Center for Computational Mathematics

University of Colorado at Denver

Denver, CO 80217-3364

Application of neural networks for guiding solutions of large numerical
problems is an emerging area of research. Automatic generation of subdomains
from large 3-D finite element meshes is a key preprocessing step in domain
decomposition techniques and extremely important for load balancing, reducing
communication bandwidth and latency, and efficient processor coordination and
synchronization in a parallel computing environment. It is desired that the
subdomains are of approximately the same size, and the total number of
interface nodes between adjacent subdomains is minimal. We propose two neural
network algorithms employing the philosophy of competitive learning and
Hopfield network, that can automatically generate substructures from large 3-D
meshes with reasonable speed. Both these techniques are implemented in such
as a way that they have almost *linear complexity* w.r.t. to the problem
size for serial execution. Experimental results show more than 25%
improvement over an existing greedy algorithm.

Contributed December 16, 1992.