[petsc-users] discontinuous viscosity stokes equation 3D staggered grid
Bishesh Khanal
bisheshkh at gmail.com
Tue Aug 6 10:59:10 CDT 2013
On Tue, Aug 6, 2013 at 4:40 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Tue, Aug 6, 2013 at 8:06 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>
>>
>>
>>
>> On Mon, Aug 5, 2013 at 4:14 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>
>>> On Mon, Aug 5, 2013 at 8:48 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>>
>>>>
>>>>
>>>>
>>>> On Mon, Aug 5, 2013 at 3:17 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>>
>>>>> On Mon, Aug 5, 2013 at 7:54 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). 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.
>>>>>>>
>>>>>>
>>>>>> I was trying to assemble the inverse viscosity diagonal matrix to use
>>>>>> as the preconditioner for the Schur complement solve step as you suggested.
>>>>>> I've few questions about the ways to implement this in Petsc:
>>>>>> A naive approach that I can think of would be to create a vector with
>>>>>> its components as reciprocal viscosities of the cell centers corresponding
>>>>>> to the pressure variables, and then create a diagonal matrix from this
>>>>>> vector. However I'm not sure about:
>>>>>> How can I make this matrix, (say S_p) compatible to the Petsc
>>>>>> distribution of the different rows of the main system matrix over different
>>>>>> processors ? The main matrix was created using the DMDA structure with 4
>>>>>> dof as explained before.
>>>>>> The main matrix correspond to the DMDA with 4 dofs but for the S_p
>>>>>> matrix would correspond to only pressure space. Should the distribution of
>>>>>> the rows of S_p among different processor not correspond to the
>>>>>> distribution of the rhs vector, say h' if it is solving for p with Sp = h'
>>>>>> where S = A11 inv(A00) A01 ?
>>>>>>
>>>>>
>>>>> PETSc distributed vertices, not dofs, so it never breaks blocks. The P
>>>>> distribution is the same as the entire problem divided by 4.
>>>>>
>>>>
>>>> Thanks Matt. So if I create a new DMDA with same grid size but with
>>>> dof=1 instead of 4, the vertices for this new DMDA will be identically
>>>> distributed as for the original DMDA ? Or should I inform PETSc by calling
>>>> a particular function to make these two DMDA have identical distribution of
>>>> the vertices ?
>>>>
>>>
>>> Yes.
>>>
>>>
>>>> Even then I think there might be a problem due to the presence of
>>>> "fictitious pressure vertices". The system matrix (A) contains an identity
>>>> corresponding to these fictitious pressure nodes, thus when using a
>>>> -pc_fieldsplit_detect_saddle_point, will detect a A11 zero block of size
>>>> that correspond to only non-fictitious P-nodes. So the preconditioner S_p
>>>> for the Schur complement outer solve with Sp = h' will also need to
>>>> correspond to only the non-fictitious P-nodes. This means its size does not
>>>> directly correspond to the DMDA grid defined for the original problem.
>>>> Could you please suggest an efficient way of assembling this S_p matrix ?
>>>>
>>>
>>> Don't use detect_saddle, but split it by fields -pc_fieldsplit_0_fields
>>> 0,1,2 -pc_fieldsplit_1_fields 4
>>>
>>
>> How can I set this split in the code itself without giving it as a
>> command line option when the system matrix is assembled from the DMDA for
>> the whole system with 4 dofs. (i.e. *without* using the DMComposite or *
>> without* using the nested block matrices to assemble different blocks
>> separately and then combine them together).
>> I need the split to get access to the fieldsplit_1_ksp in my code,
>> because not using detect_saddle_point means I cannot use
>> -fieldsplit_1_ksp_constant_null_space due to the presence of identity for
>> the fictitious pressure nodes present in the fieldsplit_1_ block. I need to
>> use PCFieldSplitGetSubKsp() so that I can set proper null-space basis.
>>
>
> This is currently a real problem with the DMDA. In the unstructured case,
> where we always need specialized spaces, you can
> use something like
>
> PetscObject pressure;
> MatNullSpace nullSpacePres;
>
> ierr = DMGetField(dm, 1, &pressure);CHKERRQ(ierr);
> ierr = MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0,
> NULL, &nullSpacePres);CHKERRQ(ierr);
> ierr = PetscObjectCompose(pressure, "nullspace", (PetscObject)
> nullSpacePres);CHKERRQ(ierr);
> ierr = MatNullSpaceDestroy(&nullSpacePres);CHKERRQ(ierr);
>
> and then DMGetSubDM() uses this information to attach the null space to
> the IS that is created using the information in the PetscSection.
> If you use a PetscSection to set the data layout over the DMDA, I think
> this works correctly, but this has not been tested at all and is very
> new code. Eventually, I think we want all DMs to use this mechanism, but
> we are still working it out.
>
Currently I do not use PetscSection. If this makes a cleaner approach, I'd
try it too but may a bit later (right now I'd like test my model with a
quickfix even if it means a little dirty code!)
>
> Bottom line: For custom null spaces using the default layout in DMDA, you
> need to take apart the PCFIELDSPLIT after it has been setup,
> which is somewhat subtle. You need to call KSPSetUp() and then reach in
> and get the PC, and the subKSPs. I don't like this at all, but we
> have not reorganized that code (which could be very simple and inflexible
> since its very structured).
>
So I tried to get this approach working but I could not succeed and
encountered some errors. Here is a code snippet:
//mDa is the DMDA that describes the whole grid with all 4 dofs (3 velocity
components and 1 pressure comp.)
ierr = DMKSPSetComputeRHS(mDa,computeRHSTaras3D,this);CHKERRQ(ierr);
ierr =
DMKSPSetComputeOperators(mDa,computeMatrixTaras3D,this);CHKERRQ(ierr);
ierr = KSPSetDM(mKsp,mDa);CHKERRQ(ierr);
ierr = KSPSetNullSpace(mKsp,mNullSpaceSystem);CHKERRQ(ierr); //I've
the mNullSpaceSystem based on mDa, that contains a null space basis for the
complete system.
ierr =
KSPSetFromOptions(mKsp);CHKERRQ(ierr);
//This I expect would register these options I give:-pc_type fieldsplit
-pc_fieldsplit_type schur -pc_fieldsplit_0_fields 0,1,2
//-pc_fieldsplit_1_fields 3
ierr = KSPSetUp(mKsp);CHKERRQ(ierr);
ierr = KSPGetPC(mKsp,&mPcOuter); //Now get the PC that was obtained
from the options (fieldsplit)
ierr =
PCFieldSplitSchurPrecondition(mPcOuter,PC_FIELDSPLIT_SCHUR_PRE_USER,mPcForSc);CHKERRQ(ierr);
//I have created the matrix mPcForSc using a DMDA with identical //size to
mDa but with dof=1 corresponding to the pressure nodes (say mDaPressure).
ierr = PCSetUp(mPcOuter);CHKERRQ(ierr);
KSP *kspSchur;
PetscInt kspSchurPos = 1;
ierr =
PCFieldSplitGetSubKSP(mPcOuter,&kspSchurPos,&kspSchur);CHKERRQ(ierr);
ierr =
KSPSetNullSpace(kspSchur[1],mNullSpacePressure);CHKERRQ(ierr);
//The null space is the one that correspond to only pressure nodes, created
using the mDaPressure.
ierr = PetscFree(kspSchur);CHKERRQ(ierr);
ierr = KSPSolve(mKsp,NULL,NULL);CHKERRQ(ierr);
The errors I get when running with options: -pc_type fieldsplit
-pc_fieldsplit_type schur -pc_fieldsplit_0_fields 0,1,2
-pc_fieldsplit_1_fields 3
[0]PETSC ERROR: --------------------- Error Message
------------------------------------
[0]PETSC ERROR: No support for this operation for this object type!
[0]PETSC ERROR: Support only implemented for 2d!
[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 Tue Aug 6 17:35:30 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
--with-cxx=g++ --download-f-blas-lapack=1 --download-mpich=1
-with-clanguage=cxx --download-hypre=1
[0]PETSC ERROR:
------------------------------------------------------------------------
[0]PETSC ERROR: DMCreateSubDM_DA() line 188 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/dm/impls/da/dacreate.c
[0]PETSC ERROR: DMCreateSubDM() line 1267 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/dm/interface/dm.c
[0]PETSC ERROR: PCFieldSplitSetDefaults() line 337 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/fieldsplit/fieldsplit.c
[0]PETSC ERROR: PCSetUp_FieldSplit() line 458 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/fieldsplit/fieldsplit.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: solveModel() line 181 in
"unknowndirectory/"/user/bkhanal/home/works/AdLemModel/src/PetscAdLemTaras3D.cxx
WARNING! There are options you set that were not used!
WARNING! could be spelling mistake, etc!
Option left: name:-pc_fieldsplit_1_fields value: 3
>
> Matt
>
>
>>
>>> Matt
>>>
>>>
>>>>
>>>>> Matt
>>>>>
>>>>> --
>>>>> 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
>>>>>
>>>>
>>>>
>>>
>>>
>>> --
>>> 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
>>>
>>
>>
>
>
> --
> 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
>
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