Automatic Mesh Generation (for Finite Element Method) Using Self-Organizing Neural Networks

Proceedings of the Fourth Bar-Ilan Symposium on Foundations of Artificial Intelligence

Volume

Proceedings of the Fourth Bar-Ilan Symposium on Foundations of Artificial Intelligence

Contents

In the paper, we present a method to automatically fit a topological grid (mesh) to the geometry of a given domain in such a way as place the density of nodes in close correspondence with a given density across the domain. This is important in, for example, the preprocessing of the finite element method; where one wants to get the best possible approximation to a solution of a partial differential equation for a given computational resource. Here the density function corresponds to the areas of interest in the domain. Our method uses the notion of a self-organizing neural network (due to Kohonen and others) for the basic organization with some additional adaptations appropriate for our problem. We have also implemented an improvement on the algorithm suggested by Tzvi and Iaakov.