Feature-sensitive tetrahedral mesh generation with guaranteed quality

Abstract

Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is provably guaranteed: the smallest dihedral angle is always greater than 5.71°. The meshes generated by our method are not only adaptive from the interior to the boundary, but also feature-sensitive on the surface with denser elements in high-curvature regions where geometric feature most likely reside. A variety of experimental results are presented to demonstrate the effectiveness and robustness of this algorithm.

Free Tools and Strategies for the Generation of 3D Finite Element Meshes: Modeling of the Cardiac Structures

“…The success of the Finite Element Method depends on the shapes of these tetrahedra. For instance, tetrahedra constructed with too small or too large dihedral angles can cause interpolation errors and lead to numerical simulation with higher instability and less accuracy [33, 34]. The desired quality is the one in which the values of dihedral angles are close to the values set on a regular tetrahedron [26, 34, 35].…”

“…The desired quality is the one in which the values of dihedral angles are close to the values set on a regular tetrahedron [26, 34, 35]. This can be verified in histograms constructed with the total of dihedral angles present in ranges of angles, as well as identification of the smallest and largest values involved [33, 34]. …”

Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

“…They describe a computer-assisted proof to compute quality bounds for their isosurface stuffing algorithm. Wang and Yu [47] employ a similar approach. The proposed method shares several aspects of the Labelle and Shewchuk method.…”

New software developments for quality mesh generation and optimization from biomedical imaging data

“…More details can be found in [59]. For simplicity of description, we consider only tetrahedral mesh generation inside a given surface mesh, although our algorithms can be readily modified to generate tetrahedra outside a domain surface, as demonstrated in the Result section below.…”

“…We have shown in [59] that the method outlined above can produce adaptive tetrahedral meshes with a minimal dihedral angle of 5.71°. The resulting tetrahedral mesh quality can be further improved by using a tetrahedral mesh smoothing technique, as described below.…”