Numerical grid generation: foundations and applications
Numerical grid generation: foundations and applications
A Framework for Variational Grid Generation: Conditioning the Jacobian Matrix with Matrix Norms
SIAM Journal on Scientific Computing
Self-Organizing Maps
A Moving Mesh Method Based on the Geometric Conservation Law
SIAM Journal on Scientific Computing
Approaches for generating moving adaptive meshes: location versus velocity
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Composite algorithm for adaptive mesh construction based on self-organizing maps
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
Neural network approach for parallel construction of adaptive meshes
PaCT'05 Proceedings of the 8th international conference on Parallel Computing Technologies
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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.