Composition of Self Organizing Maps for Adaptive Mesh Construction on Complex-shaped Domains

Abstract

In this paper, an important application of Self-Organizing Maps (SOM) to construction of adaptive meshes is considered. It is shown that application of the basic SOM model leads to a number of problems like inaccurate fitting the border of a physical domain, mesh self-crossings, etc. The composite SOM model is proposed which is based on the composition of a number of SOM models interacting in a special way and self-organizing over their own set of input data. A core of the composite SOM model is the colored SOM model with nonadjustable neurons which provides us a technique to control the neuron weights adjustment taking into account the fixed ones and the general layout of the mesh. As a result, the composite SOM model allows us to approximate an arbitrary complex physical domains with well topology preservation.