A NEW APPROACH TO MINIMIZING THE FRONTWIDTH IN FINITE-ELEMENT CALCULATIONS

We propose a new approach to determine the element ordering that minim ises the frontwidth in finite element computations. The optimisation p roblem is formulated using graph theoretic concepts. We develop a divi de-and-conquer strategy which defines a series of graph partitioning s ubproblems. The latter are tackled by means of three different heurist ics, namely the Kernighan-Lin deterministic technique, and the non-det erministic Simulated Annealing and Stochastic Evolution algorithms. Re sults obtained for various 2D and 3D finite element meshes, whether st ructured or non-structured, reveal the superiority of the proposed app roach relative to the standard Cuthill-McKee 'greedy' algorithms. Rela tive 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 tha t uses the Stochastic Evolution partitioning heuristic. Numerical expe riments indicate that the two non-deterministic variants of our divide -and-conquer approach are robust with respect to mesh refinement and v ary little in solution quality from one run to another.