The Neural Network Approach to Automatic Construction of Adaptive Meshes on Multiply-connected Domains

The neural network approach to automatic construction of adaptive meshes, which we have developed for simply-connected domains, is here extended to the case of multiply-connected domains, i.e. those with holes. This approach is based on Kohonen´s self-organizing maps (SOM) and refers to a class of methods in which an adaptive mesh is a result of transformation of a fixed uniform mesh. Within the approach, a composite algorithm has been proposed in which the SOM algorithm is applied alternatively to boundary and interior mesh nodes. In the case of multiply-connected domains, this algorithm is applied to specify automatically the holes in a fixed mesh. Also, a modified composite algorithm is proposed that provides the consistency of SOM algorithms alternatively applied to both the outer and inner borders and to the interior of the domain. The mesh smoothing algorithm is proposed for multiply-connected domains. The quality of the resulting meshes is admissible according to generally accepted quality criteria.