| ca04dac2 | 24-Aug-2015 |
Toby Isaac <tisaac@ices.utexas.edu> |
Plex: shift tree in DMPlexCreateGhosts()
- Ancestor faces don't create ghosts: only leaves are used for flux
calculations
- Shift the indices in the tree.
*NOTE* This should not work yet. I hav
Plex: shift tree in DMPlexCreateGhosts()
- Ancestor faces don't create ghosts: only leaves are used for flux
calculations
- Shift the indices in the tree.
*NOTE* This should not work yet. I haven't been conforming to Matt's
(cells, vertices, edges, faces) ordering of strata, I've been doing
(cells, edges, faces, vertices). DMPlexShiftPoint_Internal() assumes
Matt's ordering, I'd like to make it agnostic.
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| 3fe31fa2 | 07-Aug-2015 |
Toby Isaac <tisaac@ices.utexas.edu> |
plex: fix tet refinement for stable element shape
Each refined tetrahedron defines a change of bases that maps the corners
of the parent to the corners of the child. If we rescale this transform
so
plex: fix tet refinement for stable element shape
Each refined tetrahedron defines a change of bases that maps the corners
of the parent to the corners of the child. If we rescale this transform
so that the determinant is 1, we get a volume preserving distortion of
the parent tetrahedron.
One sufficient condition for stable tetrahedral refinement is for all of
these transforms to form a finite group: then each of the recursively
refined tets will fall into one of a fixed set of congruency classes.
A classic stable refinement pattern from Freudenthal [1] and Bey [2] is
used by HHG grids [3], which is good for producing refinement patterns
that match regular grids and only a few congruency classes. This
method, however, inverts the signed volume of some refined tetrahedra,
which we don't want in DMPlex. Sign reversal could be avoid, but we
would have to tag two different types of tetrahedra, which we also don't
want in DMPlex.
I did a brute force search for a transformation. Starting with the old,
unstable refinement pattern, I wrote a script that rotated the four
interior tetrahedra independently, reporting all the combinations that
formed a finite group. There turned out to be a few, so I selected the
one with the smallest group size (12, which is twice the size of the
group using Freudenthal-Bey refinement). I then somehow figured out how
to apply these rotations in the CellRefiner code.
As a result, testing shape regularity with plex ex1 now yields:
$ ./ex1 -dim 3 -interpolate -dm_refine_hierarchy 5 -test_shape
Mesh with 196608 cells, shape condition numbers: min = 3, max = 8.77496, mean = 5.27739, stddev = 1.26754
Mesh with 24576 cells, shape condition numbers: min = 3, max = 8.77496, mean = 5.28768, stddev = 1.2648
Mesh with 3072 cells, shape condition numbers: min = 3, max = 8.77496, mean = 5.28715, stddev = 1.26312
Mesh with 384 cells, shape condition numbers: min = 3, max = 8.77496, mean = 5.23795, stddev = 1.263
Mesh with 48 cells, shape condition numbers: min = 4, max = 8.77496, mean = 5.01933, stddev = 1.2307
Mesh with 6 cells, shape condition numbers: min = 4, max = 5.47723, mean = 4.2462, stddev = 0.550529
I am now a tetrahedron. Like the old Shaker hymn says, "'Tis a gift to
be simplicial."
[1] Freudenthal, H.: Simplizialzerlegungen von beschraenkter Flachheit.
Ann. Math. 43, 580-582 (1992).
[2] Bey, J.: Tetrahedral Grid Refinement. Computing 55, 355-378 (1995).
[3] Bergen, B., Gradl, T., Ruede, U., Huelsemann, F.: A massively
parallel multigrid method for finite elements
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