GRUMMP's approach to isotropic mesh adaptation is to apply a concatenation
of existing functionality to produce a high-quality mesh that meets
the specified length scale requirement. (See Section 2.1
for information on how to specify a length scale.) This is done as
the first step in mesh optimization (executables meshopt2d
and meshopt3d). The steps taken are:
If this sounds simple, that's because it is: the driver for this process
has eight lines of code, not counting diagnostic output, comments,
and blank lines.
- Coarsen the mesh where necessary to make sure vertices are not too
close together (where ``too close'' means that the distance between
them is less than the average of their length scales).
- Swap the mesh to make it Delaunay; this step is a necessary prerequisite
to mesh refinement.
- Refine the mesh to ensure that no cells are larger than the local
length scale and that no badly-shaped cells remain. This step is identical
to what GRUMMP does in generating a mesh after the initial triangulation
/ tetrahedralization is complete.
- Postprocessing by smoothing and swapping. In 2D, two passes of smoothing
are sufficient to ensure excellent meshes in both theory and practice.
In 3D, some swapping is typically required to eliminate slivers, which
the insertion process alone cannot remove.