dolfin team mailing list archive

[Douglas N Arnold <arnold@xxxxxxx>]

In my opinion this is a major problem.  In 2D one can
test convergence by computing on an initial mesh and
then repeating calling refine.  The error decreases
with the expected power.  This does not happen at
all in 3D, even in the simplest cases.

There are many mesh refinement algorithms for 3D.
The one I know, when applied repeatedly to the mesh
given by UnitCube(1,1,1) will create the meshes
given by UnitCube(2,2,2), UnitCube(4,4,4), ...
The current refine is not doing that, which seems
wrong to me.

Examples of refinement algorithms that would work
are the one in paper
http://umn.edu/~arnold/papers/bistet.pdf
or related algorithms by Maubach, Bansch, or Joe
and Liu, which are referenced in that paper.
Even the very simple to implement Rivara longest edge
bisection would do the trick.


On 10/07/2010 03:54 AM, Marie Rognes wrote:
> Something slightly peculiar seems to happen with 3d refinement. Refining
> a 1 x 1 x 1 Unit Cube 3 times gives largest cell diameter that is
> increasing (but smallest cell diameter  that is decreasing as expected).
> It does not seem to (only) be a bug in hmax()/hmin(), odd convergence
> rates are also observed. Any ideas?
>
> Example:
>
> from dolfin import *
>
> mesh = UnitCube(1, 1, 1)
>
> for i in range(3):
>      mesh = refine(mesh)
>
>      print "Refinement level = ", i
>      print "h_max = ", mesh.hmax()
>      print "h_min = ", mesh.hmin()
>
> gives:
>
> Refinement level =  0
> h_max =  1.65831239518
> h_min =  0.866025403784
> Refinement level =  1
> h_max =  1.47901994577
> h_min =  0.433012701892
> Refinement level =  2
> h_max =  1.7809758561
> h_min =  0.216506350946
>
> --
> Marie