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CivilComp Proceedings
ISSN 17593433 CCP: 65
FINITE ELEMENTS: TECHNIQUES AND DEVELOPMENTS Edited by: B.H.V. Topping
Paper II.2
A Multilevel Finite Element Nodal Ordering using Algebraic Graph Theory A. Kaveh+ and H.A. Rahimi Bondarabady#
+Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran
A. Kaveh, H.A. Rahimi Bondarabady, "A Multilevel Finite Element Nodal Ordering using Algebraic Graph Theory", in B.H.V. Topping, (Editor), "Finite Elements: Techniques and Developments", CivilComp Press, Edinburgh, UK, pp 3542, 2000. doi:10.4203/ccp.65.2.2
Abstract
In this paper an efficient method is developed for nodal and
element ordering of structures and finite element models. The
present method is based on concepts from algebraic graph
theory and comprises an efficient algorithm for calculating
the Fiedler vector of the Laplacian matrix of a graph. The
problem of finding 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 finite element models. In order to
increase the efficiency of the algebraic graph theoretical
method a multilevel scheme is adopted in which the graph
model corresponding to a finite element mesh is coarsened in
various levels to reduce the size of the problem. Then an
efficient algebraic method is applied and with an
uncoarsening process, the final ordering of the graph and
hence that of the corresponding finite element model is
obtained.
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