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Neural network approach to construction of 3 D surface and volume adaptive meshes based on self-organization

The main goal of this investigation is to develop an efficient method for adaptive mesh construction in 3D space based on Kohonen’s Self Organizing Maps (SOM) and using the results obtained in 2D case. We considered an important class of meshes in which a mesh is an image under an appropriate mapping of some fixed mesh. The proposed neural network approach is an alternative to conventional methods, which generally require solving complicated partial differential equations and, thus, lead to overwhelming difficulties. Within the approach, the composite algorithms has been proposed for 3D meshes. This algorithm is based on alternative application of SOM learning algorithm to border and interior of a physical domain.