[petsc-users] discontinuous viscosity stokes equation 3D staggered grid
Matthew Knepley
knepley at gmail.com
Wed Aug 7 07:15:01 CDT 2013
On Wed, Aug 7, 2013 at 7:07 AM, Bishesh Khanal <bisheshkh at gmail.com> wrote:
>
>
>
> On Tue, Aug 6, 2013 at 11:34 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Tue, Aug 6, 2013 at 10:59 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>
>>>
>>>
>>>
>>> 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);
>>>
>>
>> Sorry, you need to return to the old DMDA behavior, so you want
>>
>> -pc_fieldsplit_dm_splits 0
>>
>
> Thanks, with this it seems I can attach the null space properly, but I
> have a question regarding whether the Schur complement ksp solver is
> actually using the preconditioner matrix I provide.
> When using -ksp_view, the outer level pc object of type fieldsplit does
> report that: "Preconditioner for the Schur complement formed from user
> provided matrix", but in the KSP solver for Schur complement S, the pc
> object (fieldsplit_1_) is of type ilu and doesn't say that it is using the
> matrix I provide. Am I missing something here ?
> Below are the relevant commented code snippet and the output of the
> -ksp_view
> (The options I used: -pc_type fieldsplit -pc_fieldsplit_type schur
> -pc_fieldsplit_dm_splits 0 -pc_fieldsplit_0_fields 0,1,2
> -pc_fieldsplit_1_fields 3 -ksp_converged_reason -ksp_view )
>
If ILU does not error, it means it is using your matrix, because the Schur
complement matrix cannot be factored, and FS says it is using your matrix.
Matt
> Code snippet:
> ierr = KSPSetNullSpace(mKsp,mNullSpaceSystem);CHKERRQ(ierr); //The
> nullspace for the whole system
> ierr = KSPSetFromOptions(mKsp);CHKERRQ(ierr);
> ierr = KSPSetUp(mKsp);CHKERRQ(ierr); //Set up mKsp
> with the options provided with fieldsplit and the fields associated with
> the two splits.
>
> ierr = KSPGetPC(mKsp,&mPcOuter);CHKERRQ(ierr); //Get
> the fieldsplit pc set up from the options
>
> ierr =
> PCFieldSplitSchurPrecondition(mPcOuter,PC_FIELDSPLIT_SCHUR_PRE_USER,mPcForSc);CHKERRQ(ierr);
> //Use mPcForSc as the preconditioner for Schur Complement
>
> KSP *kspSchur;
> PetscInt kspSchurPos = 1;
> ierr =
> PCFieldSplitGetSubKSP(mPcOuter,&kspSchurPos,&kspSchur);CHKERRQ(ierr);
> ierr =
> KSPSetNullSpace(kspSchur[1],mNullSpacePressure);CHKERRQ(ierr);
> //Attach the null-space for the Schur complement ksp solver.
> ierr = PetscFree(kspSchur);CHKERRQ(ierr);
>
> ierr = KSPSolve(mKsp,NULL,NULL);CHKERRQ(ierr);
>
>
>
> the output of the -ksp_view
> KSP Object: 1 MPI processes
> type: gmres
> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> GMRES: happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
> left preconditioning
> has attached null space
> using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: fieldsplit
> FieldSplit with Schur preconditioner, blocksize = 4, factorization FULL
> Preconditioner for the Schur complement formed from user provided
> matrix
> Split info:
> Split number 0 Fields 0, 1, 2
> Split number 1 Fields 3
> KSP solver for A00 block
> KSP Object: (fieldsplit_0_) 1 MPI processes
> type: gmres
> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> GMRES: happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: (fieldsplit_0_) 1 MPI processes
> type: ilu
> ILU: out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> using diagonal shift on blocks to prevent zero pivot
> matrix ordering: natural
> factor fill ratio given 1, needed 1
> Factored matrix follows:
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=2187, cols=2187
> package used to perform factorization: petsc
> total: nonzeros=140625, allocated nonzeros=140625
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 729 nodes, limit used is 5
> linear system matrix = precond matrix:
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=2187, cols=2187
> total: nonzeros=140625, allocated nonzeros=140625
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 729 nodes, limit used is 5
> KSP solver for S = A11 - A10 inv(A00) A01
> KSP Object: (fieldsplit_1_) 1 MPI processes
> type: gmres
> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> GMRES: happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
> left preconditioning
> has attached null space
> using PRECONDITIONED norm type for convergence test
> PC Object: (fieldsplit_1_) 1 MPI processes
> type: ilu
> ILU: out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> using diagonal shift on blocks to prevent zero pivot
> matrix ordering: natural
> factor fill ratio given 1, needed 1
> Factored matrix follows:
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=729, cols=729
> package used to perform factorization: petsc
> total: nonzeros=15625, allocated nonzeros=15625
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> linear system matrix followed by preconditioner matrix:
> Matrix Object: 1 MPI processes
> type: schurcomplement
> rows=729, cols=729
> Schur complement A11 - A10 inv(A00) A01
> A11
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=729, cols=729
> total: nonzeros=15625, allocated nonzeros=15625
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> A10
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=729, cols=2187
> total: nonzeros=46875, allocated nonzeros=46875
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> KSP of A00
> KSP Object: (fieldsplit_0_) 1 MPI
> processes
> type: gmres
> GMRES: restart=30, using Classical (unmodified)
> Gram-Schmidt Orthogonalization with no iterative refinement
> GMRES: happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50,
> divergence=10000
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: (fieldsplit_0_) 1 MPI
> processes
> type: ilu
> ILU: out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> using diagonal shift on blocks to prevent zero pivot
> matrix ordering: natural
> factor fill ratio given 1, needed 1
> Factored matrix follows:
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=2187, cols=2187
> package used to perform factorization: petsc
> total: nonzeros=140625, allocated nonzeros=140625
> total number of mallocs used during MatSetValues
> calls =0
> using I-node routines: found 729 nodes, limit
> used is 5
> linear system matrix = precond matrix:
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=2187, cols=2187
> total: nonzeros=140625, allocated nonzeros=140625
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 729 nodes, limit used is 5
> A01
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=2187, cols=729
> total: nonzeros=46875, allocated nonzeros=46875
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 729 nodes, limit used is 5
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=729, cols=729
> total: nonzeros=15625, allocated nonzeros=15625
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> linear system matrix = precond matrix:
> Matrix Object: 1 MPI processes
> type: seqaij
> rows=2916, cols=2916, bs=4
> total: nonzeros=250000, allocated nonzeros=250000
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 729 nodes, limit used is 5
>
>
>
>
>
>>
>> or
>>
>> PCFieldSplitSetDMSplits(pc, PETSC_FALSE)
>>
>> Thanks,
>>
>> Matt
>>
>>
>>> 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
>>>>
>>>
>>>
>>
>>
>> --
>> 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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