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Hexahedral Mesh Generation for the Simulation of the Human Mandible

Kober, Cornelia; Müller-Hannemann, Matthias

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.