Parallel construction of moving adaptive meshes based on self-organization

A new highly parallelizable method of moving mesh construction based on the Kohonen's Self-Organizing Maps (SOM) is proposed. This method belongs to a class of methods in which the mesh is an image under an appropriate mapping of a fixed mesh over a computational domain. Unlike the conventional methods of this class, the proposed method doesn't require solving complicated systems of nonlinear partial differential equations and is able to work with arbitrary time-dependent mesh density function. High efficiency of parallelization is conditioned by the inherent parallelism of the underlying stochastic SOM algorithm. Sequential as well as detailed parallel algorithms for moving mesh construction are proposed.