# [petsc-users] discontinuous viscosity stokes equation 3D staggered grid

Bishesh Khanal bisheshkh at gmail.com
Fri Jul 26 10:13:07 CDT 2013

```On Fri, Jul 26, 2013 at 4:22 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Fri, Jul 26, 2013 at 9:11 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>
>>
>>
>>
>> On Fri, Jul 26, 2013 at 2:32 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>
>>> On Fri, Jul 26, 2013 at 7:28 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>>
>>>>
>>>>
>>>>
>>>> On Wed, Jul 17, 2013 at 9:48 PM, Jed Brown <jedbrown at mcs.anl.gov>wrote:
>>>>
>>>>> Bishesh Khanal <bisheshkh at gmail.com> writes:
>>>>>
>>>>> > Now, I implemented two different approaches, each for both 2D and
>>>>> 3D, in
>>>>> > MATLAB. It works for the smaller sizes but I have problems solving
>>>>> it for
>>>>> > the problem size I need (250^3 grid size).
>>>>> > I use staggered grid with p on cell centers, and components of v on
>>>>> cell
>>>>> > faces. Similar split up of K to cell center and faces to account for
>>>>> the
>>>>> > variable viscosity case)
>>>>>
>>>>> Okay, you're using a staggered-grid finite difference discretization of
>>>>> variable-viscosity Stokes.  This is a common problem and I recommend
>>>>> starting with PCFieldSplit with Schur complement reduction (make that
>>>>> work first, then switch to block preconditioner).
>>>>
>>>>
>>>> Ok, I made my 3D problem work with PCFieldSplit with Schur complement
>>>> reduction using the options:
>>>> -fieldsplit_1_ksp_constant_null_space
>>>>
>>>>
>>>> You can use PCLSC or
>>>>> (probably better for you), assemble a preconditioning matrix containing
>>>>> the inverse viscosity in the pressure-pressure block.  This diagonal
>>>>> matrix is a spectrally equivalent (or nearly so, depending on
>>>>> discretization) approximation of the Schur complement.  The velocity
>>>>> block can be solved with algebraic multigrid.  Read the PCFieldSplit
>>>>> docs (follow papers as appropriate) and let us know if you get stuck.
>>>>>
>>>>
>>>> Now,  I got a little confused in how exactly to use command line
>>>> options to use multigrid for the velocity bock and PCLS for the pressure
>>>> block. After going through the manual I tried the following:
>>>>
>>>
>>> You want Algebraic Multigrid
>>>
>>> -pc_fieldsplit_type schur
>>>   -fieldsplit_0_pc_type gamg
>>>    -fieldsplit_1_ksp_type fgmres
>>>    -fieldsplit_1_ksp_constant_null_space
>>>    -fieldsplit_1_ksp_monitor_short
>>>    -fieldsplit_1_pc_type lsc
>>> -ksp_converged_reason
>>>
>>> I tried the above set of options but the solution I get seem to be not
>> correct. The velocity field I get are quite different than the one I got
>> before without using gamg which were the expected one.
>> -fieldsplit_1_ksp_gmres_restart 100 , because the fieldsplit_1_ksp residual
>> norm did not converge within default 30 iterations before restarting).
>>
>
> These are all iterative solvers. You have to make sure everything
> converges.
>

When I set restart to 100, and do -ksp_monitor, it does converge (for the
fieldsplit_1_ksp). Are you saying that in spite of having
-ksp_converged_reason in the option and petsc completing the run with the
message "Linear solve converged due to CONVERGED_RTOL .." not enough to
make sure that everything is converging ? If that is the case what should I
do for this particular problem ?

I have used the MAC scheme with indexing as shown in:  fig 7.5, page 96 of:

Thus I have a DM with 4 dof but there are several "ghost values" set to 0.
Would this cause any problem when using the multigrid ? (This has worked
fine when not using the multigrid.)

> I do this problem in the tutorial with
> a constant viscosity.
>

Which tutorial are you referring to ? Could you please provide me the link

>     Matt
>
>
>>     Matt
>>>
>>>
>>>> but I get the following errror:
>>>>
>>>> [0]PETSC ERROR: --------------------- Error Message
>>>> ------------------------------------
>>>> [0]PETSC ERROR: Null argument, when expecting valid pointer!
>>>> [0]PETSC ERROR: Null Object: Parameter # 2!
>>>> [0]PETSC ERROR:
>>>> ------------------------------------------------------------------------
>>>> [0]PETSC ERROR: Petsc Release Version 3.4.2, Jul, 02, 2013
>>>> [0]PETSC ERROR: See docs/changes/index.html for recent updates.
>>>> [0]PETSC ERROR: See docs/faq.html for hints about trouble shooting.
>>>> [0]PETSC ERROR: See docs/index.html for manual pages.
>>>> [0]PETSC ERROR:
>>>> ------------------------------------------------------------------------
>>>> [0]PETSC ERROR: src/AdLemMain on a arch-linux2-cxx-debug named edwards
>>>> by bkhanal Fri Jul 26 14:23:40 2013
>>>> [0]PETSC ERROR: Libraries linked from
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/arch-linux2-cxx-debug/lib
>>>> [0]PETSC ERROR: Configure run at Fri Jul 19 14:25:01 2013
>>>> [0]PETSC ERROR: Configure options --with-cc=gcc --with-fc=g77
>>>> [0]PETSC ERROR:
>>>> ------------------------------------------------------------------------
>>>> [0]PETSC ERROR: MatPtAP() line 8166 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/mat/interface/matrix.c
>>>> [0]PETSC ERROR: PCSetUp_MG() line 628 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/mg/mg.c
>>>> [0]PETSC ERROR: PCSetUp() line 890 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/interface/precon.c
>>>> [0]PETSC ERROR: KSPSetUp() line 278 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c
>>>> [0]PETSC ERROR: KSPSolve() line 399 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c
>>>> [0]PETSC ERROR: PCApply_FieldSplit_Schur() line 807 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/fieldsplit/fieldsplit.c
>>>> [0]PETSC ERROR: PCApply() line 442 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/interface/precon.c
>>>> [0]PETSC ERROR: KSP_PCApply() line 227 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/include/petsc-private/kspimpl.h
>>>> [0]PETSC ERROR: KSPInitialResidual() line 64 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itres.c
>>>> [0]PETSC ERROR: KSPSolve_GMRES() line 239 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/impls/gmres/gmres.c
>>>> [0]PETSC ERROR: KSPSolve() line 441 in
>>>> /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c
>>>>
>>>>
>>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> -- Norbert Wiener
>>>
>>
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their