Using Self Organizing Maps for 3D surface and volume adaptive mesh generation
Olga Nechaeva · InTech eBooks · 2010
Self-Organizing Maps 124GeomRandom (Nechaeva, 2009) packages and tested on a number of physical domains.The quality of resulting meshes is acceptable according to the commonly used quality criteria.In order to support this alternative approach to mesh generation, a Theorem of Correspondence is proved, that states that goals of traditional PDE approach to construction of adaptive meshes from the considered class are equivalent to the goals of learning for Self Organizing Maps.The obtained results showed that the neural network approach provides us a highly parallelizable technique (Nechaeva, 2005) for automatic construction of qualitative adaptive meshes and possesses the following properties: (1) due to the self organizing principles the algorithm transforms the mesh automatically, starting with arbitrary initial nodes positions, and does not require to fix the boundary nodes beforehand; (2) stochastic nature of the algorithm enables us to illuminate any limitations on the mesh density function; (3) internal parallelism of the method allows us to parallelize the mesh construction process, taking into account the requirements on the parallel implementation of a problem to be solved on the mesh; (4) the method uses the same algorithms for different dimensionalities of a physical domain that proves the universality of the proposed method. How to referenceIn order to correctly reference this scholarly work, feel free to copy and paste the following: Olga Nechaeva (2010).Using Self Organizing Maps for 3D surface and volume adaptive mesh generation, Self-Organizing Maps, George K Matsopoulos (Ed.),