Subdomain Epoch % Improvement Subdomain Epoch % Improvement Substructure Generation in the 2-d Nite Element Mesh Shown in Fig. 2 Using Competitive Learning. Subdomain Epoch % Improvement Subdomain Epoch % Improvement

(b). Substructure generation in the 3-D nite element mesh shown in Fig. 4 using Competitive learning. tures for domain decomposition using ANN paradigms. This study demonstrates the usefulness of neural networks for solving large optimization problems with reasonable speed, that are nontrivial, but may not be as hard as for example, the traveling salesman problem. Both techniques yield signicantly better outputs compared to a popular greedy algorithm, when only element to element connectiv-ity in the FE mesh is used. Sparse implementation of the connection weight matrix (with a threshold) is being studied to reduce storage requirements. Future research will concentrate on incorporating the aspect ratio requirement explicitly into the optimization process; use of fast ANN algorithms, e.g., VFSR [5] and Mean eld [7] type, that attempt to avoid local minima; automatic selection of the network parameters; and employing physical properties of the elements, e.g., elasticity, conductance etc. Generation of 3-D hexahedral nite element meshes, given 3-D node points, is a similar problem and will be studied following a similar philosophy. Automatic partitioning of unstruc-tured meshes for the parallel solution of problems in computational mechanics, Intl. Acknowledgments The implementation of the greedy algorithm and the test problems in Figures 3 and 4 have been provided by Charbel Farhat, at Boulder. We also would like to thank Ellen Applebaum for her suggestions regarding competitive learning.