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Mesh Quality

The evaluation of the mesh quality is significantly complicated by two aspects. Firstly, the use of criteria analogous to those applied in Section Mesh Quality (Sequential Mesh Generation) is not straightforward as the elements (quadrilaterals and hexahedrons) are generally warped, which is the consequence of both the mapping between the parametric and real spaces and the mesh smoothing. Therefore angle-based criteria should be employed. However, their application is affected by the second aspect consisting in the fact that mixed meshes are considered. Since no particular evaluation of the mesh quality has been implemented in the presented work, only some general statements concerning the mesh quality are provided. In the tree-based approaches, where the templates are used to discretize individual tree cells, the element quality is strongly dependent on the shape of the cells. The conventional tree-based techniques (quadtree, octree) offer usually elements of a reasonable quality because the tree cells are typically equilateral (square, cube). However, this is not the case in the present approach which uses the parametric tree structure. The shape of a cell is therefore influenced by the mapping between the parametric and real spaces. Whereas the aspect ratio of the tree cell is kept at a reasonable value by implementation of the tree in the generalized form, the skewness of the tree cell is completely dependent on the mapping. Discretization of poorly parameterized model entities or well parameterized model entities of a ``skew'' shape typically results in worse quality elements. Thus the mesh quality generally depends on the model in terms of the shape and parameterization of individual model entities. The mesh smoothing, which is usually applied to considerably improve the mesh quality, does not have the desirable effect, which is caused primarily by the mixed nature of the mesh. Therefore some other ways of the mesh optimization, including topological transformations, would be worthwhile to improve the overall mesh quality.



Next: Computational Complexity Up: Mesh Generator Evaluation Previous: Mesh Validity

Daniel Rypl
2005-12-07