[petsc-users] Diagnosing Convergence Issue in Fieldsplit Problem
Colton Bryant
coltonbryant2021 at u.northwestern.edu
Thu May 23 13:16:28 CDT 2024
Hi Barry,
I saw that was reporting as an unused option and the error message I sent
was run with -fieldsplit_0_ksp_type preonly.
-Colton
On Thu, May 23, 2024 at 12:13 PM Barry Smith <bsmith at petsc.dev> wrote:
>
>
> Sorry I gave the wrong option. Use -fieldsplit_0_ksp_type preonly
>
> Barry
>
> On May 23, 2024, at 12:51 PM, Colton Bryant <
> coltonbryant2021 at u.northwestern.edu> wrote:
>
> That produces the error:
>
> [0]PETSC ERROR: Residual norm computed by GMRES recursion formula
> 2.68054e-07 is far from the computed residual norm 6.86309e-06 at restart,
> residual norm at start of cycle 2.68804e-07
>
> The rest of the error is identical.
>
> On Thu, May 23, 2024 at 10:46 AM Barry Smith <bsmith at petsc.dev> wrote:
>
>>
>> Use -pc_fieldsplit_0_ksp_type preonly
>>
>>
>>
>> On May 23, 2024, at 12:43 PM, Colton Bryant <
>> coltonbryant2021 at u.northwestern.edu> wrote:
>>
>> That produces the following error:
>>
>> [0]PETSC ERROR: Residual norm computed by GMRES recursion formula
>> 2.79175e-07 is far from the computed residual norm 0.000113154 at restart,
>> residual norm at start of cycle 2.83065e-07
>> [0]PETSC ERROR: See https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!YLXuNRxByL1dnyRsgWMPWhX1eOTPS4pBuZhlznx9VQ0x0leG4k2SO8f3Npwu5xHosiut0INu8lZbKQhw0idfYmzNC541iK5ZvTg-hvOzSJA$ for trouble shooting.
>> [0]PETSC ERROR: Petsc Release Version 3.21.0, unknown
>> [0]PETSC ERROR: ./mainOversetLS_exe on a arch-linux-c-opt named glass by
>> colton Thu May 23 10:41:09 2024
>> [0]PETSC ERROR: Configure options --download-mpich --with-cc=gcc
>> --with-cxx=g++ --with-debugging=no --with-fc=gfortran COPTFLAGS=-O3
>> CXXOPTFLAGS=-O3 FOPTFLAGS=-O3 PETSC_ARCH=arch-linux-c-opt --download-sowing
>> [0]PETSC ERROR: #1 KSPGMRESCycle() at
>> /home/colton/petsc/src/ksp/ksp/impls/gmres/gmres.c:115
>> [0]PETSC ERROR: #2 KSPSolve_GMRES() at
>> /home/colton/petsc/src/ksp/ksp/impls/gmres/gmres.c:227
>> [0]PETSC ERROR: #3 KSPSolve_Private() at
>> /home/colton/petsc/src/ksp/ksp/interface/itfunc.c:905
>> [0]PETSC ERROR: #4 KSPSolve() at
>> /home/colton/petsc/src/ksp/ksp/interface/itfunc.c:1078
>> [0]PETSC ERROR: #5 PCApply_FieldSplit_Schur() at
>> /home/colton/petsc/src/ksp/pc/impls/fieldsplit/fieldsplit.c:1203
>> [0]PETSC ERROR: #6 PCApply() at
>> /home/colton/petsc/src/ksp/pc/interface/precon.c:497
>> [0]PETSC ERROR: #7 KSP_PCApply() at
>> /home/colton/petsc/include/petsc/private/kspimpl.h:409
>> [0]PETSC ERROR: #8 KSPFGMRESCycle() at
>> /home/colton/petsc/src/ksp/ksp/impls/gmres/fgmres/fgmres.c:123
>> [0]PETSC ERROR: #9 KSPSolve_FGMRES() at
>> /home/colton/petsc/src/ksp/ksp/impls/gmres/fgmres/fgmres.c:235
>> [0]PETSC ERROR: #10 KSPSolve_Private() at
>> /home/colton/petsc/src/ksp/ksp/interface/itfunc.c:905
>> [0]PETSC ERROR: #11 KSPSolve() at
>> /home/colton/petsc/src/ksp/ksp/interface/itfunc.c:1078
>> [0]PETSC ERROR: #12 solveStokes() at cartesianStokesGrid.cpp:1403
>>
>>
>>
>> On Thu, May 23, 2024 at 10:33 AM Barry Smith <bsmith at petsc.dev> wrote:
>>
>>>
>>> Run the failing case with also -ksp_error_if_not_converged so we see
>>> exactly where the problem is first detected.
>>>
>>>
>>>
>>>
>>> On May 23, 2024, at 11:51 AM, Colton Bryant <
>>> coltonbryant2021 at u.northwestern.edu> wrote:
>>>
>>> Hi Barry,
>>>
>>> Thanks for letting me know about the need to use fgmres in this case. I
>>> ran a smaller problem (1230 in the first block) and saw similar behavior in
>>> the true residual.
>>>
>>> I also ran the same problem with the options -fieldsplit_0_pc_type svd
>>> -fieldsplit_0_pc_svd_monitor and get the following output:
>>> SVD: condition number 1.933639985881e+03, 0 of 1230 singular
>>> values are (nearly) zero
>>> SVD: smallest singular values: 4.132036392141e-03
>>> 4.166444542385e-03 4.669534028645e-03 4.845532162256e-03 5.047038625390e-03
>>> SVD: largest singular values : 7.947990616611e+00
>>> 7.961437414477e+00 7.961851612473e+00 7.971335373142e+00 7.989870790960e+00
>>>
>>> I would be surprised if the A_{00} block is ill conditioned as it's just
>>> a standard discretization of the laplacian with some rows replaced with
>>> ones on the diagonal due to interpolations from the overset mesh. I'm
>>> wondering if I'm somehow violating a solvability condition of the problem?
>>>
>>> Thanks for the help!
>>>
>>> -Colton
>>>
>>> On Wed, May 22, 2024 at 6:09 PM Barry Smith <bsmith at petsc.dev> wrote:
>>>
>>>>
>>>> Thanks for the info. I see you are using GMRES inside the Schur
>>>> complement solver, this is ok but when you do you need to use fgmres as the
>>>> outer solver. But this is unlikely to be the cause of the exact problem you
>>>> are seeing.
>>>>
>>>> I'm not sure why the Schur complement KSP is suddenly seeing a large
>>>> increase in the true residual norm. Is it possible the A_{00} block is
>>>> ill-conditioned?
>>>>
>>>> Can you run with a smaller problem? Say 2,000 or so in the first
>>>> block? Is there still a problem?
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> On May 22, 2024, at 6:00 PM, Colton Bryant <
>>>> coltonbryant2021 at u.northwestern.edu> wrote:
>>>>
>>>> Hi Barry,
>>>>
>>>> I have not used any other solver parameters in the code and the full
>>>> set of solver related command line options are those I mentioned in the
>>>> previous email.
>>>>
>>>> Below is the output from -ksp_view:
>>>>
>>>> KSP Object: (back_) 1 MPI process
>>>> type: gmres
>>>> restart=30, using Classical (unmodified) Gram-Schmidt
>>>> Orthogonalization with no iterative refinement
>>>> happy breakdown tolerance 1e-30
>>>> maximum iterations=10000, initial guess is zero
>>>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000.
>>>> left preconditioning
>>>> using PRECONDITIONED norm type for convergence test
>>>> PC Object: (back_) 1 MPI process
>>>> type: fieldsplit
>>>> FieldSplit with Schur preconditioner, blocksize = 1, factorization
>>>> FULL
>>>> Preconditioner for the Schur complement formed from S itself
>>>> Split info:
>>>> Split number 0 Defined by IS
>>>> Split number 1 Defined by IS
>>>> KSP solver for A00 block
>>>> KSP Object: (back_fieldsplit_0_) 1 MPI process
>>>> type: gmres
>>>> restart=30, using Classical (unmodified) Gram-Schmidt
>>>> Orthogonalization with no iterative refinement
>>>> 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: (back_fieldsplit_0_) 1 MPI process
>>>> type: lu
>>>> out-of-place factorization
>>>> tolerance for zero pivot 2.22045e-14
>>>> matrix ordering: nd
>>>> factor fill ratio given 5., needed 8.83482
>>>> Factored matrix follows:
>>>> Mat Object: (back_fieldsplit_0_) 1 MPI process
>>>> type: seqaij
>>>> rows=30150, cols=30150
>>>> package used to perform factorization: petsc
>>>> total: nonzeros=2649120, allocated nonzeros=2649120
>>>> using I-node routines: found 15019 nodes, limit used
>>>> is 5
>>>> linear system matrix = precond matrix:
>>>> Mat Object: (back_fieldsplit_0_) 1 MPI process
>>>> type: seqaij
>>>> rows=30150, cols=30150
>>>> total: nonzeros=299850, allocated nonzeros=299850
>>>> total number of mallocs used during MatSetValues calls=0
>>>> using I-node routines: found 15150 nodes, limit used is 5
>>>> KSP solver for S = A11 - A10 inv(A00) A01
>>>> KSP Object: (back_fieldsplit_1_) 1 MPI process
>>>> type: gmres
>>>> restart=30, using Classical (unmodified) Gram-Schmidt
>>>> Orthogonalization with no iterative refinement
>>>> happy breakdown tolerance 1e-30
>>>> maximum iterations=10000, initial guess is zero
>>>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000.
>>>> left preconditioning
>>>> using PRECONDITIONED norm type for convergence test
>>>> PC Object: (back_fieldsplit_1_) 1 MPI process
>>>> type: none
>>>> linear system matrix = precond matrix:
>>>> Mat Object: (back_fieldsplit_1_) 1 MPI process
>>>> type: schurcomplement
>>>> rows=15000, cols=15000
>>>> Schur complement A11 - A10 inv(A00) A01
>>>> A11
>>>> Mat Object: (back_fieldsplit_1_) 1 MPI process
>>>> type: seqaij
>>>> rows=15000, cols=15000
>>>> total: nonzeros=74700, allocated nonzeros=74700
>>>> total number of mallocs used during MatSetValues calls=0
>>>> not using I-node routines
>>>> A10
>>>> Mat Object: 1 MPI process
>>>> type: seqaij
>>>> rows=15000, cols=30150
>>>> total: nonzeros=149550, allocated nonzeros=149550
>>>> total number of mallocs used during MatSetValues calls=0
>>>> not using I-node routines
>>>> KSP solver for A00 block viewable with the additional
>>>> option -back_fieldsplit_0_ksp_view
>>>> A01
>>>> Mat Object: 1 MPI process
>>>> type: seqaij
>>>> rows=30150, cols=15000
>>>> total: nonzeros=149550, allocated nonzeros=149550
>>>> total number of mallocs used during MatSetValues calls=0
>>>> using I-node routines: found 15150 nodes, limit used
>>>> is 5
>>>> linear system matrix = precond matrix:
>>>> Mat Object: (back_) 1 MPI process
>>>> type: seqaij
>>>> rows=45150, cols=45150
>>>> total: nonzeros=673650, allocated nonzeros=673650
>>>> total number of mallocs used during MatSetValues calls=0
>>>> has attached null space
>>>> using I-node routines: found 15150 nodes, limit used is 5
>>>>
>>>> Thanks again!
>>>>
>>>> -Colton
>>>>
>>>> On Wed, May 22, 2024 at 3:39 PM Barry Smith <bsmith at petsc.dev> wrote:
>>>>
>>>>>
>>>>> Are you using any other command line options or did you hardwire any
>>>>> solver parameters in the code with, like, KSPSetXXX() or PCSetXXX() Please
>>>>> send all of them.
>>>>>
>>>>> Something funky definitely happened when the true residual norms
>>>>> jumped up.
>>>>>
>>>>> Could you run the same thing with -ksp_view and don't use any thing
>>>>> like -ksp_error_if_not_converged so we can see exactly what is being run.
>>>>>
>>>>> Barry
>>>>>
>>>>>
>>>>> On May 22, 2024, at 3:21 PM, Colton Bryant <
>>>>> coltonbryant2021 at u.northwestern.edu> wrote:
>>>>>
>>>>> This Message Is From an External Sender
>>>>> This message came from outside your organization.
>>>>> Hello,
>>>>>
>>>>> I am solving the Stokes equations on a MAC grid discretized by finite
>>>>> differences using a DMSTAG object. I have tested the solver quite
>>>>> extensively on manufactured problems and it seems to work well. As I am
>>>>> still just trying to get things working and not yet worried about speed I
>>>>> am using the following solver options:
>>>>> -pc_type fieldsplit
>>>>> -pc_fieldsplit_detect_saddle_point
>>>>> -fieldsplit_0_pc_type lu
>>>>> -fieldsplit_1_ksp_rtol 1.e-8
>>>>>
>>>>> However I am now using this solver as an inner step of a larger code
>>>>> and have run into issues. The code repeatedly solves the Stokes equations
>>>>> with varying right hand sides coming from changing problem geometry (the
>>>>> solver is a part of an overset grid scheme coupled to a level set method
>>>>> evolving in time). After a couple timesteps I observe the following output
>>>>> when running with -fieldsplit_1_ksp_converged_reason
>>>>> -fieldsplit_1_ksp_monitor_true_residual:
>>>>>
>>>>> Residual norms for back_fieldsplit_1_ solve.
>>>>> 0 KSP preconditioned resid norm 2.826514299465e-02 true resid norm
>>>>> 2.826514299465e-02 ||r(i)||/||b|| 1.000000000000e+00
>>>>> 1 KSP preconditioned resid norm 7.286621865915e-03 true resid norm
>>>>> 7.286621865915e-03 ||r(i)||/||b|| 2.577953300039e-01
>>>>> 2 KSP preconditioned resid norm 1.500598474492e-03 true resid norm
>>>>> 1.500598474492e-03 ||r(i)||/||b|| 5.309007192273e-02
>>>>> 3 KSP preconditioned resid norm 3.796396924978e-04 true resid norm
>>>>> 3.796396924978e-04 ||r(i)||/||b|| 1.343137349666e-02
>>>>> 4 KSP preconditioned resid norm 8.091057439816e-05 true resid norm
>>>>> 8.091057439816e-05 ||r(i)||/||b|| 2.862556697960e-03
>>>>> 5 KSP preconditioned resid norm 3.689113122359e-05 true resid norm
>>>>> 3.689113122359e-05 ||r(i)||/||b|| 1.305181128239e-03
>>>>> 6 KSP preconditioned resid norm 2.116450533352e-05 true resid norm
>>>>> 2.116450533352e-05 ||r(i)||/||b|| 7.487846545662e-04
>>>>> 7 KSP preconditioned resid norm 3.968234031201e-06 true resid norm
>>>>> 3.968234031200e-06 ||r(i)||/||b|| 1.403932055801e-04
>>>>> 8 KSP preconditioned resid norm 6.666949419511e-07 true resid norm
>>>>> 6.666949419506e-07 ||r(i)||/||b|| 2.358717739644e-05
>>>>> 9 KSP preconditioned resid norm 1.941522884928e-07 true resid norm
>>>>> 1.941522884931e-07 ||r(i)||/||b|| 6.868965372998e-06
>>>>> 10 KSP preconditioned resid norm 6.729545258682e-08 true resid norm
>>>>> 6.729545258626e-08 ||r(i)||/||b|| 2.380863687793e-06
>>>>> 11 KSP preconditioned resid norm 3.009070131709e-08 true resid norm
>>>>> 3.009070131735e-08 ||r(i)||/||b|| 1.064586912687e-06
>>>>> 12 KSP preconditioned resid norm 7.849353009588e-09 true resid norm
>>>>> 7.849353009903e-09 ||r(i)||/||b|| 2.777043445840e-07
>>>>> 13 KSP preconditioned resid norm 2.306283345754e-09 true resid norm
>>>>> 2.306283346677e-09 ||r(i)||/||b|| 8.159461097060e-08
>>>>> 14 KSP preconditioned resid norm 9.336302495083e-10 true resid norm
>>>>> 9.336302502503e-10 ||r(i)||/||b|| 3.303115255517e-08
>>>>> 15 KSP preconditioned resid norm 6.537456143401e-10 true resid norm
>>>>> 6.537456141617e-10 ||r(i)||/||b|| 2.312903968982e-08
>>>>> 16 KSP preconditioned resid norm 6.389159552788e-10 true resid norm
>>>>> 6.389159550304e-10 ||r(i)||/||b|| 2.260437724130e-08
>>>>> 17 KSP preconditioned resid norm 6.380905134246e-10 true resid norm
>>>>> 6.380905136023e-10 ||r(i)||/||b|| 2.257517372981e-08
>>>>> 18 KSP preconditioned resid norm 6.380440605992e-10 true resid norm
>>>>> 6.380440604688e-10 ||r(i)||/||b|| 2.257353025207e-08
>>>>> 19 KSP preconditioned resid norm 6.380427156582e-10 true resid norm
>>>>> 6.380427157894e-10 ||r(i)||/||b|| 2.257348267830e-08
>>>>> 20 KSP preconditioned resid norm 6.380426714897e-10 true resid norm
>>>>> 6.380426714004e-10 ||r(i)||/||b|| 2.257348110785e-08
>>>>> 21 KSP preconditioned resid norm 6.380426656970e-10 true resid norm
>>>>> 6.380426658839e-10 ||r(i)||/||b|| 2.257348091268e-08
>>>>> 22 KSP preconditioned resid norm 6.380426650538e-10 true resid norm
>>>>> 6.380426650287e-10 ||r(i)||/||b|| 2.257348088242e-08
>>>>> 23 KSP preconditioned resid norm 6.380426649918e-10 true resid norm
>>>>> 6.380426645888e-10 ||r(i)||/||b|| 2.257348086686e-08
>>>>> 24 KSP preconditioned resid norm 6.380426649803e-10 true resid norm
>>>>> 6.380426644294e-10 ||r(i)||/||b|| 2.257348086122e-08
>>>>> 25 KSP preconditioned resid norm 6.380426649796e-10 true resid norm
>>>>> 6.380426649774e-10 ||r(i)||/||b|| 2.257348088061e-08
>>>>> 26 KSP preconditioned resid norm 6.380426649795e-10 true resid norm
>>>>> 6.380426653788e-10 ||r(i)||/||b|| 2.257348089481e-08
>>>>> 27 KSP preconditioned resid norm 6.380426649795e-10 true resid norm
>>>>> 6.380426646744e-10 ||r(i)||/||b|| 2.257348086989e-08
>>>>> 28 KSP preconditioned resid norm 6.380426649795e-10 true resid norm
>>>>> 6.380426650818e-10 ||r(i)||/||b|| 2.257348088430e-08
>>>>> 29 KSP preconditioned resid norm 6.380426649795e-10 true resid norm
>>>>> 6.380426649518e-10 ||r(i)||/||b|| 2.257348087970e-08
>>>>> 30 KSP preconditioned resid norm 6.380426652142e-10 true resid norm
>>>>> 6.380426652142e-10 ||r(i)||/||b|| 2.257348088898e-08
>>>>> 31 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426646799e-10 ||r(i)||/||b|| 2.257348087008e-08
>>>>> 32 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426648077e-10 ||r(i)||/||b|| 2.257348087460e-08
>>>>> 33 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426649048e-10 ||r(i)||/||b|| 2.257348087804e-08
>>>>> 34 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426648142e-10 ||r(i)||/||b|| 2.257348087483e-08
>>>>> 35 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426651079e-10 ||r(i)||/||b|| 2.257348088522e-08
>>>>> 36 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650433e-10 ||r(i)||/||b|| 2.257348088294e-08
>>>>> 37 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426649765e-10 ||r(i)||/||b|| 2.257348088057e-08
>>>>> 38 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650364e-10 ||r(i)||/||b|| 2.257348088269e-08
>>>>> 39 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650051e-10 ||r(i)||/||b|| 2.257348088159e-08
>>>>> 40 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426651154e-10 ||r(i)||/||b|| 2.257348088549e-08
>>>>> 41 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650246e-10 ||r(i)||/||b|| 2.257348088227e-08
>>>>> 42 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650702e-10 ||r(i)||/||b|| 2.257348088389e-08
>>>>> 43 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426651686e-10 ||r(i)||/||b|| 2.257348088737e-08
>>>>> 44 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650870e-10 ||r(i)||/||b|| 2.257348088448e-08
>>>>> 45 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426651208e-10 ||r(i)||/||b|| 2.257348088568e-08
>>>>> 46 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426651441e-10 ||r(i)||/||b|| 2.257348088650e-08
>>>>> 47 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650955e-10 ||r(i)||/||b|| 2.257348088478e-08
>>>>> 48 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650877e-10 ||r(i)||/||b|| 2.257348088451e-08
>>>>> 49 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426651240e-10 ||r(i)||/||b|| 2.257348088579e-08
>>>>> 50 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426650534e-10 ||r(i)||/||b|| 2.257348088329e-08
>>>>> 51 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426648615e-10 ||r(i)||/||b|| 2.257348087651e-08
>>>>> 52 KSP preconditioned resid norm 6.380426652141e-10 true resid norm
>>>>> 6.380426649523e-10 ||r(i)||/||b|| 2.257348087972e-08
>>>>> 53 KSP preconditioned resid norm 6.380426652140e-10 true resid norm
>>>>> 6.380426652601e-10 ||r(i)||/||b|| 2.257348089061e-08
>>>>> 54 KSP preconditioned resid norm 6.380426652125e-10 true resid norm
>>>>> 6.380427512852e-10 ||r(i)||/||b|| 2.257348393411e-08
>>>>> 55 KSP preconditioned resid norm 6.380426651849e-10 true resid norm
>>>>> 6.380603444402e-10 ||r(i)||/||b|| 2.257410636701e-08
>>>>> 56 KSP preconditioned resid norm 6.380426646751e-10 true resid norm
>>>>> 6.439925413105e-10 ||r(i)||/||b|| 2.278398313542e-08
>>>>> 57 KSP preconditioned resid norm 6.380426514019e-10 true resid norm
>>>>> 2.674218007058e-09 ||r(i)||/||b|| 9.461186902765e-08
>>>>> 58 KSP preconditioned resid norm 6.380425077384e-10 true resid norm
>>>>> 2.406759314486e-08 ||r(i)||/||b|| 8.514937691775e-07
>>>>> 59 KSP preconditioned resid norm 6.380406171326e-10 true resid norm
>>>>> 3.100137288622e-07 ||r(i)||/||b|| 1.096805803957e-05
>>>>> Linear back_fieldsplit_1_ solve did not converge due to
>>>>> DIVERGED_BREAKDOWN iterations 60
>>>>>
>>>>> Any advice on steps I could take to elucidate the issue would be
>>>>> greatly appreciated. Thanks so much for any help in advance!
>>>>>
>>>>> Best,
>>>>> Colton Bryant
>>>>>
>>>>>
>>>>>
>>>>
>>>
>>
>
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