[petsc-users] How to speed up geometric multigrid

Michele Rosso mrosso at uci.edu
Mon Sep 23 11:34:35 CDT 2013

On 09/23/2013 09:24 AM, Mark F. Adams wrote:
> On Sep 23, 2013, at 11:55 AM, Michele Rosso <mrosso at uci.edu 
> <mailto:mrosso at uci.edu>> wrote:
>> Hi,
>> I am successfully using PETSc to solve a 3D Poisson's equation with 
>> CG + MG .  Such equation arises from a projection algorithm for a 
>> multiphase incompressible flow simulation.
>> I set up the solver as I was suggested to do in a previous thread 
>> (title: "GAMG speed") and run a test case (liquid droplet with 
>> surface tension falling under the effect of gravity in a quiescent 
>> fluid).
>> The solution of the Poisson Equation via multigrid is correct but it 
>> becomes progressively slower and slower as the simulation progresses 
>> (I am performing successive solves) due to an increase in the number 
>> of iterations.
>> Since the solution of the Poisson equation is mission-critical, I 
>> need to speed it up as much as I can.
>> Could you please help me out with this?
> Just to add, it is not unusual as structures develop in your 
> simulation to see an increase in iterations.  If you plot the material 
> coefficients I suspect that you will see sharper structures developing 
> in time.  Can you look at this in some way or generate some statistics 
> like (max) gradient of material coefficients or even just max & min 
> coefficients?
Yes, I suspected that this may have been a reason. Initially both phases 
are at rest, so basically no fluid structures are present, thus the 
convergence is very fast(6 iterations maximum). Then vortices start 
developing both inside and outside the droplet and at that point the 
number of iteration increases. I noticed that the convergence rate 
becomes almost steady at a certain point, I guess when the flow is fully 
developed. I would like to speed up the solve for this last scenario.

>> I run the test case with the following options:
>> -pc_type mg  -pc_mg_galerkin  -pc_mg_levels 5 -mg_levels_ksp_type 
>> richardson -mg_levels_ksp_max_it 1
>> -mg_coarse_pc_type lu -mg_coarse_pc_factor_mat_solver_package 
>> superlu_dist
>> -log_summary -ksp_view  -ksp_monitor_true_residual -options_left
>> Please find the diagnostic for the final solve in the attached file 
>> "final.txt'.
>> Thank you,
>> Michele
>> <final.txt>

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