[petsc-users] PCFieldSplit gives different results for direct and iterative solver

Y. Shidi ys453 at cam.ac.uk
Tue Mar 19 06:34:49 CDT 2019 

> Perhaps you need a better preconditioner for it.

Hello Matt,
Thank you for your help.
Yes, I think I need a better preconditioner;
it requires about 600 iterations for Schur complement.
Is there any tutorials for this? Or shall I just
try different combinations and find the most suitable
one?

Kind Regards,
Shidi

On 2019-03-19 11:17, Matthew Knepley wrote:
> On Tue, Mar 19, 2019 at 6:59 AM Y. Shidi via petsc-users
> <petsc-users at mcs.anl.gov> wrote:
> 
>> Hello Barry,
>> 
>> Thank you for your reply.
>> 
>> I reduced the tolerances and get desired solution.
>> 
>> I am solving a multiphase incompressible n-s problems and currently
>> we are using augmented lagrangina technique with uzawa iteration.
>> Because the problems are getting larger, we are also looking for
>> some
>> other methods for solving the linear system.
>> I follow pcfieldsplit tutorial from:
>> 
> https://www.mcs.anl.gov/petsc/documentation/tutorials/MSITutorial.pdf
>> [1]
>> 
>> However, it takes about 10s to finish one iteration and overall
>> it requires like 150s to complete one time step with 100k unknowns,
>> which is a long time compared to our current solver 10s for one
>> time step.
> 
> The first thing to do is look at how many Schur complement iterations
> you are doing:
> 
>   -fieldsplit_pressure_ksp_monitor_true_residual
> 
> Perhaps you need a better preconditioner for it.
> 
>   Thanks,
> 
>     Matt
> 
>> I tried the following options:
>> 1).
>> -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur
>> -pc_fieldsplit_schur_factorization_type lower
>> -fieldsplit_velocity_ksp_type preonly
>> -fieldsplit_velocity_pc_type gamg
>> -fieldsplit_pressure_ksp_type minres
>> -fieldsplit_pressure_pc_type none
>> 2).
>> -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur
>> -pc_fieldsplit_schur_factorization_type diag
>> -fieldsplit_velocity_ksp_type preonly
>> -fieldsplit_velocity_pc_type gamg
>> -fieldsplit_pressure_ksp_type minres
>> -fieldsplit_pressure_pc_type none
>> 3).
>> -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur
>> -pc_fieldsplit_schur_factorization_type full
>> -fieldsplit_velocity_ksp_type preonly
>> -fieldsplit_velocity_pc_type lu
>> -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type
>> jacobi
>> 
>> So I am wondering if there is any other options that can help
>> improve
>> the
>> pcfieldsplit performance.
>> 
>> Kind Regards,
>> Shidi
>> 
>> On 2019-03-17 00:05, Smith, Barry F. wrote:
>>>> On Mar 16, 2019, at 6:50 PM, Y. Shidi via petsc-users
>>>> <petsc-users at mcs.anl.gov> wrote:
>>>> 
>>>> Hello,
>>>> 
>>>> I am trying to solve the incompressible n-s equations by
>>>> PCFieldSplit.
>>>> 
>>>> The large matrix and vectors are formed by MatCreateNest()
>>>> and VecCreateNest().
>>>> The system is solved directly by the following command:
>>>> -ksp_type fgmres
>>>> -pc_type fieldsplit
>>>> -pc_fieldsplit_type schur
>>>> -pc_fieldsplit_schur_fact_type full
>>>> -ksp_converged_reason
>>>> -ksp_monitor_true_residual
>>>> -fieldsplit_0_ksp_type preonly
>>>> -fieldsplit_0_pc_type cholesky
>>>> -fieldsplit_0_pc_factor_mat_solver_package mumps
>>>> -mat_mumps_icntl_28 2
>>>> -mat_mumps_icntl_29 2
>>>> -fieldsplit_1_ksp_type preonly
>>>> -fieldsplit_1_pc_type jacobi
>>>> Output:
>>>> 0 KSP unpreconditioned resid norm 1.214252932161e+04 true resid
>> norm
>>>> 1.214252932161e+04 ||r(i)||/||b|| 1.000000000000e+00
>>>> 1 KSP unpreconditioned resid norm 1.642782495109e-02 true resid
>> norm
>>>> 1.642782495109e-02 ||r(i)||/||b|| 1.352916226594e-06
>>>> Linear solve converged due to CONVERGED_RTOL iterations 1
>>>> 
>>>> The system is solved iteratively by the following command:
>>>> -ksp_type fgmres
>>>> -pc_type fieldsplit
>>>> -pc_fieldsplit_type schur
>>>> -pc_fieldsplit_schur_factorization_type diag
>>>> -ksp_converged_reason
>>>> -ksp_monitor_true_residual
>>>> -fieldsplit_0_ksp_type preonly
>>>> -fieldsplit_0_pc_type gamg
>>>> -fieldsplit_1_ksp_type minres
>>>> -fieldsplit_1_pc_type none
>>>> Output:
>>>> 0 KSP unpreconditioned resid norm 1.214252932161e+04 true resid
>> norm
>>>> 1.214252932161e+04 ||r(i)||/||b|| 1.000000000000e+00
>>>> 1 KSP unpreconditioned resid norm 2.184037364915e+02 true resid
>> norm
>>>> 2.184037364915e+02 ||r(i)||/||b|| 1.798667565109e-02
>>>> 2 KSP unpreconditioned resid norm 2.120097409539e+02 true resid
>> norm
>>>> 2.120097409635e+02 ||r(i)||/||b|| 1.746009709742e-02
>>>> 3 KSP unpreconditioned resid norm 4.364091658268e+01 true resid
>> norm
>>>> 4.364091658575e+01 ||r(i)||/||b|| 3.594054865332e-03
>>>> 4 KSP unpreconditioned resid norm 2.632671796885e+00 true resid
>> norm
>>>> 2.632671797020e+00 ||r(i)||/||b|| 2.168141189773e-04
>>>> 5 KSP unpreconditioned resid norm 2.209213998004e+00 true resid
>> norm
>>>> 2.209213980361e+00 ||r(i)||/||b|| 1.819401808180e-04
>>>> 6 KSP unpreconditioned resid norm 4.683775185840e-01 true resid
>> norm
>>>> 4.683775085753e-01 ||r(i)||/||b|| 3.857330677735e-05
>>>> 7 KSP unpreconditioned resid norm 3.042503284736e-02 true resid
>> norm
>>>> 3.042503349258e-02 ||r(i)||/||b|| 2.505658638883e-06
>>>> 
>>>> 
>>>> Both methods give answers, but they are different
>>> 
>>> What do you mean the answers are different? Do you mean the
>>> solution x from KSPSolve() is different? How are you calculating
>> their
>>> difference and how different are they?
>>> 
>>> Since the solutions are only approximate; true residual norm
>> is
>>> around 1.642782495109e-02 and 3.042503349258e-02 for the two
>>> different solvers there will only be a certain number of
>> identical
>>> digits in the two solutions (which depends on the condition
>> number of
>>> the original matrix). You can run both solvers with -ksp_rtol
>> 1.e-12
>>> and then (assuming everything is working correctly) the two
>> solutions
>>> will be much closer to each other.
>>> 
>>> Barry
>>> 
>>>> so I am wondering
>>>> if it is possible that you can help me figure out which part I
>> am
>>>> doing wrong.
>>>> 
>>>> Thank you for your time.
>>>> 
>>>> Kind Regards,
>>>> Shidi
> 
> --
> 
> 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
> 
> https://www.cse.buffalo.edu/~knepley/ [2]
> 
> 
> Links:
> ------
> [1] 
> https://www.mcs.anl.gov/petsc/documentation/tutorials/MSITutorial.pdf
> [2] http://www.cse.buffalo.edu/~knepley/

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