[petsc-users] How to speed up geometric multigrid

Wed Oct 2 17:57:08 CDT 2013

   Ok, so piecewise constant pressures. The default DMDA multigrid is using piecewise linear interpolation. Isn't going to work well at all. You need to first add   ierr = DMDASetInterpolationType(da, DMDA_Q0);CHKERRQ(ierr); after you create the DM.  You should be seeing much better convergence. see ksp/ksp/examples/tutorials/ex34.c

   Barry

On Oct 2, 2013, at 5:25 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Oct 2, 2013 at 5:12 PM, Michele Rosso <mrosso at uci.edu> wrote:
> Barry,
> 
> sorry for not replying to your other e-mail earlier.
> The equation I am solving is:
> 
> <tblatex-5.png>
> 
> where <tblatex-4.png> is the pressure field, <tblatex-3.png> the density field and <tblatex-2.png>  the velocity field. 
> Since I am using finite difference on a staggered grid, the pressure is defined on "cell" centers, while the velocity components on "cell" faces, even if
> no cell is actually defined.
> 
> If you just prescribe a constant rho, do you get 3-5 iterates? What about a simple step through the domain?
> Starting on the hardest problem does not sound like that way to understand what is going on.
> 
>   Matt
>  
> I am simulating a bi-phase flow, thus both density and pressure are discontinuos, but not the velocity (no mass trasfer is included at the moment).
> Therefore the right-hand-side (rhs) of the above equation does not have jumps, while $p$ and $rho$ do.
> In order to deal with such jumps, I am using a Ghost Fluid approach. Therefore the resulting linear system is slighly different from the typical Poisson system, though
> simmetry and diagonal dominance of the matrix are mantained.
> The boundary conditions are periodic in all the three space directions, therefore the system is singular. Thus I removed the nullspace of the matrix by using:
> 
>         call MatNullSpaceCreate( PETSC_COMM_WORLD,PETSC_TRUE,PETSC_NULL_INTEGER,&
>                                & PETSC_NULL_INTEGER,nullspace,ierr)
>         call KSPSetNullspace(ksp,nullspace,ierr)
>         call MatNullSpaceDestroy(nullspace,ierr)  
> 
> Hope this helps. Please let me know if you need any other info.
> Also, I use the pressure at the previous time step as starting point for the solve. Could this be a reason why the convergence is so slow?
> Thanks a lot,
> 
> Michele
> 
> 
> 
> 
> 
> 
> 
> On 10/02/2013 11:39 AM, Barry Smith wrote:
>>   Something is wrong, you should be getting better convergence. Please answer my other email.
>> 
>> 
>> On Oct 2, 2013, at 1:10 PM, Michele Rosso 
>> <mrosso at uci.edu>
>>  wrote:
>> 
>> 
>>> Thank you all for your contribution.
>>> So far the fastest solution is still the initial one proposed by Jed in an earlier round:
>>> 
>>> -ksp_atol 1e-9  -ksp_monitor_true_residual  -ksp_view  -log_summary -mg_coarse_pc_factor_mat_solver_package superlu_dist
>>> -mg_coarse_pc_type lu    -mg_levels_ksp_max_it 3 -mg_levels_ksp_type richardson  -options_left -pc_mg_galerkin
>>> -pc_mg_levels 5  -pc_mg_log  -pc_type mg
>>> 
>>> where I used  -mg_levels_ksp_max_it 3  as Barry suggested instead of  -mg_levels_ksp_max_it 1.
>>> I attached the diagnostics for this case. Any further idea?
>>> Thank you,
>>> 
>>> Michele
>>> 
>>> 
>>> On 10/01/2013 11:44 PM, Barry Smith wrote:
>>> 
>>>> On Oct 2, 2013, at 12:28 AM, Jed Brown <jedbrown at mcs.anl.gov>
>>>>  wrote:
>>>> 
>>>> 
>>>>> "Mark F. Adams" <mfadams at lbl.gov>
>>>>>  writes:
>>>>> 
>>>>>> run3.txt uses:
>>>>>> 
>>>>>> -ksp_type richardson
>>>>>> 
>>>>>> This is bad and I doubt anyone recommended it intentionally.
>>>>>> 
>>>>    Hell this is normal multigrid without a Krylov accelerator. Under normal circumstances with geometric multigrid this should be fine, often the best choice.
>>>> 
>>>> 
>>>>> I would have expected FGMRES, but Barry likes Krylov smoothers and
>>>>> Richardson is one of a few methods that can tolerate nonlinear
>>>>> preconditioners.
>>>>> 
>>>>> 
>>>>>> You also have, in this file,
>>>>>> 
>>>>>> -mg_levels_ksp_type gmres
>>>>>> 
>>>>>> did you or the recommenders mean
>>>>>> 
>>>>>> -mg_levels_ksp_type richardson  ???
>>>>>> 
>>>>>> you are using gmres here, which forces you to use fgmres in the outer solver.  This is a safe thing to use you if you apply your BCa symmetrically with a low order discretization then
>>>>>> 
>>>>>> -ksp_type cg
>>>>>> -mg_levels_ksp_type richardson
>>>>>> -mg_levels_pc_type sor
>>>>>> 
>>>>>> is what I'd recommend.
>>>>>> 
>>>>> I thought that was tried in an earlier round.
>>>>> 
>>>>> I don't understand why SOR preconditioning in the Krylov smoother is so
>>>>> drastically more expensive than BJacobi/ILU and why SOR is called so
>>>>> many more times even though the number of outer iterations
>>>>> 
>>>>> bjacobi: PCApply              322 1.0 4.1021e+01 1.0 6.44e+09 1.0 3.0e+07 1.6e+03 4.5e+04 74 86 98 88 92 28160064317351226 20106
>>>>> bjacobi: KSPSolve              46 1.0 4.6268e+01 1.0 7.52e+09 1.0 3.0e+07 1.8e+03 4.8e+04 83100100 99 99 31670065158291309 20800
>>>>> 
>>>>> sor:     PCApply             1132 1.0 1.5532e+02 1.0 2.30e+10 1.0 1.0e+08 1.6e+03 1.6e+05 69 88 99 88 93 21871774317301274 18987
>>>>> sor:     KSPSolve             201 1.0 1.7101e+02 1.0 2.63e+10 1.0 1.1e+08 1.8e+03 1.7e+05 75100100 99 98 24081775248221352 19652
>>>>> 
>>> <best.txt>
>>> 
> 
> 
> 
> 
> -- 
> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
> -- Norbert Wiener