On 9/9/20 12:31 PM, Paras Kumar wrote:
This does not say anything about the *absolute level of accuracy*. I would
not
be surprised if for a mesh like the one you show (in which pretty much every
hexahedron is poorly shaped), the solution is less than for the
corresponding
tetrahedal mesh. But if you refine it a couple of times, you should get a
more
accurate solution. Is this not the case?
We also tried with a refined mesh (resulting in 360K elements as compared to
120K elements for the mesh in pic-2.png), but the irregularities still remain
as can be seen in pic-4.png.Considering that fact that we wish to model
multi-particle systems, such large number of elements would render such a
mehsing approach computationally infeasible.
Right. But it helps illuminate where the problem may be.
From the look of it, the solution is at least smoother. That might suggest
that the issue is not a bug in the code, but that the solution really does
converge, though maybe slowly. Do you have the resources to do one more
refinement, just to see whether the solution continues to get better? That's
not going to be a production run, but a one-time computation that might take a
day or two if necessary.
The quality of meshes matters for the absolute level of error. The hex
meshes
you get by subdividing tets are generally quite poor, though I know of
people
who are using these routinely and report that they nevertheless get good
accuracy. A better approach is certainly to see if you can find ways to
*directly* create hex meshes. gmsh can do this to some degree. For the
sphere
you show, deal.II can also generate a high-quality mesh itself.
We have already tried several options available in GMSH, but it did not seem
to work. Could you please suggest some tool for automatic "direct" Hex mesh
generation.
I'm no expert in using gmsh, so if you say that you couldn't get it to work,
then I have no other suggestion either.
Is it not a good idea to use the tet-to-hex approach for generating Hex
meshes, since this appears to be the only feasible option with GMSH
considering the complexity of the geometry.
The actual geometry in the current case comprises a spherical particle of
material-2 embedded in a cube of material-1 (later, it could be 50 such
particles embedded in the matrix). I went through the grid generation
functions of deal.II but could not find any possibilities of doing an
"intersection" between triangulations as would be necessary for the matrix
material. Did I miss something?
If it's just one sphere in a ball, then take a look at the various functions
in namespace GridGenerator that build geometries with holes. If you take a
look at these functions and how they are implemented, you will probably
understand how you can generate a mesh for a single hole in a cube, and then
combine it with a mesh for the spherical hole via GridGenerator::hyper_sphere.
That won't work if you have many inclusions. We generally deal with many
inclusions by just using a regular mesh for the domain and at each quadrature
point asking whether it is inside an inclusion or in the background material.
Here is an example of how this could be done:
https://github.com/geodynamics/aspect/blob/master/benchmarks/nsinker/nsinker.cc
The value() returns the coefficient at a particular point. The mesh does not
actually to to mesh these inclusions, we just leave it to each quadrature
point. The benchmark this file implements is like this:
https://geodynamics.org/cig/news/research-highlights/november-2019/
You can find more information about this "nsinker" benchmark here:
https://tigerprints.clemson.edu/cgi/viewcontent.cgi?article=3528&context=all_dissertations
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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