Proposal of Benchmarks for 3D Unstructured Tetrahedral Mesh Optimization
Dompierre, Julien, Paul Labbe, Francois Guibault, Ricardo Camarero
Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.459-478, October 1998
7th International Meshing Roundtable
Centre de Recherche en Calcul App1ique (CERCA)
According to the scientific method, one should be able to test a published optimization strategy, reproduce results published elsewhere and compare these results to the ones obtained with other strategies. This is seldom the case in the field of mesh optimization, largely because of the lack of standardization of published test cases. It is thus felt that the definition of a series of benchmarks that would help to establish a basis of comparison constitutes a significant contribution to the field of mesh optimization.
In this paper, a first series of benchmark test cases is proposed that should help compare three-dimensional, optimization meshing techniques on tetrahedra. For each case, the inputs of the benchmarks are clearly defined ( 2), as well as the measures relating to the optimization process ( 3) and the ones pertaining to the quality of the results ( 4). These benchmarks are designed to test the generation and optimization of unstructured tetrahedral meshes. They are not universal or suitable for all meshing problems.
The second part of the paper presents the authors own optimization strategy, implemented in the ADP3D package ( 5). The benchmarking process is initialized by evaluating the results of ADP3D ( 6) followed by an analysis of the results ( 7).
Finally, we conclude that using the benchmarks helps to evaluate the results of tetrahedral mesh optimization algorithms. We feel that the Meshing Roundtable is a good forum to discuss this benchmarks proposal and that it will encourage its use.
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