[petsc-users] fieldsplit preconditioner for indefinite matrix
Hoang Giang Bui
hgbk2008 at gmail.com
Thu Sep 15 09:07:30 CDT 2016
Hi Matt
Thanks for the comment. After looking carefully into the manual again, the
key take away is that with selfp there is no option to compute the exact
Schur, there are only two options to approximate the inv(A00) for selfp,
which are lump and diag (diag by default). I misunderstood this previously.
There is online manual entry mentioned about PC_FIELDSPLIT_SCHUR_PRE_FULL,
which is not documented elsewhere in the offline manual. I tried to access
that by setting
-pc_fieldsplit_schur_precondition full
but it gives the error
[0]PETSC ERROR: --------------------- Error Message
--------------------------------------------------------------
[0]PETSC ERROR: Arguments are incompatible
[0]PETSC ERROR: MatMatMult requires A, mpiaij, to be compatible with B,
seqaij
[0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for
trouble shooting.
[0]PETSC ERROR: Petsc Release Version 3.7.3, Jul, 24, 2016
[0]PETSC ERROR: python on a arch-linux2-c-opt named bermuda by hbui Thu Sep
15 15:46:56 2016
[0]PETSC ERROR: Configure options --with-shared-libraries
--with-debugging=0 --with-pic --download-fblaslapack=yes
--download-suitesparse --download-ptscotch=yes --download-metis=yes
--download-parmetis=yes --download-scalapack=yes --download-mumps=yes
--download-hypre=yes --download-ml=yes --download-pastix=yes
--with-mpi-dir=/opt/openmpi-1.10.1 --prefix=/home/hbui/opt/petsc-3.7.3
[0]PETSC ERROR: #1 MatMatMult() line 9514 in
/home/hbui/sw/petsc-3.7.3/src/mat/interface/matrix.c
[0]PETSC ERROR: #2 MatSchurComplementComputeExplicitOperator() line 526 in
/home/hbui/sw/petsc-3.7.3/src/ksp/ksp/utils/schurm.c
[0]PETSC ERROR: #3 PCSetUp_FieldSplit() line 792 in
/home/hbui/sw/petsc-3.7.3/src/ksp/pc/impls/fieldsplit/fieldsplit.c
[0]PETSC ERROR: #4 PCSetUp() line 968 in
/home/hbui/sw/petsc-3.7.3/src/ksp/pc/interface/precon.c
[0]PETSC ERROR: #5 KSPSetUp() line 390 in
/home/hbui/sw/petsc-3.7.3/src/ksp/ksp/interface/itfunc.c
[0]PETSC ERROR: #6 KSPSolve() line 599 in
/home/hbui/sw/petsc-3.7.3/src/ksp/ksp/interface/itfunc.c
Please excuse me to insist on forming the exact Schur complement, but as
you said, I would like to track down what creates problem in my code by
starting from a very exact but ineffective solution.
Giang
On Thu, Sep 15, 2016 at 2:56 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Thu, Sep 15, 2016 at 4:11 AM, Hoang Giang Bui <hgbk2008 at gmail.com>
> wrote:
>
>> Dear Barry
>>
>> Thanks for the clarification. I got exactly what you said if the code
>> changed to
>> ierr = KSPSetOperators(ksp_S,B,B);CHKERRQ(ierr);
>> Residual norms for stokes_ solve.
>> 0 KSP Residual norm 1.327791371202e-02
>> Residual norms for stokes_fieldsplit_p_ solve.
>> 0 KSP preconditioned resid norm 0.000000000000e+00 true resid norm
>> 0.000000000000e+00 ||r(i)||/||b|| -nan
>> 1 KSP Residual norm 3.997711925708e-17
>>
>> but I guess we solve a different problem if B is used for the linear
>> system.
>>
>> in addition, changed to
>> ierr = KSPSetOperators(ksp_S,A,A);CHKERRQ(ierr);
>> also works but inner iteration converged not in one iteration
>>
>> Residual norms for stokes_ solve.
>> 0 KSP Residual norm 1.327791371202e-02
>> Residual norms for stokes_fieldsplit_p_ solve.
>> 0 KSP preconditioned resid norm 5.308049264070e+02 true resid norm
>> 5.775755720828e-02 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 1.853645192358e+02 true resid norm
>> 1.537879609454e-02 ||r(i)||/||b|| 2.662646558801e-01
>> 2 KSP preconditioned resid norm 2.282724981527e+01 true resid norm
>> 4.440700864158e-03 ||r(i)||/||b|| 7.688519180519e-02
>> 3 KSP preconditioned resid norm 3.114190504933e+00 true resid norm
>> 8.474158485027e-04 ||r(i)||/||b|| 1.467194752449e-02
>> 4 KSP preconditioned resid norm 4.273258497986e-01 true resid norm
>> 1.249911370496e-04 ||r(i)||/||b|| 2.164065502267e-03
>> 5 KSP preconditioned resid norm 2.548558490130e-02 true resid norm
>> 8.428488734654e-06 ||r(i)||/||b|| 1.459287605301e-04
>> 6 KSP preconditioned resid norm 1.556370641259e-03 true resid norm
>> 2.866605637380e-07 ||r(i)||/||b|| 4.963169801386e-06
>> 7 KSP preconditioned resid norm 2.324584224817e-05 true resid norm
>> 6.975804113442e-09 ||r(i)||/||b|| 1.207773398083e-07
>> 8 KSP preconditioned resid norm 8.893330367907e-06 true resid norm
>> 1.082096232921e-09 ||r(i)||/||b|| 1.873514541169e-08
>> 9 KSP preconditioned resid norm 6.563740470820e-07 true resid norm
>> 2.212185528660e-10 ||r(i)||/||b|| 3.830123079274e-09
>> 10 KSP preconditioned resid norm 1.460372091709e-08 true resid norm
>> 3.859545051902e-12 ||r(i)||/||b|| 6.682320441607e-11
>> 11 KSP preconditioned resid norm 1.041947844812e-08 true resid norm
>> 2.364389912927e-12 ||r(i)||/||b|| 4.093645969827e-11
>> 12 KSP preconditioned resid norm 1.614713897816e-10 true resid norm
>> 1.057061924974e-14 ||r(i)||/||b|| 1.830170762178e-13
>> 1 KSP Residual norm 1.445282647127e-16
>>
>>
>> Seem like zero pivot does not happen, but why the solver for Schur takes
>> 13 steps if the preconditioner is direct solver?
>>
>
> Look at the -ksp_view. I will bet that the default is to shift (add a
> multiple of the identity) the matrix instead of failing. This
> gives an inexact PC, but as you see it can converge.
>
> Thanks,
>
> Matt
>
>
>>
>> I also so tried another problem which I known does have a nonsingular
>> Schur (at least A11 != 0) and it also have the same problem: 1 step outer
>> convergence but multiple step inner convergence.
>>
>> Any ideas?
>>
>> Giang
>>
>> On Fri, Sep 9, 2016 at 1:04 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>
>>>
>>> Normally you'd be absolutely correct to expect convergence in one
>>> iteration. However in this example note the call
>>>
>>> ierr = KSPSetOperators(ksp_S,A,B);CHKERRQ(ierr);
>>>
>>> It is solving the linear system defined by A but building the
>>> preconditioner (i.e. the entire fieldsplit process) from a different matrix
>>> B. Since A is not B you should not expect convergence in one iteration. If
>>> you change the code to
>>>
>>> ierr = KSPSetOperators(ksp_S,B,B);CHKERRQ(ierr);
>>>
>>> you will see exactly what you expect, convergence in one iteration.
>>>
>>> Sorry about this, the example is lacking clarity and documentation its
>>> author obviously knew too well what he was doing that he didn't realize
>>> everyone else in the world would need more comments in the code. If you
>>> change the code to
>>>
>>> ierr = KSPSetOperators(ksp_S,A,A);CHKERRQ(ierr);
>>>
>>> it will stop without being able to build the preconditioner because LU
>>> factorization of the Sp matrix will result in a zero pivot. This is why
>>> this "auxiliary" matrix B is used to define the preconditioner instead of A.
>>>
>>> Barry
>>>
>>>
>>>
>>>
>>> > On Sep 8, 2016, at 5:30 PM, Hoang Giang Bui <hgbk2008 at gmail.com>
>>> wrote:
>>> >
>>> > Sorry I slept quite a while in this thread. Now I start to look at it
>>> again. In the last try, the previous setting doesn't work either (in fact
>>> diverge). So I would speculate if the Schur complement in my case is
>>> actually not invertible. It's also possible that the code is wrong
>>> somewhere. However, before looking at that, I want to understand thoroughly
>>> the settings for Schur complement
>>> >
>>> > I experimented ex42 with the settings:
>>> > mpirun -np 1 ex42 \
>>> > -stokes_ksp_monitor \
>>> > -stokes_ksp_type fgmres \
>>> > -stokes_pc_type fieldsplit \
>>> > -stokes_pc_fieldsplit_type schur \
>>> > -stokes_pc_fieldsplit_schur_fact_type full \
>>> > -stokes_pc_fieldsplit_schur_precondition selfp \
>>> > -stokes_fieldsplit_u_ksp_type preonly \
>>> > -stokes_fieldsplit_u_pc_type lu \
>>> > -stokes_fieldsplit_u_pc_factor_mat_solver_package mumps \
>>> > -stokes_fieldsplit_p_ksp_type gmres \
>>> > -stokes_fieldsplit_p_ksp_monitor_true_residual \
>>> > -stokes_fieldsplit_p_ksp_max_it 300 \
>>> > -stokes_fieldsplit_p_ksp_rtol 1.0e-12 \
>>> > -stokes_fieldsplit_p_ksp_gmres_restart 300 \
>>> > -stokes_fieldsplit_p_ksp_gmres_modifiedgramschmidt \
>>> > -stokes_fieldsplit_p_pc_type lu \
>>> > -stokes_fieldsplit_p_pc_factor_mat_solver_package mumps
>>> >
>>> > In my understanding, the solver should converge in 1 (outer) step.
>>> Execution gives:
>>> > Residual norms for stokes_ solve.
>>> > 0 KSP Residual norm 1.327791371202e-02
>>> > Residual norms for stokes_fieldsplit_p_ solve.
>>> > 0 KSP preconditioned resid norm 0.000000000000e+00 true resid norm
>>> 0.000000000000e+00 ||r(i)||/||b|| -nan
>>> > 1 KSP Residual norm 7.656238881621e-04
>>> > Residual norms for stokes_fieldsplit_p_ solve.
>>> > 0 KSP preconditioned resid norm 1.512059266251e+03 true resid norm
>>> 1.000000000000e+00 ||r(i)||/||b|| 1.000000000000e+00
>>> > 1 KSP preconditioned resid norm 1.861905708091e-12 true resid norm
>>> 2.934589919911e-16 ||r(i)||/||b|| 2.934589919911e-16
>>> > 2 KSP Residual norm 9.895645456398e-06
>>> > Residual norms for stokes_fieldsplit_p_ solve.
>>> > 0 KSP preconditioned resid norm 3.002531529083e+03 true resid norm
>>> 1.000000000000e+00 ||r(i)||/||b|| 1.000000000000e+00
>>> > 1 KSP preconditioned resid norm 6.388584944363e-12 true resid norm
>>> 1.961047000344e-15 ||r(i)||/||b|| 1.961047000344e-15
>>> > 3 KSP Residual norm 1.608206702571e-06
>>> > Residual norms for stokes_fieldsplit_p_ solve.
>>> > 0 KSP preconditioned resid norm 3.004810086026e+03 true resid norm
>>> 1.000000000000e+00 ||r(i)||/||b|| 1.000000000000e+00
>>> > 1 KSP preconditioned resid norm 3.081350863773e-12 true resid norm
>>> 7.721720636293e-16 ||r(i)||/||b|| 7.721720636293e-16
>>> > 4 KSP Residual norm 2.453618999882e-07
>>> > Residual norms for stokes_fieldsplit_p_ solve.
>>> > 0 KSP preconditioned resid norm 3.000681887478e+03 true resid norm
>>> 1.000000000000e+00 ||r(i)||/||b|| 1.000000000000e+00
>>> > 1 KSP preconditioned resid norm 3.909717465288e-12 true resid norm
>>> 1.156131245879e-15 ||r(i)||/||b|| 1.156131245879e-15
>>> > 5 KSP Residual norm 4.230399264750e-08
>>> >
>>> > Looks like the "selfp" does construct the Schur nicely. But does
>>> "full" really construct the full block preconditioner?
>>> >
>>> > Giang
>>> > P/S: I'm also generating a smaller size of the previous problem for
>>> checking again.
>>> >
>>> >
>>> > On Sun, Apr 17, 2016 at 3:16 PM, Matthew Knepley <knepley at gmail.com>
>>> wrote:
>>> > On Sun, Apr 17, 2016 at 4:25 AM, Hoang Giang Bui <hgbk2008 at gmail.com>
>>> wrote:
>>> >
>>> > It could be taking time in the MatMatMult() here if that matrix is
>>> dense. Is there any reason to
>>> > believe that is a good preconditioner for your problem?
>>> >
>>> > This is the first approach to the problem, so I chose the most simple
>>> setting. Do you have any other recommendation?
>>> >
>>> > This is in no way the simplest PC. We need to make it simpler first.
>>> >
>>> > 1) Run on only 1 proc
>>> >
>>> > 2) Use -pc_fieldsplit_schur_fact_type full
>>> >
>>> > 3) Use -fieldsplit_lu_ksp_type gmres -fieldsplit_lu_ksp_monitor_tru
>>> e_residual
>>> >
>>> > This should converge in 1 outer iteration, but we will see how good
>>> your Schur complement preconditioner
>>> > is for this problem.
>>> >
>>> > You need to start out from something you understand and then start
>>> making approximations.
>>> >
>>> > Matt
>>> >
>>> > For any solver question, please send us the output of
>>> >
>>> > -ksp_view -ksp_monitor_true_residual -ksp_converged_reason
>>> >
>>> >
>>> > I sent here the full output (after changed to fgmres), again it takes
>>> long at the first iteration but after that, it does not converge
>>> >
>>> > -ksp_type fgmres
>>> > -ksp_max_it 300
>>> > -ksp_gmres_restart 300
>>> > -ksp_gmres_modifiedgramschmidt
>>> > -pc_fieldsplit_type schur
>>> > -pc_fieldsplit_schur_fact_type diag
>>> > -pc_fieldsplit_schur_precondition selfp
>>> > -pc_fieldsplit_detect_saddle_point
>>> > -fieldsplit_u_ksp_type preonly
>>> > -fieldsplit_u_pc_type lu
>>> > -fieldsplit_u_pc_factor_mat_solver_package mumps
>>> > -fieldsplit_lu_ksp_type preonly
>>> > -fieldsplit_lu_pc_type lu
>>> > -fieldsplit_lu_pc_factor_mat_solver_package mumps
>>> >
>>> > 0 KSP unpreconditioned resid norm 3.037772453815e+06 true resid norm
>>> 3.037772453815e+06 ||r(i)||/||b|| 1.000000000000e+00
>>> > 1 KSP unpreconditioned resid norm 3.024368791893e+06 true resid norm
>>> 3.024368791296e+06 ||r(i)||/||b|| 9.955876673705e-01
>>> > 2 KSP unpreconditioned resid norm 3.008534454663e+06 true resid norm
>>> 3.008534454904e+06 ||r(i)||/||b|| 9.903751846607e-01
>>> > 3 KSP unpreconditioned resid norm 4.633282412600e+02 true resid norm
>>> 4.607539866185e+02 ||r(i)||/||b|| 1.516749505184e-04
>>> > 4 KSP unpreconditioned resid norm 4.630592911836e+02 true resid norm
>>> 4.605625897903e+02 ||r(i)||/||b|| 1.516119448683e-04
>>> > 5 KSP unpreconditioned resid norm 2.145735509629e+02 true resid norm
>>> 2.111697416683e+02 ||r(i)||/||b|| 6.951466736857e-05
>>> > 6 KSP unpreconditioned resid norm 2.145734219762e+02 true resid norm
>>> 2.112001242378e+02 ||r(i)||/||b|| 6.952466896346e-05
>>> > 7 KSP unpreconditioned resid norm 1.892914067411e+02 true resid norm
>>> 1.831020928502e+02 ||r(i)||/||b|| 6.027511791420e-05
>>> > 8 KSP unpreconditioned resid norm 1.892906351597e+02 true resid norm
>>> 1.831422357767e+02 ||r(i)||/||b|| 6.028833250718e-05
>>> > 9 KSP unpreconditioned resid norm 1.891426729822e+02 true resid norm
>>> 1.835600473014e+02 ||r(i)||/||b|| 6.042587128964e-05
>>> > 10 KSP unpreconditioned resid norm 1.891425181679e+02 true resid norm
>>> 1.855772578041e+02 ||r(i)||/||b|| 6.108991395027e-05
>>> > 11 KSP unpreconditioned resid norm 1.891417382057e+02 true resid norm
>>> 1.833302669042e+02 ||r(i)||/||b|| 6.035023020699e-05
>>> > 12 KSP unpreconditioned resid norm 1.891414749001e+02 true resid norm
>>> 1.827923591605e+02 ||r(i)||/||b|| 6.017315712076e-05
>>> > 13 KSP unpreconditioned resid norm 1.891414702834e+02 true resid norm
>>> 1.849895606391e+02 ||r(i)||/||b|| 6.089645075515e-05
>>> > 14 KSP unpreconditioned resid norm 1.891414687385e+02 true resid norm
>>> 1.852700958573e+02 ||r(i)||/||b|| 6.098879974523e-05
>>> > 15 KSP unpreconditioned resid norm 1.891399614701e+02 true resid norm
>>> 1.817034334576e+02 ||r(i)||/||b|| 5.981469521503e-05
>>> > 16 KSP unpreconditioned resid norm 1.891393964580e+02 true resid norm
>>> 1.823173574739e+02 ||r(i)||/||b|| 6.001679199012e-05
>>> > 17 KSP unpreconditioned resid norm 1.890868604964e+02 true resid norm
>>> 1.834754811775e+02 ||r(i)||/||b|| 6.039803308740e-05
>>> > 18 KSP unpreconditioned resid norm 1.888442703508e+02 true resid norm
>>> 1.852079421560e+02 ||r(i)||/||b|| 6.096833945658e-05
>>> > 19 KSP unpreconditioned resid norm 1.888131521870e+02 true resid norm
>>> 1.810111295757e+02 ||r(i)||/||b|| 5.958679668335e-05
>>> > 20 KSP unpreconditioned resid norm 1.888038471618e+02 true resid norm
>>> 1.814080717355e+02 ||r(i)||/||b|| 5.971746550920e-05
>>> > 21 KSP unpreconditioned resid norm 1.885794485272e+02 true resid norm
>>> 1.843223565278e+02 ||r(i)||/||b|| 6.067681478129e-05
>>> > 22 KSP unpreconditioned resid norm 1.884898771362e+02 true resid norm
>>> 1.842766260526e+02 ||r(i)||/||b|| 6.066176083110e-05
>>> > 23 KSP unpreconditioned resid norm 1.884840498049e+02 true resid norm
>>> 1.813011285152e+02 ||r(i)||/||b|| 5.968226102238e-05
>>> > 24 KSP unpreconditioned resid norm 1.884105698955e+02 true resid norm
>>> 1.811513025118e+02 ||r(i)||/||b|| 5.963294001309e-05
>>> > 25 KSP unpreconditioned resid norm 1.881392557375e+02 true resid norm
>>> 1.835706567649e+02 ||r(i)||/||b|| 6.042936380386e-05
>>> > 26 KSP unpreconditioned resid norm 1.881234481250e+02 true resid norm
>>> 1.843633799886e+02 ||r(i)||/||b|| 6.069031923609e-05
>>> > 27 KSP unpreconditioned resid norm 1.852572648925e+02 true resid norm
>>> 1.791532195358e+02 ||r(i)||/||b|| 5.897519391579e-05
>>> > 28 KSP unpreconditioned resid norm 1.852177694782e+02 true resid norm
>>> 1.800935543889e+02 ||r(i)||/||b|| 5.928474141066e-05
>>> > 29 KSP unpreconditioned resid norm 1.844720976468e+02 true resid norm
>>> 1.806835899755e+02 ||r(i)||/||b|| 5.947897438749e-05
>>> > 30 KSP unpreconditioned resid norm 1.843525447108e+02 true resid norm
>>> 1.811351238391e+02 ||r(i)||/||b|| 5.962761417881e-05
>>> > 31 KSP unpreconditioned resid norm 1.834262885149e+02 true resid norm
>>> 1.778584233423e+02 ||r(i)||/||b|| 5.854896179565e-05
>>> > 32 KSP unpreconditioned resid norm 1.833523213017e+02 true resid norm
>>> 1.773290649733e+02 ||r(i)||/||b|| 5.837470306591e-05
>>> > 33 KSP unpreconditioned resid norm 1.821645929344e+02 true resid norm
>>> 1.781151248933e+02 ||r(i)||/||b|| 5.863346501467e-05
>>> > 34 KSP unpreconditioned resid norm 1.820831279534e+02 true resid norm
>>> 1.789778939067e+02 ||r(i)||/||b|| 5.891747872094e-05
>>> > 35 KSP unpreconditioned resid norm 1.814860919375e+02 true resid norm
>>> 1.757339506869e+02 ||r(i)||/||b|| 5.784960965928e-05
>>> > 36 KSP unpreconditioned resid norm 1.812512010159e+02 true resid norm
>>> 1.764086437459e+02 ||r(i)||/||b|| 5.807171090922e-05
>>> > 37 KSP unpreconditioned resid norm 1.804298150360e+02 true resid norm
>>> 1.780147196442e+02 ||r(i)||/||b|| 5.860041275333e-05
>>> > 38 KSP unpreconditioned resid norm 1.799675012847e+02 true resid norm
>>> 1.780554543786e+02 ||r(i)||/||b|| 5.861382216269e-05
>>> > 39 KSP unpreconditioned resid norm 1.793156052097e+02 true resid norm
>>> 1.747985717965e+02 ||r(i)||/||b|| 5.754169361071e-05
>>> > 40 KSP unpreconditioned resid norm 1.789109248325e+02 true resid norm
>>> 1.734086984879e+02 ||r(i)||/||b|| 5.708416319009e-05
>>> > 41 KSP unpreconditioned resid norm 1.788931581371e+02 true resid norm
>>> 1.766103879126e+02 ||r(i)||/||b|| 5.813812278494e-05
>>> > 42 KSP unpreconditioned resid norm 1.785522436483e+02 true resid norm
>>> 1.762597032909e+02 ||r(i)||/||b|| 5.802268141233e-05
>>> > 43 KSP unpreconditioned resid norm 1.783317950582e+02 true resid norm
>>> 1.752774080448e+02 ||r(i)||/||b|| 5.769932103530e-05
>>> > 44 KSP unpreconditioned resid norm 1.782832982797e+02 true resid norm
>>> 1.741667594885e+02 ||r(i)||/||b|| 5.733370821430e-05
>>> > 45 KSP unpreconditioned resid norm 1.781302427969e+02 true resid norm
>>> 1.760315735899e+02 ||r(i)||/||b|| 5.794758372005e-05
>>> > 46 KSP unpreconditioned resid norm 1.780557458973e+02 true resid norm
>>> 1.757279911034e+02 ||r(i)||/||b|| 5.784764783244e-05
>>> > 47 KSP unpreconditioned resid norm 1.774691940686e+02 true resid norm
>>> 1.729436852773e+02 ||r(i)||/||b|| 5.693108615167e-05
>>> > 48 KSP unpreconditioned resid norm 1.771436357084e+02 true resid norm
>>> 1.734001323688e+02 ||r(i)||/||b|| 5.708134332148e-05
>>> > 49 KSP unpreconditioned resid norm 1.756105727417e+02 true resid norm
>>> 1.740222172981e+02 ||r(i)||/||b|| 5.728612657594e-05
>>> > 50 KSP unpreconditioned resid norm 1.756011794480e+02 true resid norm
>>> 1.736979026533e+02 ||r(i)||/||b|| 5.717936589858e-05
>>> > 51 KSP unpreconditioned resid norm 1.751096154950e+02 true resid norm
>>> 1.713154407940e+02 ||r(i)||/||b|| 5.639508666256e-05
>>> > 52 KSP unpreconditioned resid norm 1.712639990486e+02 true resid norm
>>> 1.684444278579e+02 ||r(i)||/||b|| 5.544998199137e-05
>>> > 53 KSP unpreconditioned resid norm 1.710183053728e+02 true resid norm
>>> 1.692712952670e+02 ||r(i)||/||b|| 5.572217729951e-05
>>> > 54 KSP unpreconditioned resid norm 1.655470115849e+02 true resid norm
>>> 1.631767858448e+02 ||r(i)||/||b|| 5.371593439788e-05
>>> > 55 KSP unpreconditioned resid norm 1.648313805392e+02 true resid norm
>>> 1.617509396670e+02 ||r(i)||/||b|| 5.324656211951e-05
>>> > 56 KSP unpreconditioned resid norm 1.643417766012e+02 true resid norm
>>> 1.614766932468e+02 ||r(i)||/||b|| 5.315628332992e-05
>>> > 57 KSP unpreconditioned resid norm 1.643165564782e+02 true resid norm
>>> 1.611660297521e+02 ||r(i)||/||b|| 5.305401645527e-05
>>> > 58 KSP unpreconditioned resid norm 1.639561245303e+02 true resid norm
>>> 1.616105878219e+02 ||r(i)||/||b|| 5.320035989496e-05
>>> > 59 KSP unpreconditioned resid norm 1.636859175366e+02 true resid norm
>>> 1.601704798933e+02 ||r(i)||/||b|| 5.272629281109e-05
>>> > 60 KSP unpreconditioned resid norm 1.633269681891e+02 true resid norm
>>> 1.603249334191e+02 ||r(i)||/||b|| 5.277713714789e-05
>>> > 61 KSP unpreconditioned resid norm 1.633257086864e+02 true resid norm
>>> 1.602922744638e+02 ||r(i)||/||b|| 5.276638619280e-05
>>> > 62 KSP unpreconditioned resid norm 1.629449737049e+02 true resid norm
>>> 1.605812790996e+02 ||r(i)||/||b|| 5.286152321842e-05
>>> > 63 KSP unpreconditioned resid norm 1.629422151091e+02 true resid norm
>>> 1.589656479615e+02 ||r(i)||/||b|| 5.232967589850e-05
>>> > 64 KSP unpreconditioned resid norm 1.624767340901e+02 true resid norm
>>> 1.601925152173e+02 ||r(i)||/||b|| 5.273354658809e-05
>>> > 65 KSP unpreconditioned resid norm 1.614000473427e+02 true resid norm
>>> 1.600055285874e+02 ||r(i)||/||b|| 5.267199272497e-05
>>> > 66 KSP unpreconditioned resid norm 1.599192711038e+02 true resid norm
>>> 1.602225820054e+02 ||r(i)||/||b|| 5.274344423136e-05
>>> > 67 KSP unpreconditioned resid norm 1.562002802473e+02 true resid norm
>>> 1.582069452329e+02 ||r(i)||/||b|| 5.207991962471e-05
>>> > 68 KSP unpreconditioned resid norm 1.552436010567e+02 true resid norm
>>> 1.584249134588e+02 ||r(i)||/||b|| 5.215167227548e-05
>>> > 69 KSP unpreconditioned resid norm 1.507627069906e+02 true resid norm
>>> 1.530713322210e+02 ||r(i)||/||b|| 5.038933447066e-05
>>> > 70 KSP unpreconditioned resid norm 1.503802419288e+02 true resid norm
>>> 1.526772130725e+02 ||r(i)||/||b|| 5.025959494786e-05
>>> > 71 KSP unpreconditioned resid norm 1.483645684459e+02 true resid norm
>>> 1.509599328686e+02 ||r(i)||/||b|| 4.969428591633e-05
>>> > 72 KSP unpreconditioned resid norm 1.481979533059e+02 true resid norm
>>> 1.535340885300e+02 ||r(i)||/||b|| 5.054166856281e-05
>>> > 73 KSP unpreconditioned resid norm 1.481400704979e+02 true resid norm
>>> 1.509082933863e+02 ||r(i)||/||b|| 4.967728678847e-05
>>> > 74 KSP unpreconditioned resid norm 1.481132272449e+02 true resid norm
>>> 1.513298398754e+02 ||r(i)||/||b|| 4.981605507858e-05
>>> > 75 KSP unpreconditioned resid norm 1.481101708026e+02 true resid norm
>>> 1.502466334943e+02 ||r(i)||/||b|| 4.945947590828e-05
>>> > 76 KSP unpreconditioned resid norm 1.481010335860e+02 true resid norm
>>> 1.533384206564e+02 ||r(i)||/||b|| 5.047725693339e-05
>>> > 77 KSP unpreconditioned resid norm 1.480865328511e+02 true resid norm
>>> 1.508354096349e+02 ||r(i)||/||b|| 4.965329428986e-05
>>> > 78 KSP unpreconditioned resid norm 1.480582653674e+02 true resid norm
>>> 1.493335938981e+02 ||r(i)||/||b|| 4.915891370027e-05
>>> > 79 KSP unpreconditioned resid norm 1.480031554288e+02 true resid norm
>>> 1.505131104808e+02 ||r(i)||/||b|| 4.954719708903e-05
>>> > 80 KSP unpreconditioned resid norm 1.479574822714e+02 true resid norm
>>> 1.540226621640e+02 ||r(i)||/||b|| 5.070250142355e-05
>>> > 81 KSP unpreconditioned resid norm 1.479574535946e+02 true resid norm
>>> 1.498368142318e+02 ||r(i)||/||b|| 4.932456808727e-05
>>> > 82 KSP unpreconditioned resid norm 1.479436001532e+02 true resid norm
>>> 1.512355315895e+02 ||r(i)||/||b|| 4.978500986785e-05
>>> > 83 KSP unpreconditioned resid norm 1.479410419985e+02 true resid norm
>>> 1.513924042216e+02 ||r(i)||/||b|| 4.983665054686e-05
>>> > 84 KSP unpreconditioned resid norm 1.477087197314e+02 true resid norm
>>> 1.519847216835e+02 ||r(i)||/||b|| 5.003163469095e-05
>>> > 85 KSP unpreconditioned resid norm 1.477081559094e+02 true resid norm
>>> 1.507153721984e+02 ||r(i)||/||b|| 4.961377933660e-05
>>> > 86 KSP unpreconditioned resid norm 1.476420890986e+02 true resid norm
>>> 1.512147907360e+02 ||r(i)||/||b|| 4.977818221576e-05
>>> > 87 KSP unpreconditioned resid norm 1.476086929880e+02 true resid norm
>>> 1.508513380647e+02 ||r(i)||/||b|| 4.965853774704e-05
>>> > 88 KSP unpreconditioned resid norm 1.475729830724e+02 true resid norm
>>> 1.521640656963e+02 ||r(i)||/||b|| 5.009067269183e-05
>>> > 89 KSP unpreconditioned resid norm 1.472338605465e+02 true resid norm
>>> 1.506094588356e+02 ||r(i)||/||b|| 4.957891386713e-05
>>> > 90 KSP unpreconditioned resid norm 1.472079944867e+02 true resid norm
>>> 1.504582871439e+02 ||r(i)||/||b|| 4.952914987262e-05
>>> > 91 KSP unpreconditioned resid norm 1.469363056078e+02 true resid norm
>>> 1.506425446156e+02 ||r(i)||/||b|| 4.958980532804e-05
>>> > 92 KSP unpreconditioned resid norm 1.469110799022e+02 true resid norm
>>> 1.509842019134e+02 ||r(i)||/||b|| 4.970227500870e-05
>>> > 93 KSP unpreconditioned resid norm 1.468779696240e+02 true resid norm
>>> 1.501105195969e+02 ||r(i)||/||b|| 4.941466876770e-05
>>> > 94 KSP unpreconditioned resid norm 1.468777757710e+02 true resid norm
>>> 1.491460779150e+02 ||r(i)||/||b|| 4.909718558007e-05
>>> > 95 KSP unpreconditioned resid norm 1.468774588833e+02 true resid norm
>>> 1.519041612996e+02 ||r(i)||/||b|| 5.000511513258e-05
>>> > 96 KSP unpreconditioned resid norm 1.468771672305e+02 true resid norm
>>> 1.508986277767e+02 ||r(i)||/||b|| 4.967410498018e-05
>>> > 97 KSP unpreconditioned resid norm 1.468771086724e+02 true resid norm
>>> 1.500987040931e+02 ||r(i)||/||b|| 4.941077923878e-05
>>> > 98 KSP unpreconditioned resid norm 1.468769529855e+02 true resid norm
>>> 1.509749203169e+02 ||r(i)||/||b|| 4.969921961314e-05
>>> > 99 KSP unpreconditioned resid norm 1.468539019917e+02 true resid norm
>>> 1.505087391266e+02 ||r(i)||/||b|| 4.954575808916e-05
>>> > 100 KSP unpreconditioned resid norm 1.468527260351e+02 true resid norm
>>> 1.519470484364e+02 ||r(i)||/||b|| 5.001923308823e-05
>>> > 101 KSP unpreconditioned resid norm 1.468342327062e+02 true resid norm
>>> 1.489814197970e+02 ||r(i)||/||b|| 4.904298200804e-05
>>> > 102 KSP unpreconditioned resid norm 1.468333201903e+02 true resid norm
>>> 1.491479405434e+02 ||r(i)||/||b|| 4.909779873608e-05
>>> > 103 KSP unpreconditioned resid norm 1.468287736823e+02 true resid norm
>>> 1.496401088908e+02 ||r(i)||/||b|| 4.925981493540e-05
>>> > 104 KSP unpreconditioned resid norm 1.468269778777e+02 true resid norm
>>> 1.509676608058e+02 ||r(i)||/||b|| 4.969682986500e-05
>>> > 105 KSP unpreconditioned resid norm 1.468214752527e+02 true resid norm
>>> 1.500441644659e+02 ||r(i)||/||b|| 4.939282541636e-05
>>> > 106 KSP unpreconditioned resid norm 1.468208033546e+02 true resid norm
>>> 1.510964155942e+02 ||r(i)||/||b|| 4.973921447094e-05
>>> > 107 KSP unpreconditioned resid norm 1.467590018852e+02 true resid norm
>>> 1.512302088409e+02 ||r(i)||/||b|| 4.978325767980e-05
>>> > 108 KSP unpreconditioned resid norm 1.467588908565e+02 true resid norm
>>> 1.501053278370e+02 ||r(i)||/||b|| 4.941295969963e-05
>>> > 109 KSP unpreconditioned resid norm 1.467570731153e+02 true resid norm
>>> 1.485494378220e+02 ||r(i)||/||b|| 4.890077847519e-05
>>> > 110 KSP unpreconditioned resid norm 1.467399860352e+02 true resid norm
>>> 1.504418099302e+02 ||r(i)||/||b|| 4.952372576205e-05
>>> > 111 KSP unpreconditioned resid norm 1.467095654863e+02 true resid norm
>>> 1.507288583410e+02 ||r(i)||/||b|| 4.961821882075e-05
>>> > 112 KSP unpreconditioned resid norm 1.467065865602e+02 true resid norm
>>> 1.517786399520e+02 ||r(i)||/||b|| 4.996379493842e-05
>>> > 113 KSP unpreconditioned resid norm 1.466898232510e+02 true resid norm
>>> 1.491434236258e+02 ||r(i)||/||b|| 4.909631181838e-05
>>> > 114 KSP unpreconditioned resid norm 1.466897921426e+02 true resid norm
>>> 1.505605420512e+02 ||r(i)||/||b|| 4.956281102033e-05
>>> > 115 KSP unpreconditioned resid norm 1.466593121787e+02 true resid norm
>>> 1.500608650677e+02 ||r(i)||/||b|| 4.939832306376e-05
>>> > 116 KSP unpreconditioned resid norm 1.466590894710e+02 true resid norm
>>> 1.503102560128e+02 ||r(i)||/||b|| 4.948041971478e-05
>>> > 117 KSP unpreconditioned resid norm 1.465338856917e+02 true resid norm
>>> 1.501331730933e+02 ||r(i)||/||b|| 4.942212604002e-05
>>> > 118 KSP unpreconditioned resid norm 1.464192893188e+02 true resid norm
>>> 1.505131429801e+02 ||r(i)||/||b|| 4.954720778744e-05
>>> > 119 KSP unpreconditioned resid norm 1.463859793112e+02 true resid norm
>>> 1.504355712014e+02 ||r(i)||/||b|| 4.952167204377e-05
>>> > 120 KSP unpreconditioned resid norm 1.459254939182e+02 true resid norm
>>> 1.526513923221e+02 ||r(i)||/||b|| 5.025109505170e-05
>>> > 121 KSP unpreconditioned resid norm 1.456973020864e+02 true resid norm
>>> 1.496897691500e+02 ||r(i)||/||b|| 4.927616252562e-05
>>> > 122 KSP unpreconditioned resid norm 1.456904663212e+02 true resid norm
>>> 1.488752755634e+02 ||r(i)||/||b|| 4.900804053853e-05
>>> > 123 KSP unpreconditioned resid norm 1.449254956591e+02 true resid norm
>>> 1.494048196254e+02 ||r(i)||/||b|| 4.918236039628e-05
>>> > 124 KSP unpreconditioned resid norm 1.448408616171e+02 true resid norm
>>> 1.507801939332e+02 ||r(i)||/||b|| 4.963511791142e-05
>>> > 125 KSP unpreconditioned resid norm 1.447662934870e+02 true resid norm
>>> 1.495157701445e+02 ||r(i)||/||b|| 4.921888404010e-05
>>> > 126 KSP unpreconditioned resid norm 1.446934748257e+02 true resid norm
>>> 1.511098625097e+02 ||r(i)||/||b|| 4.974364104196e-05
>>> > 127 KSP unpreconditioned resid norm 1.446892504333e+02 true resid norm
>>> 1.493367018275e+02 ||r(i)||/||b|| 4.915993679512e-05
>>> > 128 KSP unpreconditioned resid norm 1.446838883996e+02 true resid norm
>>> 1.510097796622e+02 ||r(i)||/||b|| 4.971069491153e-05
>>> > 129 KSP unpreconditioned resid norm 1.446696373784e+02 true resid norm
>>> 1.463776964101e+02 ||r(i)||/||b|| 4.818586600396e-05
>>> > 130 KSP unpreconditioned resid norm 1.446690766798e+02 true resid norm
>>> 1.495018999638e+02 ||r(i)||/||b|| 4.921431813499e-05
>>> > 131 KSP unpreconditioned resid norm 1.446480744133e+02 true resid norm
>>> 1.499605592408e+02 ||r(i)||/||b|| 4.936530353102e-05
>>> > 132 KSP unpreconditioned resid norm 1.446220543422e+02 true resid norm
>>> 1.498225445439e+02 ||r(i)||/||b|| 4.931987066895e-05
>>> > 133 KSP unpreconditioned resid norm 1.446156526760e+02 true resid norm
>>> 1.481441673781e+02 ||r(i)||/||b|| 4.876736807329e-05
>>> > 134 KSP unpreconditioned resid norm 1.446152477418e+02 true resid norm
>>> 1.501616466283e+02 ||r(i)||/||b|| 4.943149920257e-05
>>> > 135 KSP unpreconditioned resid norm 1.445744489044e+02 true resid norm
>>> 1.505958339620e+02 ||r(i)||/||b|| 4.957442871432e-05
>>> > 136 KSP unpreconditioned resid norm 1.445307936181e+02 true resid norm
>>> 1.502091787932e+02 ||r(i)||/||b|| 4.944714624841e-05
>>> > 137 KSP unpreconditioned resid norm 1.444543817248e+02 true resid norm
>>> 1.491871661616e+02 ||r(i)||/||b|| 4.911071136162e-05
>>> > 138 KSP unpreconditioned resid norm 1.444176915911e+02 true resid norm
>>> 1.478091693367e+02 ||r(i)||/||b|| 4.865709054379e-05
>>> > 139 KSP unpreconditioned resid norm 1.444173719058e+02 true resid norm
>>> 1.495962731374e+02 ||r(i)||/||b|| 4.924538470600e-05
>>> > 140 KSP unpreconditioned resid norm 1.444075340820e+02 true resid norm
>>> 1.515103203654e+02 ||r(i)||/||b|| 4.987546719477e-05
>>> > 141 KSP unpreconditioned resid norm 1.444050342939e+02 true resid norm
>>> 1.498145746307e+02 ||r(i)||/||b|| 4.931724706454e-05
>>> > 142 KSP unpreconditioned resid norm 1.443757787691e+02 true resid norm
>>> 1.492291154146e+02 ||r(i)||/||b|| 4.912452057664e-05
>>> > 143 KSP unpreconditioned resid norm 1.440588930707e+02 true resid norm
>>> 1.485032724987e+02 ||r(i)||/||b|| 4.888558137795e-05
>>> > 144 KSP unpreconditioned resid norm 1.438299468441e+02 true resid norm
>>> 1.506129385276e+02 ||r(i)||/||b|| 4.958005934200e-05
>>> > 145 KSP unpreconditioned resid norm 1.434543079403e+02 true resid norm
>>> 1.471733741230e+02 ||r(i)||/||b|| 4.844779402032e-05
>>> > 146 KSP unpreconditioned resid norm 1.433157223870e+02 true resid norm
>>> 1.481025707968e+02 ||r(i)||/||b|| 4.875367495378e-05
>>> > 147 KSP unpreconditioned resid norm 1.430111913458e+02 true resid norm
>>> 1.485000481919e+02 ||r(i)||/||b|| 4.888451997299e-05
>>> > 148 KSP unpreconditioned resid norm 1.430056153071e+02 true resid norm
>>> 1.496425172884e+02 ||r(i)||/||b|| 4.926060775239e-05
>>> > 149 KSP unpreconditioned resid norm 1.429327762233e+02 true resid norm
>>> 1.467613264791e+02 ||r(i)||/||b|| 4.831215264157e-05
>>> > 150 KSP unpreconditioned resid norm 1.424230217603e+02 true resid norm
>>> 1.460277537447e+02 ||r(i)||/||b|| 4.807066887493e-05
>>> > 151 KSP unpreconditioned resid norm 1.421912821676e+02 true resid norm
>>> 1.470486188164e+02 ||r(i)||/||b|| 4.840672599809e-05
>>> > 152 KSP unpreconditioned resid norm 1.420344275315e+02 true resid norm
>>> 1.481536901943e+02 ||r(i)||/||b|| 4.877050287565e-05
>>> > 153 KSP unpreconditioned resid norm 1.420071178597e+02 true resid norm
>>> 1.450813684108e+02 ||r(i)||/||b|| 4.775912963085e-05
>>> > 154 KSP unpreconditioned resid norm 1.419367456470e+02 true resid norm
>>> 1.472052819440e+02 ||r(i)||/||b|| 4.845829771059e-05
>>> > 155 KSP unpreconditioned resid norm 1.419032748919e+02 true resid norm
>>> 1.479193155584e+02 ||r(i)||/||b|| 4.869334942209e-05
>>> > 156 KSP unpreconditioned resid norm 1.418899781440e+02 true resid norm
>>> 1.478677351572e+02 ||r(i)||/||b|| 4.867636974307e-05
>>> > 157 KSP unpreconditioned resid norm 1.418895621075e+02 true resid norm
>>> 1.455168237674e+02 ||r(i)||/||b|| 4.790247656128e-05
>>> > 158 KSP unpreconditioned resid norm 1.418061469023e+02 true resid norm
>>> 1.467147028974e+02 ||r(i)||/||b|| 4.829680469093e-05
>>> > 159 KSP unpreconditioned resid norm 1.417948698213e+02 true resid norm
>>> 1.478376854834e+02 ||r(i)||/||b|| 4.866647773362e-05
>>> > 160 KSP unpreconditioned resid norm 1.415166832324e+02 true resid norm
>>> 1.475436433192e+02 ||r(i)||/||b|| 4.856968241116e-05
>>> > 161 KSP unpreconditioned resid norm 1.414939087573e+02 true resid norm
>>> 1.468361945080e+02 ||r(i)||/||b|| 4.833679834170e-05
>>> > 162 KSP unpreconditioned resid norm 1.414544622036e+02 true resid norm
>>> 1.475730757600e+02 ||r(i)||/||b|| 4.857937123456e-05
>>> > 163 KSP unpreconditioned resid norm 1.413780373982e+02 true resid norm
>>> 1.463891808066e+02 ||r(i)||/||b|| 4.818964653614e-05
>>> > 164 KSP unpreconditioned resid norm 1.413741853943e+02 true resid norm
>>> 1.481999741168e+02 ||r(i)||/||b|| 4.878573901436e-05
>>> > 165 KSP unpreconditioned resid norm 1.413725682642e+02 true resid norm
>>> 1.458413423932e+02 ||r(i)||/||b|| 4.800930438685e-05
>>> > 166 KSP unpreconditioned resid norm 1.412970845566e+02 true resid norm
>>> 1.481492296610e+02 ||r(i)||/||b|| 4.876903451901e-05
>>> > 167 KSP unpreconditioned resid norm 1.410100899597e+02 true resid norm
>>> 1.468338434340e+02 ||r(i)||/||b|| 4.833602439497e-05
>>> > 168 KSP unpreconditioned resid norm 1.409983320599e+02 true resid norm
>>> 1.485378957202e+02 ||r(i)||/||b|| 4.889697894709e-05
>>> > 169 KSP unpreconditioned resid norm 1.407688141293e+02 true resid norm
>>> 1.461003623074e+02 ||r(i)||/||b|| 4.809457078458e-05
>>> > 170 KSP unpreconditioned resid norm 1.407072771004e+02 true resid norm
>>> 1.463217409181e+02 ||r(i)||/||b|| 4.816744609502e-05
>>> > 171 KSP unpreconditioned resid norm 1.407069670790e+02 true resid norm
>>> 1.464695099700e+02 ||r(i)||/||b|| 4.821608997937e-05
>>> > 172 KSP unpreconditioned resid norm 1.402361094414e+02 true resid norm
>>> 1.493786053835e+02 ||r(i)||/||b|| 4.917373096721e-05
>>> > 173 KSP unpreconditioned resid norm 1.400618325859e+02 true resid norm
>>> 1.465475533254e+02 ||r(i)||/||b|| 4.824178096070e-05
>>> > 174 KSP unpreconditioned resid norm 1.400573078320e+02 true resid norm
>>> 1.471993735980e+02 ||r(i)||/||b|| 4.845635275056e-05
>>> > 175 KSP unpreconditioned resid norm 1.400258865388e+02 true resid norm
>>> 1.479779387468e+02 ||r(i)||/||b|| 4.871264750624e-05
>>> > 176 KSP unpreconditioned resid norm 1.396589283831e+02 true resid norm
>>> 1.476626943974e+02 ||r(i)||/||b|| 4.860887266654e-05
>>> > 177 KSP unpreconditioned resid norm 1.395796112440e+02 true resid norm
>>> 1.443093901655e+02 ||r(i)||/||b|| 4.750500320860e-05
>>> > 178 KSP unpreconditioned resid norm 1.394749154493e+02 true resid norm
>>> 1.447914005206e+02 ||r(i)||/||b|| 4.766367551289e-05
>>> > 179 KSP unpreconditioned resid norm 1.394476969416e+02 true resid norm
>>> 1.455635964329e+02 ||r(i)||/||b|| 4.791787358864e-05
>>> > 180 KSP unpreconditioned resid norm 1.391990722790e+02 true resid norm
>>> 1.457511594620e+02 ||r(i)||/||b|| 4.797961719582e-05
>>> > 181 KSP unpreconditioned resid norm 1.391686315799e+02 true resid norm
>>> 1.460567495143e+02 ||r(i)||/||b|| 4.808021395114e-05
>>> > 182 KSP unpreconditioned resid norm 1.387654475794e+02 true resid norm
>>> 1.468215388414e+02 ||r(i)||/||b|| 4.833197386362e-05
>>> > 183 KSP unpreconditioned resid norm 1.384925240232e+02 true resid norm
>>> 1.456091052791e+02 ||r(i)||/||b|| 4.793285458106e-05
>>> > 184 KSP unpreconditioned resid norm 1.378003249970e+02 true resid norm
>>> 1.453421051371e+02 ||r(i)||/||b|| 4.784496118351e-05
>>> > 185 KSP unpreconditioned resid norm 1.377904214978e+02 true resid norm
>>> 1.441752187090e+02 ||r(i)||/||b|| 4.746083549740e-05
>>> > 186 KSP unpreconditioned resid norm 1.376670282479e+02 true resid norm
>>> 1.441674745344e+02 ||r(i)||/||b|| 4.745828620353e-05
>>> > 187 KSP unpreconditioned resid norm 1.376636051755e+02 true resid norm
>>> 1.463118783906e+02 ||r(i)||/||b|| 4.816419946362e-05
>>> > 188 KSP unpreconditioned resid norm 1.363148994276e+02 true resid norm
>>> 1.432997756128e+02 ||r(i)||/||b|| 4.717264962781e-05
>>> > 189 KSP unpreconditioned resid norm 1.363051099558e+02 true resid norm
>>> 1.451009062639e+02 ||r(i)||/||b|| 4.776556126897e-05
>>> > 190 KSP unpreconditioned resid norm 1.362538398564e+02 true resid norm
>>> 1.438957985476e+02 ||r(i)||/||b|| 4.736885357127e-05
>>> > 191 KSP unpreconditioned resid norm 1.358335705250e+02 true resid norm
>>> 1.436616069458e+02 ||r(i)||/||b|| 4.729176037047e-05
>>> > 192 KSP unpreconditioned resid norm 1.337424103882e+02 true resid norm
>>> 1.432816138672e+02 ||r(i)||/||b|| 4.716667098856e-05
>>> > 193 KSP unpreconditioned resid norm 1.337419543121e+02 true resid norm
>>> 1.405274691954e+02 ||r(i)||/||b|| 4.626003801533e-05
>>> > 194 KSP unpreconditioned resid norm 1.322568117657e+02 true resid norm
>>> 1.417123189671e+02 ||r(i)||/||b|| 4.665007702902e-05
>>> > 195 KSP unpreconditioned resid norm 1.320880115122e+02 true resid norm
>>> 1.413658215058e+02 ||r(i)||/||b|| 4.653601402181e-05
>>> > 196 KSP unpreconditioned resid norm 1.312526182172e+02 true resid norm
>>> 1.420574070412e+02 ||r(i)||/||b|| 4.676367608204e-05
>>> > 197 KSP unpreconditioned resid norm 1.311651332692e+02 true resid norm
>>> 1.398984125128e+02 ||r(i)||/||b|| 4.605295973934e-05
>>> > 198 KSP unpreconditioned resid norm 1.294482397720e+02 true resid norm
>>> 1.380390703259e+02 ||r(i)||/||b|| 4.544088552537e-05
>>> > 199 KSP unpreconditioned resid norm 1.293598434732e+02 true resid norm
>>> 1.373830689903e+02 ||r(i)||/||b|| 4.522493737731e-05
>>> > 200 KSP unpreconditioned resid norm 1.265165992897e+02 true resid norm
>>> 1.375015523244e+02 ||r(i)||/||b|| 4.526394073779e-05
>>> > 201 KSP unpreconditioned resid norm 1.263813235463e+02 true resid norm
>>> 1.356820166419e+02 ||r(i)||/||b|| 4.466497037047e-05
>>> > 202 KSP unpreconditioned resid norm 1.243190164198e+02 true resid norm
>>> 1.366420975402e+02 ||r(i)||/||b|| 4.498101803792e-05
>>> > 203 KSP unpreconditioned resid norm 1.230747513665e+02 true resid norm
>>> 1.348856851681e+02 ||r(i)||/||b|| 4.440282714351e-05
>>> > 204 KSP unpreconditioned resid norm 1.198014010398e+02 true resid norm
>>> 1.325188356617e+02 ||r(i)||/||b|| 4.362368731578e-05
>>> > 205 KSP unpreconditioned resid norm 1.195977240348e+02 true resid norm
>>> 1.299721846860e+02 ||r(i)||/||b|| 4.278535889769e-05
>>> > 206 KSP unpreconditioned resid norm 1.130620928393e+02 true resid norm
>>> 1.266961052950e+02 ||r(i)||/||b|| 4.170691097546e-05
>>> > 207 KSP unpreconditioned resid norm 1.123992882530e+02 true resid norm
>>> 1.270907813369e+02 ||r(i)||/||b|| 4.183683382120e-05
>>> > 208 KSP unpreconditioned resid norm 1.063236317163e+02 true resid norm
>>> 1.182163029843e+02 ||r(i)||/||b|| 3.891545689533e-05
>>> > 209 KSP unpreconditioned resid norm 1.059802897214e+02 true resid norm
>>> 1.187516613498e+02 ||r(i)||/||b|| 3.909169075539e-05
>>> > 210 KSP unpreconditioned resid norm 9.878733567790e+01 true resid norm
>>> 1.124812677115e+02 ||r(i)||/||b|| 3.702754877846e-05
>>> > 211 KSP unpreconditioned resid norm 9.861048081032e+01 true resid norm
>>> 1.117192174341e+02 ||r(i)||/||b|| 3.677669052986e-05
>>> > 212 KSP unpreconditioned resid norm 9.169383217455e+01 true resid norm
>>> 1.102172324977e+02 ||r(i)||/||b|| 3.628225424167e-05
>>> > 213 KSP unpreconditioned resid norm 9.146164223196e+01 true resid norm
>>> 1.121134424773e+02 ||r(i)||/||b|| 3.690646491198e-05
>>> > 214 KSP unpreconditioned resid norm 8.692213412954e+01 true resid norm
>>> 1.056264039532e+02 ||r(i)||/||b|| 3.477100591276e-05
>>> > 215 KSP unpreconditioned resid norm 8.685846611574e+01 true resid norm
>>> 1.029018845366e+02 ||r(i)||/||b|| 3.387412523521e-05
>>> > 216 KSP unpreconditioned resid norm 7.808516472373e+01 true resid norm
>>> 9.749023000535e+01 ||r(i)||/||b|| 3.209267036539e-05
>>> > 217 KSP unpreconditioned resid norm 7.786400257086e+01 true resid norm
>>> 1.004515546585e+02 ||r(i)||/||b|| 3.306750462244e-05
>>> > 218 KSP unpreconditioned resid norm 6.646475864029e+01 true resid norm
>>> 9.429020541969e+01 ||r(i)||/||b|| 3.103925881653e-05
>>> > 219 KSP unpreconditioned resid norm 6.643821996375e+01 true resid norm
>>> 8.864525788550e+01 ||r(i)||/||b|| 2.918100655438e-05
>>> > 220 KSP unpreconditioned resid norm 5.625046780791e+01 true resid norm
>>> 8.410041684883e+01 ||r(i)||/||b|| 2.768489678784e-05
>>> > 221 KSP unpreconditioned resid norm 5.623343238032e+01 true resid norm
>>> 8.815552919640e+01 ||r(i)||/||b|| 2.901979346270e-05
>>> > 222 KSP unpreconditioned resid norm 4.491016868776e+01 true resid norm
>>> 8.557052117768e+01 ||r(i)||/||b|| 2.816883834410e-05
>>> > 223 KSP unpreconditioned resid norm 4.461976108543e+01 true resid norm
>>> 7.867894425332e+01 ||r(i)||/||b|| 2.590020992340e-05
>>> > 224 KSP unpreconditioned resid norm 3.535718264955e+01 true resid norm
>>> 7.609346753983e+01 ||r(i)||/||b|| 2.504910051583e-05
>>> > 225 KSP unpreconditioned resid norm 3.525592897743e+01 true resid norm
>>> 7.926812413349e+01 ||r(i)||/||b|| 2.609416121143e-05
>>> > 226 KSP unpreconditioned resid norm 2.633469451114e+01 true resid norm
>>> 7.883483297310e+01 ||r(i)||/||b|| 2.595152670968e-05
>>> > 227 KSP unpreconditioned resid norm 2.614440577316e+01 true resid norm
>>> 7.398963634249e+01 ||r(i)||/||b|| 2.435654331172e-05
>>> > 228 KSP unpreconditioned resid norm 1.988460252721e+01 true resid norm
>>> 7.147825835126e+01 ||r(i)||/||b|| 2.352982635730e-05
>>> > 229 KSP unpreconditioned resid norm 1.975927240058e+01 true resid norm
>>> 7.488507147714e+01 ||r(i)||/||b|| 2.465131033205e-05
>>> > 230 KSP unpreconditioned resid norm 1.505732242656e+01 true resid norm
>>> 7.888901529160e+01 ||r(i)||/||b|| 2.596936291016e-05
>>> > 231 KSP unpreconditioned resid norm 1.504120870628e+01 true resid norm
>>> 7.126366562975e+01 ||r(i)||/||b|| 2.345918488406e-05
>>> > 232 KSP unpreconditioned resid norm 1.163470506257e+01 true resid norm
>>> 7.142763663542e+01 ||r(i)||/||b|| 2.351316226655e-05
>>> > 233 KSP unpreconditioned resid norm 1.157114340949e+01 true resid norm
>>> 7.464790352976e+01 ||r(i)||/||b|| 2.457323735226e-05
>>> > 234 KSP unpreconditioned resid norm 8.702850618357e+00 true resid norm
>>> 7.798031063059e+01 ||r(i)||/||b|| 2.567022771329e-05
>>> > 235 KSP unpreconditioned resid norm 8.702017371082e+00 true resid norm
>>> 7.032943782131e+01 ||r(i)||/||b|| 2.315164775854e-05
>>> > 236 KSP unpreconditioned resid norm 6.422855779486e+00 true resid norm
>>> 6.800345168870e+01 ||r(i)||/||b|| 2.238595968678e-05
>>> > 237 KSP unpreconditioned resid norm 6.413921210094e+00 true resid norm
>>> 7.408432731879e+01 ||r(i)||/||b|| 2.438771449973e-05
>>> > 238 KSP unpreconditioned resid norm 4.949111361190e+00 true resid norm
>>> 7.744087979524e+01 ||r(i)||/||b|| 2.549265324267e-05
>>> > 239 KSP unpreconditioned resid norm 4.947369357666e+00 true resid norm
>>> 7.104259266677e+01 ||r(i)||/||b|| 2.338641018933e-05
>>> > 240 KSP unpreconditioned resid norm 3.873645232239e+00 true resid norm
>>> 6.908028336929e+01 ||r(i)||/||b|| 2.274044037845e-05
>>> > 241 KSP unpreconditioned resid norm 3.841473653930e+00 true resid norm
>>> 7.431718972562e+01 ||r(i)||/||b|| 2.446437014474e-05
>>> > 242 KSP unpreconditioned resid norm 3.057267436362e+00 true resid norm
>>> 7.685939322732e+01 ||r(i)||/||b|| 2.530123450517e-05
>>> > 243 KSP unpreconditioned resid norm 2.980906717815e+00 true resid norm
>>> 6.975661521135e+01 ||r(i)||/||b|| 2.296308109705e-05
>>> > 244 KSP unpreconditioned resid norm 2.415633545154e+00 true resid norm
>>> 6.989644258184e+01 ||r(i)||/||b|| 2.300911067057e-05
>>> > 245 KSP unpreconditioned resid norm 2.363923146996e+00 true resid norm
>>> 7.486631867276e+01 ||r(i)||/||b|| 2.464513712301e-05
>>> > 246 KSP unpreconditioned resid norm 1.947823635306e+00 true resid norm
>>> 7.671103669547e+01 ||r(i)||/||b|| 2.525239722914e-05
>>> > 247 KSP unpreconditioned resid norm 1.942156637334e+00 true resid norm
>>> 6.835715877902e+01 ||r(i)||/||b|| 2.250239602152e-05
>>> > 248 KSP unpreconditioned resid norm 1.675749569790e+00 true resid norm
>>> 7.111781390782e+01 ||r(i)||/||b|| 2.341117216285e-05
>>> > 249 KSP unpreconditioned resid norm 1.673819729570e+00 true resid norm
>>> 7.552508026111e+01 ||r(i)||/||b|| 2.486199391474e-05
>>> > 250 KSP unpreconditioned resid norm 1.453311843294e+00 true resid norm
>>> 7.639099426865e+01 ||r(i)||/||b|| 2.514704291716e-05
>>> > 251 KSP unpreconditioned resid norm 1.452846325098e+00 true resid norm
>>> 6.951401359923e+01 ||r(i)||/||b|| 2.288321941689e-05
>>> > 252 KSP unpreconditioned resid norm 1.335008887441e+00 true resid norm
>>> 6.912230871414e+01 ||r(i)||/||b|| 2.275427464204e-05
>>> > 253 KSP unpreconditioned resid norm 1.334477013356e+00 true resid norm
>>> 7.412281497148e+01 ||r(i)||/||b|| 2.440038419546e-05
>>> > 254 KSP unpreconditioned resid norm 1.248507835050e+00 true resid norm
>>> 7.801932499175e+01 ||r(i)||/||b|| 2.568307079543e-05
>>> > 255 KSP unpreconditioned resid norm 1.248246596771e+00 true resid norm
>>> 7.094899926215e+01 ||r(i)||/||b|| 2.335560030938e-05
>>> > 256 KSP unpreconditioned resid norm 1.208952722414e+00 true resid norm
>>> 7.101235824005e+01 ||r(i)||/||b|| 2.337645736134e-05
>>> > 257 KSP unpreconditioned resid norm 1.208780664971e+00 true resid norm
>>> 7.562936418444e+01 ||r(i)||/||b|| 2.489632299136e-05
>>> > 258 KSP unpreconditioned resid norm 1.179956701653e+00 true resid norm
>>> 7.812300941072e+01 ||r(i)||/||b|| 2.571720252207e-05
>>> > 259 KSP unpreconditioned resid norm 1.179219541297e+00 true resid norm
>>> 7.131201918549e+01 ||r(i)||/||b|| 2.347510232240e-05
>>> > 260 KSP unpreconditioned resid norm 1.160215487467e+00 true resid norm
>>> 7.222079766175e+01 ||r(i)||/||b|| 2.377426181841e-05
>>> > 261 KSP unpreconditioned resid norm 1.159115040554e+00 true resid norm
>>> 7.481372509179e+01 ||r(i)||/||b|| 2.462782391678e-05
>>> > 262 KSP unpreconditioned resid norm 1.151973184765e+00 true resid norm
>>> 7.709040836137e+01 ||r(i)||/||b|| 2.537728204907e-05
>>> > 263 KSP unpreconditioned resid norm 1.150882463576e+00 true resid norm
>>> 7.032588895526e+01 ||r(i)||/||b|| 2.315047951236e-05
>>> > 264 KSP unpreconditioned resid norm 1.137617003277e+00 true resid norm
>>> 7.004055871264e+01 ||r(i)||/||b|| 2.305655205500e-05
>>> > 265 KSP unpreconditioned resid norm 1.137134003401e+00 true resid norm
>>> 7.610459827221e+01 ||r(i)||/||b|| 2.505276462582e-05
>>> > 266 KSP unpreconditioned resid norm 1.131425778253e+00 true resid norm
>>> 7.852741072990e+01 ||r(i)||/||b|| 2.585032681802e-05
>>> > 267 KSP unpreconditioned resid norm 1.131176695314e+00 true resid norm
>>> 7.064571495865e+01 ||r(i)||/||b|| 2.325576258022e-05
>>> > 268 KSP unpreconditioned resid norm 1.125420065063e+00 true resid norm
>>> 7.138837220124e+01 ||r(i)||/||b|| 2.350023686323e-05
>>> > 269 KSP unpreconditioned resid norm 1.124779989266e+00 true resid norm
>>> 7.585594020759e+01 ||r(i)||/||b|| 2.497090923065e-05
>>> > 270 KSP unpreconditioned resid norm 1.119805446125e+00 true resid norm
>>> 7.703631305135e+01 ||r(i)||/||b|| 2.535947449079e-05
>>> > 271 KSP unpreconditioned resid norm 1.119024433863e+00 true resid norm
>>> 7.081439585094e+01 ||r(i)||/||b|| 2.331129040360e-05
>>> > 272 KSP unpreconditioned resid norm 1.115694452861e+00 true resid norm
>>> 7.134872343512e+01 ||r(i)||/||b|| 2.348718494222e-05
>>> > 273 KSP unpreconditioned resid norm 1.113572716158e+00 true resid norm
>>> 7.600475566242e+01 ||r(i)||/||b|| 2.501989757889e-05
>>> > 274 KSP unpreconditioned resid norm 1.108711406381e+00 true resid norm
>>> 7.738835220359e+01 ||r(i)||/||b|| 2.547536175937e-05
>>> > 275 KSP unpreconditioned resid norm 1.107890435549e+00 true resid norm
>>> 7.093429729336e+01 ||r(i)||/||b|| 2.335076058915e-05
>>> > 276 KSP unpreconditioned resid norm 1.103340227961e+00 true resid norm
>>> 7.145267197866e+01 ||r(i)||/||b|| 2.352140361564e-05
>>> > 277 KSP unpreconditioned resid norm 1.102897652964e+00 true resid norm
>>> 7.448617654625e+01 ||r(i)||/||b|| 2.451999867624e-05
>>> > 278 KSP unpreconditioned resid norm 1.102576754158e+00 true resid norm
>>> 7.707165090465e+01 ||r(i)||/||b|| 2.537110730854e-05
>>> > 279 KSP unpreconditioned resid norm 1.102564028537e+00 true resid norm
>>> 7.009637628868e+01 ||r(i)||/||b|| 2.307492656359e-05
>>> > 280 KSP unpreconditioned resid norm 1.100828424712e+00 true resid norm
>>> 7.059832880916e+01 ||r(i)||/||b|| 2.324016360096e-05
>>> > 281 KSP unpreconditioned resid norm 1.100686341559e+00 true resid norm
>>> 7.460867988528e+01 ||r(i)||/||b|| 2.456032537644e-05
>>> > 282 KSP unpreconditioned resid norm 1.099417185996e+00 true resid norm
>>> 7.763784632467e+01 ||r(i)||/||b|| 2.555749237477e-05
>>> > 283 KSP unpreconditioned resid norm 1.099379061087e+00 true resid norm
>>> 7.017139420999e+01 ||r(i)||/||b|| 2.309962160657e-05
>>> > 284 KSP unpreconditioned resid norm 1.097928047676e+00 true resid norm
>>> 6.983706716123e+01 ||r(i)||/||b|| 2.298956496018e-05
>>> > 285 KSP unpreconditioned resid norm 1.096490152934e+00 true resid norm
>>> 7.414445779601e+01 ||r(i)||/||b|| 2.440750876614e-05
>>> > 286 KSP unpreconditioned resid norm 1.094691490227e+00 true resid norm
>>> 7.634526287231e+01 ||r(i)||/||b|| 2.513198866374e-05
>>> > 287 KSP unpreconditioned resid norm 1.093560358328e+00 true resid norm
>>> 7.003716824146e+01 ||r(i)||/||b|| 2.305543595061e-05
>>> > 288 KSP unpreconditioned resid norm 1.093357856424e+00 true resid norm
>>> 6.964715939684e+01 ||r(i)||/||b|| 2.292704949292e-05
>>> > 289 KSP unpreconditioned resid norm 1.091881434739e+00 true resid norm
>>> 7.429955169250e+01 ||r(i)||/||b|| 2.445856390566e-05
>>> > 290 KSP unpreconditioned resid norm 1.091817808496e+00 true resid norm
>>> 7.607892786798e+01 ||r(i)||/||b|| 2.504431422190e-05
>>> > 291 KSP unpreconditioned resid norm 1.090295101202e+00 true resid norm
>>> 6.942248339413e+01 ||r(i)||/||b|| 2.285308871866e-05
>>> > 292 KSP unpreconditioned resid norm 1.089995012773e+00 true resid norm
>>> 6.995557798353e+01 ||r(i)||/||b|| 2.302857736947e-05
>>> > 293 KSP unpreconditioned resid norm 1.089975910578e+00 true resid norm
>>> 7.453210925277e+01 ||r(i)||/||b|| 2.453511919866e-05
>>> > 294 KSP unpreconditioned resid norm 1.085570944646e+00 true resid norm
>>> 7.629598425927e+01 ||r(i)||/||b|| 2.511576670710e-05
>>> > 295 KSP unpreconditioned resid norm 1.085363565621e+00 true resid norm
>>> 7.025539955712e+01 ||r(i)||/||b|| 2.312727520749e-05
>>> > 296 KSP unpreconditioned resid norm 1.083348574106e+00 true resid norm
>>> 7.003219621882e+01 ||r(i)||/||b|| 2.305379921754e-05
>>> > 297 KSP unpreconditioned resid norm 1.082180374430e+00 true resid norm
>>> 7.473048827106e+01 ||r(i)||/||b|| 2.460042330597e-05
>>> > 298 KSP unpreconditioned resid norm 1.081326671068e+00 true resid norm
>>> 7.660142838935e+01 ||r(i)||/||b|| 2.521631542651e-05
>>> > 299 KSP unpreconditioned resid norm 1.078679751898e+00 true resid norm
>>> 7.077868424247e+01 ||r(i)||/||b|| 2.329953454992e-05
>>> > 300 KSP unpreconditioned resid norm 1.078656949888e+00 true resid norm
>>> 7.074960394994e+01 ||r(i)||/||b|| 2.328996164972e-05
>>> > Linear solve did not converge due to DIVERGED_ITS iterations 300
>>> > KSP Object: 2 MPI processes
>>> > type: fgmres
>>> > GMRES: restart=300, using Modified Gram-Schmidt Orthogonalization
>>> > GMRES: happy breakdown tolerance 1e-30
>>> > maximum iterations=300, initial guess is zero
>>> > tolerances: relative=1e-09, absolute=1e-20, divergence=10000
>>> > right preconditioning
>>> > using UNPRECONDITIONED norm type for convergence test
>>> > PC Object: 2 MPI processes
>>> > type: fieldsplit
>>> > FieldSplit with Schur preconditioner, factorization DIAG
>>> > Preconditioner for the Schur complement formed from Sp, an
>>> assembled approximation to S, which uses (lumped, if requested) A00's
>>> diagonal's inverse
>>> > Split info:
>>> > Split number 0 Defined by IS
>>> > Split number 1 Defined by IS
>>> > KSP solver for A00 block
>>> > KSP Object: (fieldsplit_u_) 2 MPI processes
>>> > type: preonly
>>> > maximum iterations=10000, initial guess is zero
>>> > tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>>> > left preconditioning
>>> > using NONE norm type for convergence test
>>> > PC Object: (fieldsplit_u_) 2 MPI processes
>>> > type: lu
>>> > LU: out-of-place factorization
>>> > tolerance for zero pivot 2.22045e-14
>>> > matrix ordering: natural
>>> > factor fill ratio given 0, needed 0
>>> > Factored matrix follows:
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=184326, cols=184326
>>> > package used to perform factorization: mumps
>>> > total: nonzeros=4.03041e+08, allocated
>>> nonzeros=4.03041e+08
>>> > total number of mallocs used during MatSetValues calls
>>> =0
>>> > MUMPS run parameters:
>>> > SYM (matrix type): 0
>>> > PAR (host participation): 1
>>> > ICNTL(1) (output for error): 6
>>> > ICNTL(2) (output of diagnostic msg): 0
>>> > ICNTL(3) (output for global info): 0
>>> > ICNTL(4) (level of printing): 0
>>> > ICNTL(5) (input mat struct): 0
>>> > ICNTL(6) (matrix prescaling): 7
>>> > ICNTL(7) (sequentia matrix ordering):7
>>> > ICNTL(8) (scalling strategy): 77
>>> > ICNTL(10) (max num of refinements): 0
>>> > ICNTL(11) (error analysis): 0
>>> > ICNTL(12) (efficiency control):
>>> 1
>>> > ICNTL(13) (efficiency control):
>>> 0
>>> > ICNTL(14) (percentage of estimated workspace
>>> increase): 20
>>> > ICNTL(18) (input mat struct):
>>> 3
>>> > ICNTL(19) (Shur complement info):
>>> 0
>>> > ICNTL(20) (rhs sparse pattern):
>>> 0
>>> > ICNTL(21) (solution struct):
>>> 1
>>> > ICNTL(22) (in-core/out-of-core facility):
>>> 0
>>> > ICNTL(23) (max size of memory can be allocated
>>> locally):0
>>> > ICNTL(24) (detection of null pivot rows):
>>> 0
>>> > ICNTL(25) (computation of a null space basis):
>>> 0
>>> > ICNTL(26) (Schur options for rhs or solution):
>>> 0
>>> > ICNTL(27) (experimental parameter):
>>> -24
>>> > ICNTL(28) (use parallel or sequential ordering):
>>> 1
>>> > ICNTL(29) (parallel ordering):
>>> 0
>>> > ICNTL(30) (user-specified set of entries in
>>> inv(A)): 0
>>> > ICNTL(31) (factors is discarded in the solve
>>> phase): 0
>>> > ICNTL(33) (compute determinant):
>>> 0
>>> > CNTL(1) (relative pivoting threshold): 0.01
>>> > CNTL(2) (stopping criterion of refinement):
>>> 1.49012e-08
>>> > CNTL(3) (absolute pivoting threshold): 0
>>> > CNTL(4) (value of static pivoting): -1
>>> > CNTL(5) (fixation for null pivots): 0
>>> > RINFO(1) (local estimated flops for the
>>> elimination after analysis):
>>> > [0] 5.59214e+11
>>> > [1] 5.35237e+11
>>> > RINFO(2) (local estimated flops for the assembly
>>> after factorization):
>>> > [0] 4.2839e+08
>>> > [1] 3.799e+08
>>> > RINFO(3) (local estimated flops for the
>>> elimination after factorization):
>>> > [0] 5.59214e+11
>>> > [1] 5.35237e+11
>>> > INFO(15) (estimated size of (in MB) MUMPS internal
>>> data for running numerical factorization):
>>> > [0] 2621
>>> > [1] 2649
>>> > INFO(16) (size of (in MB) MUMPS internal data used
>>> during numerical factorization):
>>> > [0] 2621
>>> > [1] 2649
>>> > INFO(23) (num of pivots eliminated on this
>>> processor after factorization):
>>> > [0] 90423
>>> > [1] 93903
>>> > RINFOG(1) (global estimated flops for the
>>> elimination after analysis): 1.09445e+12
>>> > RINFOG(2) (global estimated flops for the assembly
>>> after factorization): 8.0829e+08
>>> > RINFOG(3) (global estimated flops for the
>>> elimination after factorization): 1.09445e+12
>>> > (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant):
>>> (0,0)*(2^0)
>>> > INFOG(3) (estimated real workspace for factors on
>>> all processors after analysis): 403041366
>>> > INFOG(4) (estimated integer workspace for factors
>>> on all processors after analysis): 2265748
>>> > INFOG(5) (estimated maximum front size in the
>>> complete tree): 6663
>>> > INFOG(6) (number of nodes in the complete tree):
>>> 2812
>>> > INFOG(7) (ordering option effectively use after
>>> analysis): 5
>>> > INFOG(8) (structural symmetry in percent of the
>>> permuted matrix after analysis): 100
>>> > INFOG(9) (total real/complex workspace to store
>>> the matrix factors after factorization): 403041366
>>> > INFOG(10) (total integer space store the matrix
>>> factors after factorization): 2265766
>>> > INFOG(11) (order of largest frontal matrix after
>>> factorization): 6663
>>> > INFOG(12) (number of off-diagonal pivots): 0
>>> > INFOG(13) (number of delayed pivots after
>>> factorization): 0
>>> > INFOG(14) (number of memory compress after
>>> factorization): 0
>>> > INFOG(15) (number of steps of iterative refinement
>>> after solution): 0
>>> > INFOG(16) (estimated size (in MB) of all MUMPS
>>> internal data for factorization after analysis: value on the most memory
>>> consuming processor): 2649
>>> > INFOG(17) (estimated size of all MUMPS internal
>>> data for factorization after analysis: sum over all processors): 5270
>>> > INFOG(18) (size of all MUMPS internal data
>>> allocated during factorization: value on the most memory consuming
>>> processor): 2649
>>> > INFOG(19) (size of all MUMPS internal data
>>> allocated during factorization: sum over all processors): 5270
>>> > INFOG(20) (estimated number of entries in the
>>> factors): 403041366
>>> > INFOG(21) (size in MB of memory effectively used
>>> during factorization - value on the most memory consuming processor): 2121
>>> > INFOG(22) (size in MB of memory effectively used
>>> during factorization - sum over all processors): 4174
>>> > INFOG(23) (after analysis: value of ICNTL(6)
>>> effectively used): 0
>>> > INFOG(24) (after analysis: value of ICNTL(12)
>>> effectively used): 1
>>> > INFOG(25) (after factorization: number of pivots
>>> modified by static pivoting): 0
>>> > INFOG(28) (after factorization: number of null
>>> pivots encountered): 0
>>> > INFOG(29) (after factorization: effective number
>>> of entries in the factors (sum over all processors)): 403041366
>>> > INFOG(30, 31) (after solution: size in Mbytes of
>>> memory used during solution phase): 2467, 4922
>>> > INFOG(32) (after analysis: type of analysis done):
>>> 1
>>> > INFOG(33) (value used for ICNTL(8)): 7
>>> > INFOG(34) (exponent of the determinant if
>>> determinant is requested): 0
>>> > linear system matrix = precond matrix:
>>> > Mat Object: (fieldsplit_u_) 2 MPI processes
>>> > type: mpiaij
>>> > rows=184326, cols=184326, bs=3
>>> > total: nonzeros=3.32649e+07, allocated nonzeros=3.32649e+07
>>> > total number of mallocs used during MatSetValues calls =0
>>> > using I-node (on process 0) routines: found 26829 nodes,
>>> limit used is 5
>>> > KSP solver for S = A11 - A10 inv(A00) A01
>>> > KSP Object: (fieldsplit_lu_) 2 MPI processes
>>> > type: preonly
>>> > maximum iterations=10000, initial guess is zero
>>> > tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>>> > left preconditioning
>>> > using NONE norm type for convergence test
>>> > PC Object: (fieldsplit_lu_) 2 MPI processes
>>> > type: lu
>>> > LU: out-of-place factorization
>>> > tolerance for zero pivot 2.22045e-14
>>> > matrix ordering: natural
>>> > factor fill ratio given 0, needed 0
>>> > Factored matrix follows:
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=2583, cols=2583
>>> > package used to perform factorization: mumps
>>> > total: nonzeros=2.17621e+06, allocated
>>> nonzeros=2.17621e+06
>>> > total number of mallocs used during MatSetValues calls
>>> =0
>>> > MUMPS run parameters:
>>> > SYM (matrix type): 0
>>> > PAR (host participation): 1
>>> > ICNTL(1) (output for error): 6
>>> > ICNTL(2) (output of diagnostic msg): 0
>>> > ICNTL(3) (output for global info): 0
>>> > ICNTL(4) (level of printing): 0
>>> > ICNTL(5) (input mat struct): 0
>>> > ICNTL(6) (matrix prescaling): 7
>>> > ICNTL(7) (sequentia matrix ordering):7
>>> > ICNTL(8) (scalling strategy): 77
>>> > ICNTL(10) (max num of refinements): 0
>>> > ICNTL(11) (error analysis): 0
>>> > ICNTL(12) (efficiency control):
>>> 1
>>> > ICNTL(13) (efficiency control):
>>> 0
>>> > ICNTL(14) (percentage of estimated workspace
>>> increase): 20
>>> > ICNTL(18) (input mat struct):
>>> 3
>>> > ICNTL(19) (Shur complement info):
>>> 0
>>> > ICNTL(20) (rhs sparse pattern):
>>> 0
>>> > ICNTL(21) (solution struct):
>>> 1
>>> > ICNTL(22) (in-core/out-of-core facility):
>>> 0
>>> > ICNTL(23) (max size of memory can be allocated
>>> locally):0
>>> > ICNTL(24) (detection of null pivot rows):
>>> 0
>>> > ICNTL(25) (computation of a null space basis):
>>> 0
>>> > ICNTL(26) (Schur options for rhs or solution):
>>> 0
>>> > ICNTL(27) (experimental parameter):
>>> -24
>>> > ICNTL(28) (use parallel or sequential ordering):
>>> 1
>>> > ICNTL(29) (parallel ordering):
>>> 0
>>> > ICNTL(30) (user-specified set of entries in
>>> inv(A)): 0
>>> > ICNTL(31) (factors is discarded in the solve
>>> phase): 0
>>> > ICNTL(33) (compute determinant):
>>> 0
>>> > CNTL(1) (relative pivoting threshold): 0.01
>>> > CNTL(2) (stopping criterion of refinement):
>>> 1.49012e-08
>>> > CNTL(3) (absolute pivoting threshold): 0
>>> > CNTL(4) (value of static pivoting): -1
>>> > CNTL(5) (fixation for null pivots): 0
>>> > RINFO(1) (local estimated flops for the
>>> elimination after analysis):
>>> > [0] 5.12794e+08
>>> > [1] 5.02142e+08
>>> > RINFO(2) (local estimated flops for the assembly
>>> after factorization):
>>> > [0] 815031
>>> > [1] 745263
>>> > RINFO(3) (local estimated flops for the
>>> elimination after factorization):
>>> > [0] 5.12794e+08
>>> > [1] 5.02142e+08
>>> > INFO(15) (estimated size of (in MB) MUMPS internal
>>> data for running numerical factorization):
>>> > [0] 34
>>> > [1] 34
>>> > INFO(16) (size of (in MB) MUMPS internal data used
>>> during numerical factorization):
>>> > [0] 34
>>> > [1] 34
>>> > INFO(23) (num of pivots eliminated on this
>>> processor after factorization):
>>> > [0] 1158
>>> > [1] 1425
>>> > RINFOG(1) (global estimated flops for the
>>> elimination after analysis): 1.01494e+09
>>> > RINFOG(2) (global estimated flops for the assembly
>>> after factorization): 1.56029e+06
>>> > RINFOG(3) (global estimated flops for the
>>> elimination after factorization): 1.01494e+09
>>> > (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant):
>>> (0,0)*(2^0)
>>> > INFOG(3) (estimated real workspace for factors on
>>> all processors after analysis): 2176209
>>> > INFOG(4) (estimated integer workspace for factors
>>> on all processors after analysis): 14427
>>> > INFOG(5) (estimated maximum front size in the
>>> complete tree): 699
>>> > INFOG(6) (number of nodes in the complete tree): 15
>>> > INFOG(7) (ordering option effectively use after
>>> analysis): 2
>>> > INFOG(8) (structural symmetry in percent of the
>>> permuted matrix after analysis): 100
>>> > INFOG(9) (total real/complex workspace to store
>>> the matrix factors after factorization): 2176209
>>> > INFOG(10) (total integer space store the matrix
>>> factors after factorization): 14427
>>> > INFOG(11) (order of largest frontal matrix after
>>> factorization): 699
>>> > INFOG(12) (number of off-diagonal pivots): 0
>>> > INFOG(13) (number of delayed pivots after
>>> factorization): 0
>>> > INFOG(14) (number of memory compress after
>>> factorization): 0
>>> > INFOG(15) (number of steps of iterative refinement
>>> after solution): 0
>>> > INFOG(16) (estimated size (in MB) of all MUMPS
>>> internal data for factorization after analysis: value on the most memory
>>> consuming processor): 34
>>> > INFOG(17) (estimated size of all MUMPS internal
>>> data for factorization after analysis: sum over all processors): 68
>>> > INFOG(18) (size of all MUMPS internal data
>>> allocated during factorization: value on the most memory consuming
>>> processor): 34
>>> > INFOG(19) (size of all MUMPS internal data
>>> allocated during factorization: sum over all processors): 68
>>> > INFOG(20) (estimated number of entries in the
>>> factors): 2176209
>>> > INFOG(21) (size in MB of memory effectively used
>>> during factorization - value on the most memory consuming processor): 30
>>> > INFOG(22) (size in MB of memory effectively used
>>> during factorization - sum over all processors): 59
>>> > INFOG(23) (after analysis: value of ICNTL(6)
>>> effectively used): 0
>>> > INFOG(24) (after analysis: value of ICNTL(12)
>>> effectively used): 1
>>> > INFOG(25) (after factorization: number of pivots
>>> modified by static pivoting): 0
>>> > INFOG(28) (after factorization: number of null
>>> pivots encountered): 0
>>> > INFOG(29) (after factorization: effective number
>>> of entries in the factors (sum over all processors)): 2176209
>>> > INFOG(30, 31) (after solution: size in Mbytes of
>>> memory used during solution phase): 16, 32
>>> > INFOG(32) (after analysis: type of analysis done):
>>> 1
>>> > INFOG(33) (value used for ICNTL(8)): 7
>>> > INFOG(34) (exponent of the determinant if
>>> determinant is requested): 0
>>> > linear system matrix followed by preconditioner matrix:
>>> > Mat Object: (fieldsplit_lu_) 2 MPI processes
>>> > type: schurcomplement
>>> > rows=2583, cols=2583
>>> > Schur complement A11 - A10 inv(A00) A01
>>> > A11
>>> > Mat Object: (fieldsplit_lu_)
>>> 2 MPI processes
>>> > type: mpiaij
>>> > rows=2583, cols=2583, bs=3
>>> > total: nonzeros=117369, allocated nonzeros=117369
>>> > total number of mallocs used during MatSetValues calls
>>> =0
>>> > not using I-node (on process 0) routines
>>> > A10
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=2583, cols=184326, rbs=3, cbs = 1
>>> > total: nonzeros=292770, allocated nonzeros=292770
>>> > total number of mallocs used during MatSetValues calls
>>> =0
>>> > not using I-node (on process 0) routines
>>> > KSP of A00
>>> > KSP Object: (fieldsplit_u_) 2
>>> MPI processes
>>> > type: preonly
>>> > maximum iterations=10000, initial guess is zero
>>> > tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000
>>> > left preconditioning
>>> > using NONE norm type for convergence test
>>> > PC Object: (fieldsplit_u_) 2
>>> MPI processes
>>> > type: lu
>>> > LU: out-of-place factorization
>>> > tolerance for zero pivot 2.22045e-14
>>> > matrix ordering: natural
>>> > factor fill ratio given 0, needed 0
>>> > Factored matrix follows:
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=184326, cols=184326
>>> > package used to perform factorization: mumps
>>> > total: nonzeros=4.03041e+08, allocated
>>> nonzeros=4.03041e+08
>>> > total number of mallocs used during
>>> MatSetValues calls =0
>>> > MUMPS run parameters:
>>> > SYM (matrix type): 0
>>> > PAR (host participation): 1
>>> > ICNTL(1) (output for error): 6
>>> > ICNTL(2) (output of diagnostic msg): 0
>>> > ICNTL(3) (output for global info): 0
>>> > ICNTL(4) (level of printing): 0
>>> > ICNTL(5) (input mat struct): 0
>>> > ICNTL(6) (matrix prescaling): 7
>>> > ICNTL(7) (sequentia matrix ordering):7
>>> > ICNTL(8) (scalling strategy): 77
>>> > ICNTL(10) (max num of refinements): 0
>>> > ICNTL(11) (error analysis): 0
>>> > ICNTL(12) (efficiency control):
>>> 1
>>> > ICNTL(13) (efficiency control):
>>> 0
>>> > ICNTL(14) (percentage of estimated
>>> workspace increase): 20
>>> > ICNTL(18) (input mat struct):
>>> 3
>>> > ICNTL(19) (Shur complement info):
>>> 0
>>> > ICNTL(20) (rhs sparse pattern):
>>> 0
>>> > ICNTL(21) (solution struct):
>>> 1
>>> > ICNTL(22) (in-core/out-of-core facility):
>>> 0
>>> > ICNTL(23) (max size of memory can be
>>> allocated locally):0
>>> > ICNTL(24) (detection of null pivot rows):
>>> 0
>>> > ICNTL(25) (computation of a null space
>>> basis): 0
>>> > ICNTL(26) (Schur options for rhs or
>>> solution): 0
>>> > ICNTL(27) (experimental parameter):
>>> -24
>>> > ICNTL(28) (use parallel or sequential
>>> ordering): 1
>>> > ICNTL(29) (parallel ordering):
>>> 0
>>> > ICNTL(30) (user-specified set of entries
>>> in inv(A)): 0
>>> > ICNTL(31) (factors is discarded in the
>>> solve phase): 0
>>> > ICNTL(33) (compute determinant):
>>> 0
>>> > CNTL(1) (relative pivoting threshold):
>>> 0.01
>>> > CNTL(2) (stopping criterion of
>>> refinement): 1.49012e-08
>>> > CNTL(3) (absolute pivoting threshold):
>>> 0
>>> > CNTL(4) (value of static pivoting):
>>> -1
>>> > CNTL(5) (fixation for null pivots):
>>> 0
>>> > RINFO(1) (local estimated flops for the
>>> elimination after analysis):
>>> > [0] 5.59214e+11
>>> > [1] 5.35237e+11
>>> > RINFO(2) (local estimated flops for the
>>> assembly after factorization):
>>> > [0] 4.2839e+08
>>> > [1] 3.799e+08
>>> > RINFO(3) (local estimated flops for the
>>> elimination after factorization):
>>> > [0] 5.59214e+11
>>> > [1] 5.35237e+11
>>> > INFO(15) (estimated size of (in MB) MUMPS
>>> internal data for running numerical factorization):
>>> > [0] 2621
>>> > [1] 2649
>>> > INFO(16) (size of (in MB) MUMPS internal
>>> data used during numerical factorization):
>>> > [0] 2621
>>> > [1] 2649
>>> > INFO(23) (num of pivots eliminated on this
>>> processor after factorization):
>>> > [0] 90423
>>> > [1] 93903
>>> > RINFOG(1) (global estimated flops for the
>>> elimination after analysis): 1.09445e+12
>>> > RINFOG(2) (global estimated flops for the
>>> assembly after factorization): 8.0829e+08
>>> > RINFOG(3) (global estimated flops for the
>>> elimination after factorization): 1.09445e+12
>>> > (RINFOG(12) RINFOG(13))*2^INFOG(34)
>>> (determinant): (0,0)*(2^0)
>>> > INFOG(3) (estimated real workspace for
>>> factors on all processors after analysis): 403041366
>>> > INFOG(4) (estimated integer workspace for
>>> factors on all processors after analysis): 2265748
>>> > INFOG(5) (estimated maximum front size in
>>> the complete tree): 6663
>>> > INFOG(6) (number of nodes in the complete
>>> tree): 2812
>>> > INFOG(7) (ordering option effectively use
>>> after analysis): 5
>>> > INFOG(8) (structural symmetry in percent
>>> of the permuted matrix after analysis): 100
>>> > INFOG(9) (total real/complex workspace to
>>> store the matrix factors after factorization): 403041366
>>> > INFOG(10) (total integer space store the
>>> matrix factors after factorization): 2265766
>>> > INFOG(11) (order of largest frontal matrix
>>> after factorization): 6663
>>> > INFOG(12) (number of off-diagonal pivots):
>>> 0
>>> > INFOG(13) (number of delayed pivots after
>>> factorization): 0
>>> > INFOG(14) (number of memory compress after
>>> factorization): 0
>>> > INFOG(15) (number of steps of iterative
>>> refinement after solution): 0
>>> > INFOG(16) (estimated size (in MB) of all
>>> MUMPS internal data for factorization after analysis: value on the most
>>> memory consuming processor): 2649
>>> > INFOG(17) (estimated size of all MUMPS
>>> internal data for factorization after analysis: sum over all processors):
>>> 5270
>>> > INFOG(18) (size of all MUMPS internal data
>>> allocated during factorization: value on the most memory consuming
>>> processor): 2649
>>> > INFOG(19) (size of all MUMPS internal data
>>> allocated during factorization: sum over all processors): 5270
>>> > INFOG(20) (estimated number of entries in
>>> the factors): 403041366
>>> > INFOG(21) (size in MB of memory
>>> effectively used during factorization - value on the most memory consuming
>>> processor): 2121
>>> > INFOG(22) (size in MB of memory
>>> effectively used during factorization - sum over all processors): 4174
>>> > INFOG(23) (after analysis: value of
>>> ICNTL(6) effectively used): 0
>>> > INFOG(24) (after analysis: value of
>>> ICNTL(12) effectively used): 1
>>> > INFOG(25) (after factorization: number of
>>> pivots modified by static pivoting): 0
>>> > INFOG(28) (after factorization: number of
>>> null pivots encountered): 0
>>> > INFOG(29) (after factorization: effective
>>> number of entries in the factors (sum over all processors)): 403041366
>>> > INFOG(30, 31) (after solution: size in
>>> Mbytes of memory used during solution phase): 2467, 4922
>>> > INFOG(32) (after analysis: type of
>>> analysis done): 1
>>> > INFOG(33) (value used for ICNTL(8)): 7
>>> > INFOG(34) (exponent of the determinant if
>>> determinant is requested): 0
>>> > linear system matrix = precond matrix:
>>> > Mat Object: (fieldsplit_u_)
>>> 2 MPI processes
>>> > type: mpiaij
>>> > rows=184326, cols=184326, bs=3
>>> > total: nonzeros=3.32649e+07, allocated
>>> nonzeros=3.32649e+07
>>> > total number of mallocs used during MatSetValues
>>> calls =0
>>> > using I-node (on process 0) routines: found 26829
>>> nodes, limit used is 5
>>> > A01
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=184326, cols=2583, rbs=3, cbs = 1
>>> > total: nonzeros=292770, allocated nonzeros=292770
>>> > total number of mallocs used during MatSetValues calls
>>> =0
>>> > using I-node (on process 0) routines: found 16098
>>> nodes, limit used is 5
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=2583, cols=2583, rbs=3, cbs = 1
>>> > total: nonzeros=1.25158e+06, allocated nonzeros=1.25158e+06
>>> > total number of mallocs used during MatSetValues calls =0
>>> > not using I-node (on process 0) routines
>>> > linear system matrix = precond matrix:
>>> > Mat Object: 2 MPI processes
>>> > type: mpiaij
>>> > rows=186909, cols=186909
>>> > total: nonzeros=3.39678e+07, allocated nonzeros=3.39678e+07
>>> > total number of mallocs used during MatSetValues calls =0
>>> > using I-node (on process 0) routines: found 26829 nodes, limit
>>> used is 5
>>> > KSPSolve completed
>>> >
>>> >
>>> > Giang
>>> >
>>> > On Sun, Apr 17, 2016 at 1:15 AM, Matthew Knepley <knepley at gmail.com>
>>> wrote:
>>> > On Sat, Apr 16, 2016 at 6:54 PM, Hoang Giang Bui <hgbk2008 at gmail.com>
>>> wrote:
>>> > Hello
>>> >
>>> > I'm solving an indefinite problem arising from mesh tying/contact
>>> using Lagrange multiplier, the matrix has the form
>>> >
>>> > K = [A P^T
>>> > P 0]
>>> >
>>> > I used the FIELDSPLIT preconditioner with one field is the main
>>> variable (displacement) and the other field for dual variable (Lagrange
>>> multiplier). The block size for each field is 3. According to the manual, I
>>> first chose the preconditioner based on Schur complement to treat this
>>> problem.
>>> >
>>> >
>>> > For any solver question, please send us the output of
>>> >
>>> > -ksp_view -ksp_monitor_true_residual -ksp_converged_reason
>>> >
>>> >
>>> > However, I will comment below
>>> >
>>> > The parameters used for the solve is
>>> > -ksp_type gmres
>>> >
>>> > You need 'fgmres' here with the options you have below.
>>> >
>>> > -ksp_max_it 300
>>> > -ksp_gmres_restart 300
>>> > -ksp_gmres_modifiedgramschmidt
>>> > -pc_fieldsplit_type schur
>>> > -pc_fieldsplit_schur_fact_type diag
>>> > -pc_fieldsplit_schur_precondition selfp
>>> >
>>> >
>>> >
>>> > It could be taking time in the MatMatMult() here if that matrix is
>>> dense. Is there any reason to
>>> > believe that is a good preconditioner for your problem?
>>> >
>>> >
>>> > -pc_fieldsplit_detect_saddle_point
>>> > -fieldsplit_u_pc_type hypre
>>> >
>>> > I would just use MUMPS here to start, especially if it works on the
>>> whole problem. Same with the one below.
>>> >
>>> > Matt
>>> >
>>> > -fieldsplit_u_pc_hypre_type boomeramg
>>> > -fieldsplit_u_pc_hypre_boomeramg_coarsen_type PMIS
>>> > -fieldsplit_lu_pc_type hypre
>>> > -fieldsplit_lu_pc_hypre_type boomeramg
>>> > -fieldsplit_lu_pc_hypre_boomeramg_coarsen_type PMIS
>>> >
>>> > For the test case, a small problem is solved on 2 processes. Due to
>>> the decomposition, the contact only happens in 1 proc, so the size of
>>> Lagrange multiplier dofs on proc 0 is 0.
>>> >
>>> > 0: mIndexU.size(): 80490
>>> > 0: mIndexLU.size(): 0
>>> > 1: mIndexU.size(): 103836
>>> > 1: mIndexLU.size(): 2583
>>> >
>>> > However, with this setup the solver takes very long at KSPSolve before
>>> going to iteration, and the first iteration seems forever so I have to stop
>>> the calculation. I guessed that the solver takes time to compute the Schur
>>> complement, but according to the manual only the diagonal of A is used to
>>> approximate the Schur complement, so it should not take long to compute
>>> this.
>>> >
>>> > Note that I ran the same problem with direct solver (MUMPS) and it's
>>> able to produce the valid results. The parameter for the solve is pretty
>>> standard
>>> > -ksp_type preonly
>>> > -pc_type lu
>>> > -pc_factor_mat_solver_package mumps
>>> >
>>> > Hence the matrix/rhs must not have any problem here. Do you have any
>>> idea or suggestion for this case?
>>> >
>>> >
>>> > Giang
>>> >
>>> >
>>> >
>>> > --
>>> > 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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