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.
