[aspect-devel] Cylindrical coordinates

[Wolfgang Bangerth]

On 05/12/2018 06:31 AM, Jonathan Perry-Houts wrote:
> The "repetitions" parameters can help with this, but refinements would
> still be isotropic. Also, I've heard tell that the repetition parameters
> aren't efficient for high-aspect-ratio meshes. My understanding is that
> the MPI partitioning makes some assumptions based on how AMR "should" work.

The only limitation I can think of is that we don't want the coarse meshes to 
become too large. We can probably deal with 10,000 cells (100 cells in radius 
and longitude, 1 in latitude), but not a million or more.


> Is there an inherent performance hit when solving in 3D with Aspect
> (beyond the ~doubling of DOF's)? I seem to remember that early on people
> were noticing a substantial slow-down for similar size solutions, when
> working in 3D.

The speed implications come from two sources:
* Larger number of DoFs: I think I would have assumed more like a factor of 10 
larger in 3d than 2d, but that clearly depends on the resolution you're 
looking for. We can do *very finely* resolved 2d models, which are completely 
infeasible in 3d even with many processors.
* A typical matrix entry in 3d has about 400 entries. In 2d, this is only 
about 60. So even in the best of cases, any time you do something with a 
matrix, it is already going to take more than 6 times as long, though I would 
not be surprised if things like setting up the algebraic multigrid 
preconditioner is actually quadratic in the number of entries per row.

I'm sure there are other places where out current code is simply not as 
efficient as could be possible, but the two issues above are independent of 
any implementation and just do to the dimensionality.

Best
  W.

-- 
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Wolfgang Bangerth          email:                 bangerth at colostate.edu
                            www: http://www.math.colostate.edu/~bangerth/