|
Volume meshing algorithm |
Observations:
For general point positions the Delaunay triangulation
is unique (parallelism).
Constrained Delaunay triangulation in 3-D does not exist
in general.
The boundary of the triangulated solid is rarely exact.
Delaunay triangulation does not provide any maxmin guarantees
for element quality.
Algorithm:
- Phase I: Check if boundary
facets are represented in the (unconstrained) Delaunay triangulation of
the point set (Rajan 1994). If this does not hold for every facet: Modify
the boundary triangulation so that its facets are faces of the
Delaunay triangulation of the whole point set (perform diagonal flips
and insert additional points).
- Phase II: Generate the tetrahedra by directly
using the Delaunay circumsphere property (form of fail-safe advancing front).
Parallelization:
Phase (i) scales as O(N^2/3 logN), and
requires some interprocess communication (N=number of points).
Phase (ii) scales as O(N logN), and does
not require any communication.