Mapping of finite-element grids onto parallel computers using neural networks

Abstract

In this paper, LSOM (Load-balancing Self-Organizing Map), a neural network based on Kohonen's self-organizing map is proposed for the problem of mapping finite-element method (FEM) grids to distributed-memory parallel computers with mesh interconnection networks. The rough global ordering produced by LSOM is then combined with the local refinement Kernighan-Lin algorithm (called LSOM-KL) to obtain the solution. LSOM-KL obtained a load imbalance of less than 0.1% and a low number of hops, comparable to results obtained with commonly used recursive bisection methods.