A New Approach To Minimizing the Frontwidth in Finite-element Calculations

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