[petsc-users] Starting point for Stokes fieldsplit
Max Rudolph
maxwellr at gmail.com
Wed Feb 22 15:29:41 CST 2012
On Tue, Feb 21, 2012 at 3:36 AM, Dave May <dave.mayhem23 at gmail.com> wrote:
> Max,
>
> >
> > The test case that I am working with is isoviscous convection, benchmark
> > case 1a from Blankenbach 1989.
> >
>
> Okay, I know this problem.
> An iso viscous problem, solved on a uniform grid using dx=dy=dz
> discretised
> via FV should be super easy to precondition.
>
> >
> >
> > I think that this is the problem. The (2,2) slot in the LHS matrix is all
> > zero (pressure does not appear in the continuity equation), so I think
> that
> > the preconditioner is meaningless. I am still confused as to why this
> choice
> > of preconditioner was suggested in the tutorial, and what is a better
> choice
> > of preconditioner for this block? Should I be using one of the Schur
> > complement methods instead of the additive or multiplicative field split?
> >
>
> No, you need to define an appropriate stokes preconditioner
> You should assemble this matrix
> B = ( K,B ; B^T, -1/eta* I )
> as the preconditioner for stokes.
> Here eta* is a measure of the local viscosity within each pressure
> control volume.
> Unless you specify to use the real diagonal
>
> Pass this into the third argument in KSPSetOperators() (i.e. the Pmat
> variable)
>
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetOperators.html
>
> Not sure how you represent A and B, but if you really want to run just
> additive with fieldsplit, you don't need the off diagonal blocks, so
> B = ( K,0 ; 0, -1/eta* I )
> would yield the same result. Depending on your matrix representation,
> this may save you some memory.
>
> PCFieldsplit will use the B(1,1) and B(2,2) to build the stokes
> preconditioner unless you ask for it to use the real diagonal - but
> for the stokes operator A, this makes no sense.
>
> This is the right thing to do (as Matt states).
> Try it out, and let us know how it goes.
>
>
> Cheers,
> Dave
>
Dave and Matt,
Thanks for your help. I had some time to work on this a little more. I now
have a stokes operator A that looks like this:
A=(K B; B^T 0) and a matrix from which the preconditioner is generated P=(K
B; B^T -1/eta*I)
I verified that I can solve this system using the default ksp and pc
settings in 77 iterations for the first timestep (initial guess zero) and
in 31 iterations for the second timestep (nonzero initial guess).
I adopted your suggestion to use the multiplicative field split as a
starting point. My reading of the PETSc manual suggests to me that the
preconditioner formed should then look like:
B = (ksp(K,K) 0;-B^T*ksp(K,K)*ksp(0,-1/eta*I) ksp(0,-1/eta*I))
My interpretation of the output suggests that the solvers within each
fieldsplit are converging nicely, but the global residual is not decreasing
after the first few iterations. Given the disparity in residual sizes, I
think that there might be a problem with the scaling of the pressure
variable (I scaled the continuity equation by eta/dx where dx is my grid
spacing). I also scaled the (1,1) block in the preconditioner by this scale
factor. Thanks again for all of your help.
Max
Options used:
-stokes_pc_fieldsplit_0_fields 0,1 -stokes_pc_fieldsplit_1_fields 2 \
-stokes_pc_type fieldsplit -stokes_pc_fieldsplit_type multiplicative \
-stokes_fieldsplit_0_pc_type ml \
-stokes_fieldsplit_0_ksp_type gmres \
-stokes_fieldsplit_0_ksp_monitor_true_residual \
-stokes_fieldsplit_0_ksp_norm_type UNPRECONDITIONED \
-stokes_fieldsplit_0_ksp_max_it 3 \
-stokes_fieldsplit_0_ksp_type gmres \
-stokes_fieldsplit_0_ksp_rtol 1.0e-4 \
-stokes_fieldsplit_0_mg_levels_ksp_type gmres \
-stokes_fieldsplit_0_mg_levels_pc_type bjacobi \
-stokes_fieldsplit_0_mg_levels_ksp_max_it 4 \
-stokes_fieldsplit_1_pc_type jacobi \
-stokes_fieldsplit_1_ksp_type preonly \
-stokes_fieldsplit_1_ksp_max_it 3 \
-stokes_fieldsplit_1_ksp_monitor_true_residual \
-stokes_ksp_type gcr \
-stokes_ksp_monitor_blocks \
-stokes_ksp_monitor_draw \
-stokes_ksp_view \
-stokes_ksp_atol 1e-6 \
-stokes_ksp_rtol 1e-6 \
-stokes_ksp_max_it 100 \
-stokes_ksp_norm_type UNPRECONDITIONED \
-stokes_ksp_monitor_true_residual \
Output:
0 KSP Component U,V,P residual norm [ 0.000000000000e+00,
1.165111661413e+06, 0.000000000000e+00 ]
Residual norms for stokes_ solve.
0 KSP unpreconditioned resid norm 1.165111661413e+06 true resid norm
1.165111661413e+06 ||r(i)||/||b|| 1.000000000000e+00
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.165111661413e+06 true resid norm
1.165111661413e+06 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 3.173622513625e+05 true resid norm
3.173622513625e+05 ||r(i)||/||b|| 2.723878421898e-01
2 KSP unpreconditioned resid norm 5.634119635158e+04 true resid norm
1.725996376799e+05 ||r(i)||/||b|| 1.481399967026e-01
3 KSP unpreconditioned resid norm 1.218418968344e+03 true resid norm
1.559727441168e+05 ||r(i)||/||b|| 1.338693528546e-01
1 KSP Component U,V,P residual norm [ 5.763380362961e+04,
1.154490085631e+05, 3.370358145704e-12 ]
1 KSP unpreconditioned resid norm 1.290353784783e+05 true resid norm
1.290353784783e+05 ||r(i)||/||b|| 1.107493665644e-01
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.290353784783e+05 true resid norm
1.290353784783e+05 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 1.655137188235e+04 true resid norm
1.655137188235e+04 ||r(i)||/||b|| 1.282700301076e-01
2 KSP unpreconditioned resid norm 1.195941831181e+03 true resid norm
4.554417355181e+03 ||r(i)||/||b|| 3.529588093508e-02
3 KSP unpreconditioned resid norm 8.479547025398e+01 true resid norm
3.817072778396e+03 ||r(i)||/||b|| 2.958159865466e-02
2 KSP Component U,V,P residual norm [ 2.026983725663e+03,
2.531521226429e+03, 3.419060873106e-12 ]
2 KSP unpreconditioned resid norm 3.243032954498e+03 true resid norm
3.243032954498e+03 ||r(i)||/||b|| 2.783452489493e-03
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 3.243032954498e+03 true resid norm
3.243032954498e+03 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 1.170090628031e+02 true resid norm
1.170090628031e+02 ||r(i)||/||b|| 3.608013376517e-02
2 KSP unpreconditioned resid norm 9.782830529900e+00 true resid norm
1.741722174777e+01 ||r(i)||/||b|| 5.370658267168e-03
3 KSP unpreconditioned resid norm 6.886950142735e-01 true resid norm
1.636749336722e+01 ||r(i)||/||b|| 5.046971028932e-03
3 KSP Component U,V,P residual norm [ 7.515013854917e+01,
7.515663601801e+01, 3.418919176066e-12 ]
3 KSP unpreconditioned resid norm 1.062829396540e+02 true resid norm
1.062829396540e+02 ||r(i)||/||b|| 9.122124786317e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.062829396540e+02 true resid norm
1.062829396540e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.373578062042e+01 true resid norm
5.373578062042e+01 ||r(i)||/||b|| 5.055917797846e-01
2 KSP unpreconditioned resid norm 1.199305097134e+00 true resid norm
3.492111756827e+01 ||r(i)||/||b|| 3.285674792393e-01
3 KSP unpreconditioned resid norm 9.508597255523e-02 true resid norm
3.452079362567e+01 ||r(i)||/||b|| 3.248008922038e-01
4 KSP Component U,V,P residual norm [ 7.495897679790e+01,
7.527868410560e+01, 3.418919160091e-12 ]
4 KSP unpreconditioned resid norm 1.062343093509e+02 true resid norm
1.062343093509e+02 ||r(i)||/||b|| 9.117950911420e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.062343093509e+02 true resid norm
1.062343093509e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.419252803207e+01 true resid norm
5.419252803207e+01 ||r(i)||/||b|| 5.101226558840e-01
2 KSP unpreconditioned resid norm 1.431134174522e+00 true resid norm
3.339055236737e+01 ||r(i)||/||b|| 3.143104386088e-01
3 KSP unpreconditioned resid norm 9.760479467902e-02 true resid norm
3.304522520358e+01 ||r(i)||/||b|| 3.110598205561e-01
5 KSP Component U,V,P residual norm [ 7.491128585963e+01,
7.523275560552e+01, 3.418919008441e-12 ]
5 KSP unpreconditioned resid norm 1.061681132221e+02 true resid norm
1.061681132221e+02 ||r(i)||/||b|| 9.112269384837e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.061681132221e+02 true resid norm
1.061681132221e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.343215079492e+01 true resid norm
5.343215079492e+01 ||r(i)||/||b|| 5.032787074508e-01
2 KSP unpreconditioned resid norm 1.288069736759e+00 true resid norm
3.308925591301e+01 ||r(i)||/||b|| 3.116684935691e-01
3 KSP unpreconditioned resid norm 9.505248953960e-02 true resid norm
3.281875055845e+01 ||r(i)||/||b|| 3.091205971589e-01
6 KSP Component U,V,P residual norm [ 7.481188568118e+01,
7.527346267608e+01, 3.418918860626e-12 ]
6 KSP unpreconditioned resid norm 1.061268694649e+02 true resid norm
1.061268694649e+02 ||r(i)||/||b|| 9.108729487455e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.061268694649e+02 true resid norm
1.061268694649e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.300383444945e+01 true resid norm
5.300383444945e+01 ||r(i)||/||b|| 4.994384053416e-01
2 KSP unpreconditioned resid norm 1.118785004087e+00 true resid norm
3.282090953364e+01 ||r(i)||/||b|| 3.092610730828e-01
3 KSP unpreconditioned resid norm 9.758015489979e-02 true resid norm
3.259718081014e+01 ||r(i)||/||b|| 3.071529479244e-01
7 KSP Component U,V,P residual norm [ 7.475024970669e+01,
7.530858268154e+01, 3.418918784089e-12 ]
7 KSP unpreconditioned resid norm 1.061083524362e+02 true resid norm
1.061083524362e+02 ||r(i)||/||b|| 9.107140195255e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.061083524362e+02 true resid norm
1.061083524362e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.296981668051e+01 true resid norm
5.296981668051e+01 ||r(i)||/||b|| 4.992049679820e-01
2 KSP unpreconditioned resid norm 9.379451887610e-01 true resid norm
3.378466967056e+01 ||r(i)||/||b|| 3.183978348066e-01
3 KSP unpreconditioned resid norm 9.102580142867e-02 true resid norm
3.360853440947e+01 ||r(i)||/||b|| 3.167378781957e-01
8 KSP Component U,V,P residual norm [ 7.464535615814e+01,
7.537007679541e+01, 3.418918790515e-12 ]
8 KSP unpreconditioned resid norm 1.060781677449e+02 true resid norm
1.060781677449e+02 ||r(i)||/||b|| 9.104549482946e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.060781677449e+02 true resid norm
1.060781677449e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.281972737642e+01 true resid norm
5.281972737642e+01 ||r(i)||/||b|| 4.979321240109e-01
2 KSP unpreconditioned resid norm 9.224594814880e-01 true resid norm
3.351285171891e+01 ||r(i)||/||b|| 3.159260046751e-01
3 KSP unpreconditioned resid norm 9.143100662935e-02 true resid norm
3.329269756083e+01 ||r(i)||/||b|| 3.138506091177e-01
9 KSP Component U,V,P residual norm [ 7.451688471900e+01,
7.544516987344e+01, 3.418918860847e-12 ]
9 KSP unpreconditioned resid norm 1.060412172952e+02 true resid norm
1.060412172952e+02 ||r(i)||/||b|| 9.101378074496e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.060412172952e+02 true resid norm
1.060412172952e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.275132249899e+01 true resid norm
5.275132249899e+01 ||r(i)||/||b|| 4.974605520805e-01
2 KSP unpreconditioned resid norm 7.755381284769e-01 true resid norm
3.453933285011e+01 ||r(i)||/||b|| 3.257161105001e-01
3 KSP unpreconditioned resid norm 7.298768665179e-02 true resid norm
3.435179316160e+01 ||r(i)||/||b|| 3.239475558447e-01
10 KSP Component U,V,P residual norm [ 7.451431102619e+01,
7.544762349626e+01, 3.418918857322e-12 ]
10 KSP unpreconditioned resid norm 1.060411544587e+02 true resid norm
1.060411544587e+02 ||r(i)||/||b|| 9.101372681321e-05
Residual norms for stokes_fieldsplit_0_ solve.
0 KSP unpreconditioned resid norm 1.060411544587e+02 true resid norm
1.060411544587e+02 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 5.276103518337e+01 true resid norm
5.276103518337e+01 ||r(i)||/||b|| 4.975524403961e-01
2 KSP unpreconditioned resid norm 7.777079890360e-01 true resid norm
3.454373663425e+01 ||r(i)||/||b|| 3.257578325186e-01
3 KSP unpreconditioned resid norm 7.356028471071e-02 true resid norm
3.435584054266e+01 ||r(i)||/||b|| 3.239859158269e-01
11 KSP Component U,V,P residual norm [ 7.438335197779e+01,
7.553731959735e+01, 3.418918856471e-12 ]
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120222/7b99222b/attachment.htm>
More information about the petsc-users
mailing list