[petsc-dev] features of GAMG

[Jed Brown]

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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