[petsc-dev] features of GAMG

Tue Dec 27 09:10:14 CST 2011

OK, I've tested ex56 with 

-mg_levels_ksp_chebychev_estimate_eigenvalues 0,0.1,0,1.1

and verified that it does indeed overwrite my eigen estimates, that I give it, and I see very similar results (ie, with and w/o this est parameter).  For instance with Cheb 1:

  0 KSP Residual norm 3.095373678236e+03 
  1 KSP Residual norm 6.191349513594e+02 
  2 KSP Residual norm 2.757450827269e+02 
  3 KSP Residual norm 1.268581869233e+02 
  4 KSP Residual norm 4.464752378561e+01 
  5 KSP Residual norm 1.695065935428e+01 
  6 KSP Residual norm 6.815970347827e+00 
  7 KSP Residual norm 2.924716764895e+00 
  8 KSP Residual norm 1.540893486351e+00 
  9 KSP Residual norm 6.455120265352e-01 
 10 KSP Residual norm 1.674033387830e-01 
 11 KSP Residual norm 5.847190034854e-02 
 12 KSP Residual norm 1.815782398062e-02 
 13 KSP Residual norm 5.013740651171e-03 
 14 KSP Residual norm 1.548353609674e-03 
 15 KSP Residual norm 4.575592583815e-04 
 16 KSP Residual norm 1.282184254689e-04 
 17 KSP Residual norm 3.708048113061e-05 
 18 KSP Residual norm 1.028830485881e-05 
 19 KSP Residual norm 2.695204689566e-06 
 20 KSP Residual norm 9.427412676529e-07 
 21 KSP Residual norm 2.719376922239e-07 
#PETSc Option Table entries:
-ksp_type cg
-mg_levels_ksp_chebychev_estimate_eigenvalues 0,0.1,0,1.1
-mg_levels_ksp_max_it 1

and Cheb-4:

  0 KSP Residual norm 3.273154874986e+03 
  1 KSP Residual norm 8.622241525141e+02 
  2 KSP Residual norm 4.096563608952e+02 
  3 KSP Residual norm 1.092011557684e+02 
  4 KSP Residual norm 2.723342496813e+01 
  5 KSP Residual norm 1.091986699964e+01 
  6 KSP Residual norm 5.433492162060e+00 
  7 KSP Residual norm 2.629892421938e+00 
  8 KSP Residual norm 5.300747644771e-01 
  9 KSP Residual norm 7.312379355566e-02 
 10 KSP Residual norm 2.279979060480e-02 
 11 KSP Residual norm 5.098259681590e-03 
 12 KSP Residual norm 1.468248636922e-03 
 13 KSP Residual norm 3.480984243626e-04 
 14 KSP Residual norm 7.966349284530e-05 
 15 KSP Residual norm 1.371697533223e-05 
 16 KSP Residual norm 3.107050969110e-06 
 17 KSP Residual norm 9.351516917154e-07 
 18 KSP Residual norm 2.555571755850e-07 
#PETSc Option Table entries:
-ksp_type cg
-mg_levels_ksp_chebychev_estimate_eigenvalues 0,0.1,0,1.1
-mg_levels_ksp_max_it 4

So I don't see anything wrong ... maybe this is just the way it is or there is a problem in the test, or algorithm/implementation.

Oh well, something to think about.

Mark

On Dec 26, 2011, at 10:27 PM, Jed Brown wrote:

> On Mon, Dec 26, 2011 at 12:43, Mark F. Adams <mark.adams at columbia.edu> wrote:
> I've just started using -ksp_rtol 1.e-10 and retested all of these test and am seeing a very slight improvement going from 1 to 4.  I would expect to see a significant drop, say 25%, in the number of iterations going from 1 to 2.  The < 5% that I am seeing seems too low but I'm not 100% sure -- maybe there is nothing wrong ...
> 
> Well, here is a different test, just for giggles. This sets up rapid coarsening so that multigrid convergence with weak smoothers isn't already "too good".
> 
> $ pwd
> /home/jed/petsc/src/snes/examples/tutorials
> $ for n in {1..4}; do echo Cheby $n; ./ex5 -da_grid_x 5 -da_grid_y 5 -da_refine 3 -da_refine_x 4 -da_refine_y 4 -snes_max_it 1 -ksp_monitor -pc_type mg -pc_mg_levels 4 -mg_levels_pc_type jacobi -mg_levels_ksp_type chebychev -mg_levels_ksp_chebychev_estimate_eigenvalues 0,0.1,0,1.1 -mg_levels_ksp_max_it $n; done
> Cheby 1
>     0 KSP Residual norm 1.621385151256e+01 
>     1 KSP Residual norm 1.247824515555e+01 
>     2 KSP Residual norm 1.278794763626e+00 
>     3 KSP Residual norm 1.116456717457e-01 
>     4 KSP Residual norm 4.348273343707e-02 
>     5 KSP Residual norm 8.348548286503e-03 
>     6 KSP Residual norm 3.951234403814e-03 
>     7 KSP Residual norm 1.058691144871e-03 
>     8 KSP Residual norm 3.264344380115e-04 
>     9 KSP Residual norm 8.173798438913e-05 
> Cheby 2
>     0 KSP Residual norm 1.891099688325e+01 
>     1 KSP Residual norm 9.980070235568e+00 
>     2 KSP Residual norm 8.251956879061e-02 
>     3 KSP Residual norm 8.973973844623e-03 
>     4 KSP Residual norm 6.086189552261e-04 
>     5 KSP Residual norm 8.406518096327e-05 
> Cheby 3
>     0 KSP Residual norm 1.990124921919e+01 
>     1 KSP Residual norm 1.111981517647e+01 
>     2 KSP Residual norm 4.888111472342e-02 
>     3 KSP Residual norm 2.109153682849e-03 
>     4 KSP Residual norm 1.680361259338e-04 
> Cheby 4
>     0 KSP Residual norm 2.051550954711e+01 
>     1 KSP Residual norm 1.049577156306e+01 
>     2 KSP Residual norm 3.445878799134e-02 
>     3 KSP Residual norm 9.302079492533e-04 
>     4 KSP Residual norm 3.995254526577e-05 
> 
> 
> I don't think the Cheby implementation is buggy and I think we are using it correctly. I agree that it is somewhat disappointing if increasing the order above 1 doesn't make a more noticeable improvement.

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