[petsc-users] KSP solver for single process

[Alan]

Hi Dr. Smith,
     Thank you so much for your reply. I tried to use the geometric 
multigrid to speed up the KSP solver with setup:
     mpiexec -np 1 ./ex29 -ksp_type cg -pc_type mg -da_refine 2 
-ksp_rtol 1.0e-7
     It do have almost the same computational rate compared with mudpack 
right now. Whereas, I have few questions here:
1. After KSPCreate(), I used a DMDACreate2d() and 
DMDASetUniformCoordinates() to build a uniform Cartesian mesh from 
PETSc. If I input imax and jmax to DMDACreate2d() as the global 
dimension of the grid, the real number of grid of x- and y-direction are 
imax and jmax, respectively, for the code with PC = GAMG; while they are 
(imax-1)*4 and (jmax-1)*4, respectively, for the code with PC = MG with 
-da_refine = 2. Is this normal? Does this indicate that the imax, jmax I 
inputed for the code with PC = MG is the global dimension for the 
coarsest level in the multi-grid?
2, Is there any command of PETSc that I can used in my code to detect 
what is the type of my preconditioner?
3, Is there any command of PETSc that I can used to know what is the 
value of -da_refine if the MG is used?
4, What is 'PCMGType'? Should I just keep it as default? In the original 
makefile for /src/ksp/ksp/tutorial/example/ex29.c, pc_mg_type was 
'full'. I tried it; it is slightly slower than the default setting.
5, What other settings I can play with to further speed up the 
computational rate?

thanks,
Alan

>     Alan,
>
>     If you can use MUDPACK then you can also use PETSc's geometric multigrid, both sequential and parallel and its performance should be fairly close to mudpack on one process.
>
>      Barry
>
> On Aug 6, 2013, at 2:56 PM, Alan <zhenglun.wei at gmail.com> wrote:
>
>>     Thanks for replies. Here I attached the log_summary for the large and small problems. The DoFs for the large problem is 4 times of that for the small problem. Few observations are listed here:
>> 1, the total number of iterations does not change much from the small problem to the large one;
>> 2, the time elapsed for KSPSolve() for the large problem is less than 4 times of that for the small problem;
>> 3, the time elapsed for PCSet() for the large problem is more than 10 times of that for the small problem;
>> 4, the time elapsed for PCGAMGProl_AGG for the large problem is more than 20 times of that for the small problem;
>>     In my code, I have solved the Poisson equation for twice with difference RHS; however, the observation above is almost consistent for these two times.
>>     Do these observation indicate that I should switch my PC from GAMG to MG for solving Poisson equation in a single process?
>>
>> best,
>> Alan
>>   
>>> On Tue, Aug 6, 2013 at 2:31 PM, Karl Rupp <rupp at mcs.anl.gov> wrote:
>>> Hi Alan,
>>>
>>> please use -log_summary to get profiling information on the run. What is
>>> the bottleneck? Is it the number of solver iterations increasing
>>> significantly? If so, consider changing the preconditioner options (more
>>> levels!). I don't expect a direct solver to be any faster in the 180k
>>> case for a Poisson problem.
>>>
>>> Mudpack is geometric multigrid: http://www2.cisl.ucar.edu/resources/legacy/mudpack
>>> This should be faster.
>>>
>>>     Matt
>>>   
>>> Best regards,
>>> Karli
>>>
>>>
>>> On 08/06/2013 02:22 PM, Alan wrote:
>>>> Dear all,
>>>> I hope you're having a nice day.
>>>> I have a quick question on solving Poisson equation with KSP solvers
>>>> (/src/ksp/ksp/example/tutorial/ex29.c). Currently, I run this solver with:
>>>> -pc_type gamg -ksp_type cg -pc_gamg_agg_nsmooths 1 -mg_levels_ksp_max_it
>>>> 1 -mg_levels_ksp_type richardson -ksp_rtol 1.0e-7
>>>> It performs very well in parallel computation and scalability is fine.
>>>> However, if I run it with a single process, the KSP solver is much
>>>> slower than direct ones, i.e. Mudpack. Briefly, the speed difference
>>>> between the KSP solver and the direct solver is negligible on dealing
>>>> with small problems (i.e.36k DoFs ) but becomes very huge for moderate
>>>> large problems (i.e. 180k DoFs). Although the direct solver inherently
>>>> has better performance for moderate large problems in the single
>>>> process, I wonder if any setup or approach can improve the performance
>>>> of this KSP Poisson solver with the single process? or even make it
>>>> obtain competitive speed (a little bit slower is fine) against direct
>>>> solvers.
>>>>
>>>> thanks in advance,
>>>> Alan
>>>>
>>>
>>>
>>>
>>> -- 
>>> 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
>> <out_large.txt><out_small.txt>