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Preprint 692-2000

Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)

Hexahedral Mesh Generation for the Simulation of the Human Mandible
Cornelia Kober and Matthias Müller-Hannemann
appeared in Proceedings of the 9th International Meshing Roundtable, New Orleans, October 2000, pp.423-434
primary: 65M50 Mesh generation and refinement
secondary: 65D18 Computer graphics and computational geometry
hexahedral mesh generation, quadrilateral mesh generation, optimized mesh smoothing, FEM simulation, human mandible
A combinatorial approach for the generation of hexahedral meshes by means of successive dual cycle elimination has been proposed by the second author in previous work.
We provide a case study for the applicability of our hexahedral mesh generation approach to the simulation of physiological stress scenarios of the human mandible. Due to its complex and very detailed free-form geometry, the mandible model is very demanding. This test case is used as a running example to report on the progress and recent advances of the cycle elimination scheme. The given input data, a surface triangulation, requires a substantial mesh reduction and a suitable conversion into a quadrilateral surface mesh as a first step, for which we use mesh clustering and b-matching techniques.
Several strategies for improved cycle elimination orders are proposed. They lead to a significant reduction in the mesh size and a better structural quality.
Based on the resulting combinatorial meshes, gradient-based optimized smoothing with the condition number of the Jacobian matrix as objective together with mesh untangling techniques yielded embeddings of a satisfactory quality.
We tested our hexahedral meshes for the mandible model in an FEM simulation under the scenario of a bite on a "hard nut." Our simulation results are in good agreement with observations from biomechanical experiments.
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