Proposal of Benchmarks for 3D Unstructured Tetrahedral Mesh Optimization

Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.459-478, October 1998

MESHING
RESEARCH
CORNER

7th International Meshing Roundtable
October 26-28, 1998
Dearborn, Michigan, USA

Centre de Recherche en Calcul App1ique (CERCA)
5160, boul. Decarie, suite 400,
Montreal, (Quebec), H3X 2H9, Canada
Email: { julien, paul, francois, ricardo } @cerca.umontrea1.ca

Introduction
Publications in the domain of three-dimensional unstructured tetrahedral mesh generation, adaptation and optimization abound. However, they tend to show results only for complex industrial test cases, for which comparisons are most often impossible and results are not reproducible. Sometimes, only images of the optimized meshes are shown, so that it is impossible to tell whether the generation, adaptation or optimization process has converged or not. Different statistics on the quality of the mesh are used, and tetrahedron shape measures may be unusual.

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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