A multi-level finite element nodal ordering using algebraic graph theory

✍ Scribed by A. Kaveh; H.A. Rahimi Bondarabady

• Book ID: 104308417
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 381 KB
• Volume: 38
• Category: Article
• ISSN: 0168-874X
• DOI: 10.1016/s0168-874x(01)00062-2

✦ Synopsis

In this paper an e cient method is developed for nodal and element ordering of structures and ÿnite element models. The present method is based on concepts from algebraic graph theory and comprises of an e cient algorithm for calculating the Fiedler vector of the Laplacian matrix of a graph. The problem of ÿnding the second eigenvalue of the Laplacian matrix is transformed into evaluating the maximal eigenvalue of the complementary Laplacian matrix. An iterative method is then employed to form the eigenvector needed for renumbering the vertices of a graph. An appropriate transformation, maps the vertex ordering of graphs into nodal and element ordering of the ÿnite element models. In order to increase the e ciency of the algebraic graph theoretical method, a multi-level scheme is adopted in which the graph model corresponding to a ÿnite element mesh is coarsened in various levels to reduce the size of the problem. Then an e cient algebraic method is applied and with an uncoarsening process, the ÿnal ordering of the graph and hence that of the corresponding ÿnite element model is obtained.