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They use well-established techniques and optimization schemes including Delaunay triangulation method, modified-octree technique, and advancing front technique. Tetrahedral mesh generators are a standard feature of commonly used Computer-Aided Engineering CAE packages. Today 4-noded tetrahedra and 8-noded hexahedra are the most commonly used types of finite elements. For additional information on mesh enhancement methods using a specific quality measure as the objective function in the optimization process we refer to Refs.Īdam Wittek, Karol Miller, in Handbook of Medical Image Computing and Computer Assisted Intervention, 2020 39.2.2 Finite element mesh generation Its application guarantees improvement of the element quality, but could also be computationally expensive. It is noted that the condition attached to all the quality enhancement methods, which requires the worst element quality to improve according to an element quality criterion, corresponds to an optimization problem. Several combined applications of the quality enhancement method usually results in a mesh with much improved quality.
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The procedure stops when the quality of the connected elements does not improve. The procedure is modified to move a node incrementally and iteratively toward each of its connecting nodes and is placed at the position that will increase the quality of the worst element. It in fact reduces the quality of the mesh. The standard Laplacian smoothing cannot be applied directly to a tetrahedral mesh. Zhu, in The Finite Element Method: its Basis and Fundamentals (Seventh Edition), 2013 17.5.3.3 Mesh smoothing
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