finite element mesh decomposition using complementary Laplacian matrix

In this paper an efficient method is developed for decomposition of finite element meshes. The present method is based on concepts from algebraic grap h theory and consists of an efficient algorithm to calculate the Fiedler ve ctor 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 correspondin g eigenvector is constructed by a simple iterative:method and applied to gr aph partitioning. An appropriate transformation maps the graph partitioning into that of domain decomposition of the corresponding finite element mesh . Copyright (C) 2000 John Wiley & Sons, Ltd.