[petsc-users] Issue of mg_coarse_ksp not converge
Matthew Knepley
knepley at gmail.com
Mon Oct 2 11:23:39 CDT 2017
On Mon, Oct 2, 2017 at 11:56 AM, Wenbo Zhao <zhaowenbo.npic at gmail.com>
wrote:
>
>
> On Mon, Oct 2, 2017 at 11:49 PM, Mark Adams <mfadams at lbl.gov> wrote:
>
>> Whenbo, do you build your PETSc?
>>
>> Yes.
> My configure option is listed below
> ./configure --with-mpi=1 --with-shared-libraries=1 \
> --with-64-bit-indices=1 --with-debugging=1
>
> And I set PETSC_DIR, PETSC_ARCH and SLEPC_DIR in my ~/.bashrc.
>
>
> The Makefile for my problem is listed below,
>
> PETSC_ARCH = arch-linux2-c-debug
> PETSC_DIR = /home/zhaowenbo/research/petsc/petsc_git
> SLEPC_DIR = /home/zhaowenbo/research/slepc/slepc_git
> #PETSC_DIR = /home/zhaowenbo/research/petsc/petsc-3.7.4
> #SLEPC_DIR = /home/zhaowenbo/research/slepc/slepc-3.7.3
> HYPRE_DIR = /usr/local/hypre
> #
> DEBUG_OPT = -g
> COMP_FLAGS = -fPIC -Wall \
> -I${SLEPC_DIR}/include -I${SLEPC_DIR}/${PETSC_ARCH}/include \
> -I${PETSC_DIR}/include -I${PETSC_DIR}/${PETSC_ARCH}/include \
> -Isrc
>
> LINK_FLAGS = -fPIC -Wall \
> -Wl,-rpath,${SLEPC_DIR}/${PETSC_ARCH}/lib -L${SLEPC_DIR}/${PETSC_ARCH}/lib
> -lslepc \
> -Wl,-rpath,${PETSC_DIR}/${PETSC_ARCH}/lib -L${PETSC_DIR}/${PETSC_ARCH}/lib
> -lpetsc \
> -llapack -lblas -lhwloc -lm -lgfortran -lquadmath
>
> step-41: src/main.o src/readinp.o src/base.o src/sp3.o src/diffu.o
> mpicxx -o step-41 $^ ${LINK_FLAGS} ${DEBUG_OPT}
>
> src/main.o: src/main.c
> mpicxx -o src/main.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT}
>
> src/readinp.o: src/readinp.c
> mpicxx -o src/readinp.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT}
>
> src/sp3.o: src/sp3.c
> mpicxx -o src/sp3.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT}
>
> src/diffu.o: src/diffu.c
> mpicxx -o src/diffu.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT}
>
> src/base.o: src/base.c
> mpicxx -o src/base.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT}
>
>
> clean:
> rm step-41 src/main.o src/readinp.o src/sp3.o src/diffu.o src/base.o
>
> runkr_smooth:
> mpirun -n ${NCORE} ./step-41 \
> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1 \
> -mata AMAT.dat -matb BMAT.dat \
> -st_gamg_est_ksp_view -st_gamg_est_ksp_monitor \
> -st_gamg_est_ksp_converged_reason \
>
Add -st_gamg_est_ksp_error_if_not_converged 0
Thanks,
Matt
-eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1
>
> runkr_nonsmooth:
> mpirun -n ${NCORE} ./step-41 \
> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 0 \
> -mata AMAT.dat -matb BMAT.dat \
> -st_gamg_est_ksp_view -st_gamg_est_ksp_monitor \
> -st_gamg_est_ksp_converged_reason \
> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_nonsmooth 2>&1
>
>
> Thanks,
> Wenbo
>
>
>
>
>> On Mon, Oct 2, 2017 at 11:45 AM, Mark Adams <mfadams at lbl.gov> wrote:
>>
>>> This is normal:
>>>
>>> Linear st_gamg_est_ solve did not converge due to DIVERGED_ITS
>>> iterations 10
>>>
>>> It looks like ksp->errorifnotconverged got set somehow. If the default
>>> changed in KSP then (SAGG) GAMG would not ever work.
>>>
>>> I assume you don't have a .petscrc file with more (crazy) options in it
>>> ...
>>>
>>>
>>> On Mon, Oct 2, 2017 at 11:39 AM, Wenbo Zhao <zhaowenbo.npic at gmail.com>
>>> wrote:
>>>
>>>>
>>>>
>>>> On Mon, Oct 2, 2017 at 11:30 PM, Matthew Knepley <knepley at gmail.com>
>>>> wrote:
>>>>
>>>>> On Mon, Oct 2, 2017 at 11:15 AM, Mark Adams <mfadams at lbl.gov> wrote:
>>>>>
>>>>>> non-smoothed aggregation is converging very fast. smoothed fails in
>>>>>> the eigen estimator.
>>>>>>
>>>>>> Run this again with -st_gamg_est_ksp_view and
>>>>>> -st_gamg_est_ksp_monitor, and see if you get more output (I'm not 100% sure
>>>>>> about these args).
>>>>>>
>>>>>
>>>>> I also want -st_gamg_est_ksp_converged_reason
>>>>>
>>>>> Thanks,
>>>>>
>>>>> Matt
>>>>>
>>>> $make NCORE=1 runkr_smooth
>>>> mpirun -n 1 ./step-41 \
>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1 \
>>>> -mata AMAT.dat -matb BMAT.dat \
>>>> -st_gamg_est_ksp_view -st_gamg_est_ksp_monitor \
>>>> -st_gamg_est_ksp_converged_reason \
>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1
>>>> makefile:43: recipe for target 'runkr_smooth' failed
>>>> make: *** [runkr_smooth] Error 91
>>>>
>>>> Thanks
>>>> Wenbo
>>>>
>>>>
>>>>>
>>>>>
>>>>>>
>>>>>> On Mon, Oct 2, 2017 at 11:06 AM, Wenbo Zhao <zhaowenbo.npic at gmail.com
>>>>>> > wrote:
>>>>>>
>>>>>>> Matt,
>>>>>>>
>>>>>>> Test 1 nonsmooth
>>>>>>> zhaowenbo at ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1
>>>>>>> runkr_nonsmooth
>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 0 \
>>>>>>> -mata AMAT.dat -matb BMAT.dat \
>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_nonsmooth
>>>>>>> 2>&1
>>>>>>>
>>>>>>> Test 2 smooth
>>>>>>> zhaowenbo at ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1
>>>>>>> runkr_smooth
>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1 \
>>>>>>> -mata AMAT.dat -matb BMAT.dat \
>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1
>>>>>>> makefile:43: recipe for target 'runkr_smooth' failed
>>>>>>> make: *** [runkr_smooth] Error 91
>>>>>>>
>>>>>>>
>>>>>>> Thanks,
>>>>>>>
>>>>>>> Wenbo
>>>>>>>
>>>>>>> On Mon, Oct 2, 2017 at 10:48 PM, Matthew Knepley <knepley at gmail.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> On Mon, Oct 2, 2017 at 10:43 AM, Wenbo Zhao <
>>>>>>>> zhaowenbo.npic at gmail.com> wrote:
>>>>>>>>
>>>>>>>>> Mark,
>>>>>>>>>
>>>>>>>>> Thanks for your reply.
>>>>>>>>>
>>>>>>>>> On Mon, Oct 2, 2017 at 9:51 PM, Mark Adams <mfadams at lbl.gov>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>> Please send the output with -st_ksp_view and -st_ksp_monitor and
>>>>>>>>>> we can start to debug it.
>>>>>>>>>>
>>>>>>>>>> Test 1 with nonsmooth and preonly is OK
>>>>>>>>> zhaowenbo at ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1
>>>>>>>>> runkr_nonsmooth
>>>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths
>>>>>>>>> 0 \
>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \
>>>>>>>>> -st_mg_coarse_ksp_type preonly -st_mg_coarse_ksp_monitor \
>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_nonsmooth
>>>>>>>>> 2>&1
>>>>>>>>>
>>>>>>>>> Test 2 smooth and preonly is not OK
>>>>>>>>> zhaowenbo at ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1
>>>>>>>>> runkr_smooth
>>>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths
>>>>>>>>> 1 \
>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \
>>>>>>>>> -st_mg_coarse_ksp_type preonly -st_mg_coarse_ksp_monitor \
>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1
>>>>>>>>> makefile:43: recipe for target 'runkr_smooth' failed
>>>>>>>>> make: *** [runkr_smooth] Error 91
>>>>>>>>>
>>>>>>>>> Test 3 nonsmooth and gmres is not OK
>>>>>>>>> zhaowenbo at ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1
>>>>>>>>> runkr_gmres
>>>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \
>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths
>>>>>>>>> 0 \
>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \
>>>>>>>>> -st_mg_coarse_ksp_type gmres -st_mg_coarse_ksp_monitor
>>>>>>>>> -st_mg_coarse_ksp_rtol 1.0e-6 \
>>>>>>>>>
>>>>>>>>
>>>>>>>> DO NOT DO THIS. Please send the output where you do NOTHING to the
>>>>>>>> coarse solver.
>>>>>>>>
>>>>>>>> Thanks,
>>>>>>>>
>>>>>>>> Matt
>>>>>>>>
>>>>>>>>
>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_gmres 2>&1
>>>>>>>>> makefile:59: recipe for target 'runkr_gmres' failed
>>>>>>>>> make: *** [runkr_gmres] Error 91
>>>>>>>>>
>>>>>>>>> log-files is attached.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You mentioned that B is not symmetric. I assume it is elliptic
>>>>>>>>>> (diffusion). Where does the asymmetry come from?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> It is a two-group diffusion equations, where group denotes neutron
>>>>>>>>> enegry discretisation.
>>>>>>>>> Matrix B consists of neutron diffusion/leakage term, removal term
>>>>>>>>> and minus neutron scatter source term between different energies, when
>>>>>>>>> matrix A denotes neutron fission source.
>>>>>>>>>
>>>>>>>>> Diffusion term(Laplace operator) is elliptic and symmetric.
>>>>>>>>> Removal term is diagonal only. However scatter term is asymmetry since
>>>>>>>>> scatter term from high energy to low energy is far greater than the term
>>>>>>>>> from low to high.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Wenbo
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> On Mon, Oct 2, 2017 at 9:39 AM, Wenbo Zhao <
>>>>>>>>>> zhaowenbo.npic at gmail.com> wrote:
>>>>>>>>>>
>>>>>>>>>>> Matt,
>>>>>>>>>>> Thanks for your reply.
>>>>>>>>>>> For the defalt option doesnt work firstly( -st_ksp_type gmres
>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1), I tried
>>>>>>>>>>> to test those options.
>>>>>>>>>>>
>>>>>>>>>>> Wenbo
>>>>>>>>>>>
>>>>>>>>>>> On Mon, Oct 2, 2017 at 9:08 PM, Matthew Knepley <
>>>>>>>>>>> knepley at gmail.com> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> On Mon, Oct 2, 2017 at 8:30 AM, Wenbo Zhao <
>>>>>>>>>>>> zhaowenbo.npic at gmail.com> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>
>>>>>>>>>>>>> Because I am not clear about what will happen using 'preonly'
>>>>>>>>>>>>> for large scale problem.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> The size of the problem has nothing to do with 'preonly'. All
>>>>>>>>>>>> it means is to apply a preconditioner without a Krylov solver.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> It seems to use a direct solver from below,
>>>>>>>>>>>>> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/
>>>>>>>>>>>>> KSP/KSPPREONLY.html
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> However, I still cannot understand why you would change the
>>>>>>>>>>>> default?
>>>>>>>>>>>>
>>>>>>>>>>>> Matt
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thanks!
>>>>>>>>>>>>> Wenbo
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Mon, Oct 2, 2017 at 5:09 PM, Matthew Knepley <
>>>>>>>>>>>>> knepley at gmail.com> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On Sun, Oct 1, 2017 at 9:53 PM, Wenbo Zhao <
>>>>>>>>>>>>>> zhaowenbo.npic at gmail.com> wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Matt,
>>>>>>>>>>>>>>> Thanks for your reply.
>>>>>>>>>>>>>>> It DOES make no sense for this problem.
>>>>>>>>>>>>>>> But I am not clear about the 'preonly' option. Which solver
>>>>>>>>>>>>>>> is used in preonly? I wonder if 'preonly' is suitable for large scale
>>>>>>>>>>>>>>> problem such as 400,000,000 unknowns.
>>>>>>>>>>>>>>> So I tried 'gmres' option and found these error messages.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I mean, why are you setting this at all. Just do not set the
>>>>>>>>>>>>>> coarse solver. The default should work fine.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Could you give me some suggestions?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Thanks.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Wenbo
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On Mon, Oct 2, 2017 at 12:34 AM, Matthew Knepley <
>>>>>>>>>>>>>>> knepley at gmail.com> wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On Sun, Oct 1, 2017 at 6:49 AM, Wenbo Zhao <
>>>>>>>>>>>>>>>> zhaowenbo.npic at gmail.com> wrote:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Hi,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I met some questions when I use PETSC/SLEPC to solve
>>>>>>>>>>>>>>>>> two-group neutron diffusion equations with finite difference method. The
>>>>>>>>>>>>>>>>> grid is 3*3*3, when DOF on each points is 2. So the matrix size is 54*54.
>>>>>>>>>>>>>>>>> It is generalized eigenvalue problem Ax=\lamda Bx, where B
>>>>>>>>>>>>>>>>> is diagonally dominant matrix but not symmetry.
>>>>>>>>>>>>>>>>> EPS is set as below,
>>>>>>>>>>>>>>>>> ierr = EPSSetProblemType(eps,EPS_GNHEP);CHKERRQ(ierr);¬
>>>>>>>>>>>>>>>>> ierr = EPSSetWhichEigenpairs(eps,EPS_
>>>>>>>>>>>>>>>>> LARGEST_REAL);CHKERRQ(ierr);¬
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Krylovschur is used as eps sovler. GAMG is used as PC.
>>>>>>>>>>>>>>>>> I tried agg_nsmooths and mg_coarse_ksp_type. Only
>>>>>>>>>>>>>>>>> non-smooths and preonly is OK.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Why are you setting the coarse solver. This makes no sense.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Thanks,
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Test 1
>>>>>>>>>>>>>>>>> $ make NCORE=1 runkr_nonsmooth
>>>>>>>>>>>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>>>>>>>>>>>> -st_ksp_type gmres \
>>>>>>>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg
>>>>>>>>>>>>>>>>> -st_pc_gamg_agg_nsmooths 0 \
>>>>>>>>>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \
>>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_type preonly
>>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_monitor \
>>>>>>>>>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view >
>>>>>>>>>>>>>>>>> log_nonsmooth 2>&1
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Test 2
>>>>>>>>>>>>>>>>> $ make NCORE=1 runkr_smooth
>>>>>>>>>>>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>>>>>>>>>>>> -st_ksp_type gmres \
>>>>>>>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg
>>>>>>>>>>>>>>>>> -st_pc_gamg_agg_nsmooths 1 \
>>>>>>>>>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \
>>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_type preonly
>>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_monitor \
>>>>>>>>>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view >
>>>>>>>>>>>>>>>>> log_smooth 2>&1
>>>>>>>>>>>>>>>>> makefile:43: recipe for target 'runkr_smooth' failed
>>>>>>>>>>>>>>>>> make: *** [runkr_smooth] Error 91
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Test 3
>>>>>>>>>>>>>>>>> $ make NCORE=1 runkr_gmres
>>>>>>>>>>>>>>>>> mpirun -n 1 ./step-41 \
>>>>>>>>>>>>>>>>> -st_ksp_type gmres \
>>>>>>>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg
>>>>>>>>>>>>>>>>> -st_pc_gamg_agg_nsmooths 0 \
>>>>>>>>>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \
>>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_type gmres -st_mg_coarse_ksp_monitor
>>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_rtol 1.0e-6 \
>>>>>>>>>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view >
>>>>>>>>>>>>>>>>> log_gmres 2>&1
>>>>>>>>>>>>>>>>> makefile:59: recipe for target 'runkr_gmres' failed
>>>>>>>>>>>>>>>>> make: *** [runkr_gmres] Error 91
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Log files were attched.
>>>>>>>>>>>>>>>>> The matrix file were also attched as AMAT.dat and BMAT.dat.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Is it correct? Or something wrong with my code or
>>>>>>>>>>>>>>>>> commad-line?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Thanks!
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Wenbo
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>> 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
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>>>>>> <http://www.caam.rice.edu/%7Emk51/>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> 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
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>>>> <http://www.caam.rice.edu/%7Emk51/>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> --
>>>>>>>>>>>> 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
>>>>>>>>>>>>
>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>> <http://www.caam.rice.edu/%7Emk51/>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> 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
>>>>>>>>
>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>> <http://www.caam.rice.edu/%7Emk51/>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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
>>>>>
>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>> <http://www.caam.rice.edu/%7Emk51/>
>>>>>
>>>>
>>>>
>>>
>>
>
--
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
https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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