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A New Approach to Minimising the Frontwidth in Finite Element Calculations

Author

Listed:
  • DE SOUZA, CC.

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • KEUNINGS, R.

    (Division of Applied Machanics, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • WOLSEY, laurence

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • ZONE, O.

    (Division of Applied Machanics, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

We propose a new approach to determine the element ordering that minimises the frontwidth in finite element computations. The optimisation problem is formulated using graph theoretic concepts. We develop a divide-and-conquer strategy which defines a series of graph partitioning subproblems. The latter are tackled by means of three different heuristics, namely the Kernighan-Lin deterministic technique, and the non-deterministic Simulated Annealing and Stochastic Evolution algorithms. Results obtained for various 2D and 3D finite element meshes, whether structured or non-structured, reveal the superiority of the proposed approach relative to the standard Cuthill-McKee "greedy" algorithms. Relative improvements in frontwidth are in the range 25 - 50% in most cases. These figures translate into a significant 2 - 4 speedup of the finite element solver phase relative to the standard Cuthill-McKee ordering. The best results are obtained with the divide-and-conquer variant that uses the Stochastic Evolution partitioning heuristic. Numerical experiments indicate that the two non-deterministic variants of our divide-and-conquer approach are robust with respect to mesh refinement and vary little in solution quality from one run to another.

Suggested Citation

  • DE SOUZA, CC. & KEUNINGS, R. & WOLSEY, laurence & ZONE, O., 1992. "A New Approach to Minimising the Frontwidth in Finite Element Calculations," LIDAM Discussion Papers CORE 1992055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1992055
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