Automatic substructuring for domain decomposition using neural networks

Application of neural networks for guiding solutions of large numerical problems is an emerging area of research. Automatic generation of subdomains from large 3D finite element meshes is a key preprocessing step in domain decomposition techniques and extremely important for proper 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 approximately of 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 3D meshes with reasonable speed. Both these techniques are implemented in such as a way that they have almost linear complexity w.r.t. the problem size for serial execution. Experimental results show more than 25% improvement over an existing greedy algorithm