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Parallel Adaptive Tetrahedral Mesh Generation
... Adaptive remeshing may be used to determine an efficient mesh by taking into account the domain error. An efficient mesh is defined as the one in which the error is equally distributed over the domain [9]. ...
The finite element method is a computationally intensive method. Effective use of the method requires setting up the computational framework in an appropriate manner, which typically requires expertise. The computational cost of generating the mesh may be much lower, comparable, or in some cases higher than the cost associated with the numeric solver of the partial differential equations, depending on the application and the specific numeric scheme at hand.The aim of this paper is to present a mesh generation approach using the application of self-organizing artificial neural networks through adaptive finite element computations. The problem domain is initially constructed using the self-organizing neural networks. This domain is used as the background mesh which forms the input for finite element analysis and from which adaptive parameters are calculated through adaptivity analysis. Subsequently, self-organizing neural network is used again to adjust the location of randomly selected mesh nodes as is the coordinates of all nodes within a certain neighborhood of the chosen node. The adjustment is a movement of the selected nodes toward a specific input point on the mesh. Thus, based on the results obtained from the adaptivity analysis, the movement of nodal points adjusts the element sizes in a way that the concentration of elements will occur in the regions of high stresses. The methods and experiments developed here are for two-dimensional triangular elements but seem naturally extendible to quadrilateral elements.
A new h-refinement adaptive tetrahedral mesh generation algorithm is presented. Three-dimensional domains, to be analysed by the finite element method, are initially modelled by a coarse background mesh of tetrahedral elements. This mesh forms the input for finite element analysis and error estimation by the Zienkiewicz-Zhu simple error estimator. Adaptive mesh refinement proceeds by selecting an element for remeshing whose longest edge is shared by elements that also require refinement. This group of elements is refined by inserting a new node at the mid-point of the shared edge thereby bisecting all elements within the group. Adaptive parameters are calculated for the new node and elements. Refinement then proceeds until no further group of elements can be found for refinement or no elements within the current mesh require further refinement. The shape quality of the current mesh is then enhanced by the iterative application of nodal relaxation plus three topological transformations. The entire refinement process is repeated iteratively until the required degree of mesh refinement is reached. Ten-noded linear strain tetrahedral finite element meshes have been used for the finite element and error estimation analyses. Four examples of adaptive tetrahedral mesh generation for linear elastic stress/displacement analysis are presented which show that this algorithm is robust and efficient in terms of reduction of the domain error with a minimum number of degrees of freedom being generated, number of iterations, and therefore finite element analyses, required and computational time for refinement when compared to the advancing front method and Delaunay triangulation.
This paper examines the application of neural networks to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite element analysis. The use of the mean field annealing (MFA) technique, which is based on the mean field theory (MFT), for finding approximate solutions to the partitioning of the finite element meshes is investigated. The partitioning is based on the recursive bisection approach. The method of mapping the mesh bisection problem onto the neural network, the solution quality and the convergence times are presented. All computational studies were carried out using a single T800 transputer.
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