[petsc-dev] Using PCFieldSplitSetIS

Fri Mar 18 06:16:14 CDT 2011

Jed, thanks for clarification. I think that I now understand whats going 
when using the fieldsplit preconditioner.

Thomas

Jed Brown wrote:
> On Wed, Mar 16, 2011 at 14:27, Thomas Witkowski 
> <thomas.witkowski at tu-dresden.de 
> <mailto:thomas.witkowski at tu-dresden.de>> wrote:
>
>
>         I'm going to guess that you still have an outer KSP that (in
>         the global norm, rather than the partitioned norm used inside
>         of splits) has a tighter tolerance, therefore it takes a few
>         outer iterations. If you use loose inner tolerances then the
>         preconditioner becomes nonlinear and you'll need to use FGMRES
>         for the outer. When in doubt, run with -ksp_view and show us
>         the results if you don't understand. Additionally, monitoring
>         inner solves separately can be useful, e.g.
>         -fieldsplit_0_ksp_converged_reason -fieldsplit_1_ksp_monitor
>         -ksp_monitor_true_residual.
>
>     Okay, I run my code with the options "-pc_fieldsplit_type schur
>     -fieldsplit_interior_ksp_type preonly -fieldsplit_interior_pc_type
>     bjacobi -fieldsplit_interior_sub_pc_type lu
>     -fieldsplit_boundary_ksp_monitor -ksp_monitor_true_residual
>     -fieldsplit_interior_ksp_converged_reason". The splits are named
>     "interior" and "boundary". The ksp output is as follows:
>
>       Linear solve converged due to CONVERGED_ITS iterations 1
>
>
> This is the initial interior solve.
>  
>
>       Residual norms for fieldsplit_boundary_ solve.
>       0 KSP Residual norm 1.790059331071e-04
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       1 KSP Residual norm 1.237356212928e-04
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       2 KSP Residual norm 7.952220245101e-05
>       Linear solve converged due to CONVERGED_ITS iterations 1
>
>
> [...]
>
> Each iteration on the boundary problem requires an interior solve. We 
> see alternating boundary residual and interior solves.
>  
>
>         
>     [0]  Petsc-Iteration 0: 0.574504
>
>
> You must be printing this somewhere.
>  
>
>      0 KSP preconditioned resid norm 5.745043818120e-01 true resid
>     norm 1.584249437360e-01 ||r(i)||/||b|| 1.000000000000e+00
>
>
> This is the norm of P^{-1} b, upon which all following norms are 
> computed. Note that this is not actually a "preconditioned residual" 
> because the initial guess was zero, however. In fact, since P is an 
> exact preconditioner for your problem, it is the solution of your 
> problem, but GMRES can't check that until it does one more iteration 
> (the output below). You can use -ksp_type richardson to cheaply 
> confirm that the norm is small, it should show a small residual after 
> one iteration. Once you are happy that the inner solve really is 
> solving your system, you can switch to -ksp_type preonly.
>  
>
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       Residual norms for fieldsplit_boundary_ solve.
>       0 KSP Residual norm 1.790059331000e-04
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       1 KSP Residual norm 1.237356237744e-04
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       2 KSP Residual norm 7.952220078415e-05
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       3 KSP Residual norm 3.502859285561e-05
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       4 KSP Residual norm 1.601086485810e-05
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       5 KSP Residual norm 8.491169384185e-06
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       6 KSP Residual norm 4.778229157872e-06
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       7 KSP Residual norm 2.571917112191e-06
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       8 KSP Residual norm 1.353977280183e-06
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       9 KSP Residual norm 7.408352317360e-07
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      10 KSP Residual norm 3.810710583336e-07
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      11 KSP Residual norm 1.955898169394e-07
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      12 KSP Residual norm 9.938892788465e-08
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      13 KSP Residual norm 4.893428546840e-08
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      14 KSP Residual norm 2.395120857135e-08
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      15 KSP Residual norm 1.2464367927 <tel:1.2464367927>84e-08
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      16 KSP Residual norm 6.316409779118e-09
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      17 KSP Residual norm 3.088649355374e-09
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      18 KSP Residual norm 1.593449602302e-09
>       Linear solve converged due to CONVERGED_ITS iterations 1
>
>
> The way GMRES computes residuals explains why we needed this Schur 
> solve, but it shouldn't do the one below. Are you using GMRES or some 
> other Krylov solver (perhaps set in an options file or inside your 
> code, -ksp_view would help)?
>  
>
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       Residual norms for fieldsplit_boundary_ solve.
>       0 KSP Residual norm 1.593449603155e-09
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       1 KSP Residual norm 1.011857676662e-09
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       2 KSP Residual norm 5.660892669788e-10
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       3 KSP Residual norm 3.046799343903e-10
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       4 KSP Residual norm 1.6004713993 <tel:1.6004713993>29e-10
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       5 KSP Residual norm 8.083216601016e-11
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       6 KSP Residual norm 4.308671648345e-11
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       7 KSP Residual norm 2.381959817139e-11
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       8 KSP Residual norm 1.264839790114e-11
>       Linear solve converged due to CONVERGED_ITS iterations 1
>       9 KSP Residual norm 6.435098853282e-12
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      10 KSP Residual norm 3.184769579797e-12
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      11 KSP Residual norm 1.5022019430 <tel:1.5022019430>16e-12
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      12 KSP Residual norm 7.099486208425e-13
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      13 KSP Residual norm 3.443222176388e-13
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      14 KSP Residual norm 1.6478434989 <tel:1.6478434989>12e-13
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      15 KSP Residual norm 8.208508173926e-14
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      16 KSP Residual norm 4.376604355287e-14
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      17 KSP Residual norm 2.596069152755e-14
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      18 KSP Residual norm 1.335744434252e-14
>       Linear solve converged due to CONVERGED_ITS iterations 1
>      1 KSP preconditioned resid norm 2.608069232839e-13 true resid
>     norm 1.449869994655e-13 ||r(i)||/||b|| 9.151778504469e-13
>
>     I have no idea how to interpret this output! Could you help me
>     with it?
>
>     Thomas
>
>