[petsc-users] negative grid complexity in GAMG
Mark Lohry
mlohry at gmail.com
Thu Oct 17 07:07:19 CDT 2019
>
> So with many fewer levels, are you saying
>
> a) It takes more iterates?
>
> b) It takes the same wall clock time?
>
Slightly more iterates but at roughly the same wall clock time. Only did a
short test but the runtime difference looks like it was in the noise.
> I think you might want to switch to beefier smoothers on those lower
> levels if you see
> more iterates.
>
I was thinking the same. I just did a quick run with 2 smoother iterates
per level instead of 1 and got maybe 20% performance benefit, so I'll play
with that a bit more. I figure ILU(0) is already a pretty beefy smoother
here especially because of the very large blocks; ILU(1) is out because of
memory consumption, unless I only do it on the coarsened levels. On much
stiffer problems I saw considerable benefit from doing gmres+ILU(0) for 5
iterations per level, so I'll give that a shot.
On Thu, Oct 17, 2019 at 6:48 AM Matthew Knepley <knepley at gmail.com> wrote:
> On Thu, Oct 17, 2019 at 6:22 AM Mark Lohry via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>> Hi Mark,
>>
>> I assume these are advection problems and smoothed aggregation does not
>>> work well.
>>>
>>
>> Correct, it stagnates immediately with smoothed aggregation.
>>
>>
>> I think '-pc_gamg_square_graph 20' should reduce the number of levels and
>>> work better for you.
>>>
>>
>> On the big problem it's producing 20 levels without -pc_gamg_square_graph
>> 20; with that on it produces 6 levels. It certainly has less of the
>> near-identical-size coarse levels, but overall convergence time is roughly
>> the same. Any suggestion of where to go from here?
>>
>
> So with many fewer levels, are you saying
>
> a) It takes more iterates?
>
> b) It takes the same wall clock time?
>
> I think you might want to switch to beefier smoothers on those lower
> levels if you see
> more iterates. Mark?
>
> Thanks,
>
> Matt
>
>
>> Original setup without pc_gamg_square_graph 20:
>>
>> [0] PCSetUp_GAMG(): level 0) N=347149550, n data rows=5, n data cols=5,
>> nnz/row (ave)=250, np=1920
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 50. nnz ave. (N=69429910)
>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
>> [0] PCGAMGProlongator_AGG(): New grid 894786 nodes
>> [0] PCSetUp_GAMG(): 1) N=4473930, n data cols=5, nnz/row (ave)=51, 1920
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 10.1761 nnz ave. (N=894786)
>> [0] PCGAMGProlongator_AGG(): New grid 184262 nodes
>> [0] PCSetUp_GAMG(): 2) N=921310, n data cols=5, nnz/row (ave)=68, 1920
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 13.0556 nnz ave. (N=184262)
>> [0] PCGAMGProlongator_AGG(): New grid 41002 nodes
>> [0] PCSetUp_GAMG(): 3) N=205010, n data cols=5, nnz/row (ave)=72, 1920
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 10.0909 nnz ave. (N=41002)
>> [0] PCGAMGProlongator_AGG(): New grid 12587 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 20 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 4) N=62935, n data cols=5, nnz/row (ave)=62, 960
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 5.33333 nnz ave. (N=12587)
>> [0] PCGAMGProlongator_AGG(): New grid 5811 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 40 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 5) N=29055, n data cols=5, nnz/row (ave)=50, 640
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.8 nnz ave. (N=5811)
>> [0] PCGAMGProlongator_AGG(): New grid 3442 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 110 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 6) N=17210, n data cols=5, nnz/row (ave)=40, 320
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 4.66176 nnz ave. (N=3442)
>> [0] PCGAMGProlongator_AGG(): New grid 2365 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 275 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 7) N=11825, n data cols=5, nnz/row (ave)=34, 240
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 4.961 nnz ave. (N=2365)
>> [0] PCGAMGProlongator_AGG(): New grid 1792 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 1125 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 8) N=8960, n data cols=5, nnz/row (ave)=28, 192
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 5.79911 nnz ave. (N=1792)
>> [0] PCGAMGProlongator_AGG(): New grid 1479 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 7395 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 9) N=7395, n data cols=5, nnz/row (ave)=24, 160
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 4.86883 nnz ave. (N=1479)
>> [0] PCGAMGProlongator_AGG(): New grid 1378 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 6890 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 10) N=6890, n data cols=5, nnz/row (ave)=22, 128
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 4.44702 nnz ave. (N=1378)
>> [0] PCGAMGProlongator_AGG(): New grid 1210 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 6050 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 11) N=6050, n data cols=5, nnz/row (ave)=18, 120
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.64298 nnz ave. (N=1210)
>> [0] PCGAMGProlongator_AGG(): New grid 1185 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=120,
>> neq(loc)=5925
>> [0] PCSetUp_GAMG(): 12) N=5925, n data cols=5, nnz/row (ave)=17, 120
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.54177 nnz ave. (N=1185)
>> [0] PCGAMGProlongator_AGG(): New grid 1165 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=120,
>> neq(loc)=5825
>> [0] PCSetUp_GAMG(): 13) N=5825, n data cols=5, nnz/row (ave)=17, 120
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.5133 nnz ave. (N=1165)
>> [0] PCGAMGProlongator_AGG(): New grid 1137 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=120,
>> neq(loc)=5685
>> [0] PCSetUp_GAMG(): 14) N=5685, n data cols=5, nnz/row (ave)=17, 120
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.48021 nnz ave. (N=1137)
>> [0] PCGAMGProlongator_AGG(): New grid 1097 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=120,
>> neq(loc)=5485
>> [0] PCSetUp_GAMG(): 15) N=5485, n data cols=5, nnz/row (ave)=16, 120
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.3938 nnz ave. (N=1097)
>> [0] PCGAMGProlongator_AGG(): New grid 1088 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=120,
>> neq(loc)=5440
>> [0] PCSetUp_GAMG(): 16) N=5440, n data cols=5, nnz/row (ave)=16, 120
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.34375 nnz ave. (N=1088)
>> [0] PCGAMGProlongator_AGG(): New grid 852 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 4260 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 17) N=4260, n data cols=5, nnz/row (ave)=15, 80
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.06103 nnz ave. (N=852)
>> [0] PCGAMGProlongator_AGG(): New grid 848 nodes
>> [0] PCSetUp_GAMG(): 18) N=4240, n data cols=5, nnz/row (ave)=15, 80
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 3.0566 nnz ave. (N=848)
>> [0] PCGAMGProlongator_AGG(): New grid 3 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 15 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 19) N=15, n data cols=5, nnz/row (ave)=11, 1 active
>> pes
>> [0] PCSetUp_GAMG(): 20 levels, grid complexity = 1.00367
>>
>> With pc_gamg_square_graph 20:
>>
>>
>> [0] PCSetUp_GAMG(): level 0) N=347149550, n data rows=5, n data cols=5,
>> nnz/row (ave)=250, np=1920
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 50. nnz ave. (N=69429910)
>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 20 to square
>> [0] PCGAMGProlongator_AGG(): New grid 894786 nodes
>> [0] PCSetUp_GAMG(): 1) N=4473930, n data cols=5, nnz/row (ave)=51, 1920
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 10.1761 nnz ave. (N=894786)
>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 2 of 20 to square
>> [0] PCGAMGProlongator_AGG(): New grid 49106 nodes
>> [0] PCSetUp_GAMG(): 2) N=245530, n data cols=5, nnz/row (ave)=80, 1920
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 14.8 nnz ave. (N=49106)
>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 3 of 20 to square
>> [0] PCGAMGProlongator_AGG(): New grid 1646 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 0 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 3) N=8230, n data cols=5, nnz/row (ave)=86, 160
>> active pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 11.5 nnz ave. (N=1646)
>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 4 of 20 to square
>> [0] PCGAMGProlongator_AGG(): New grid 56 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 0 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 4) N=280, n data cols=5, nnz/row (ave)=62, 6 active
>> pes
>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>> 12.5714 nnz ave. (N=56)
>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 5 of 20 to square
>> [0] PCGAMGProlongator_AGG(): New grid 4 nodes
>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 20 with simple
>> aggregation
>> [0] PCSetUp_GAMG(): 5) N=20, n data cols=5, nnz/row (ave)=17, 1 active pes
>> [0] PCSetUp_GAMG(): 6 levels, grid complexity = 1.00291
>>
>> On Wed, Oct 16, 2019 at 9:46 PM Mark Adams <mfadams at lbl.gov> wrote:
>>
>>> The block size refers to the number of dofs/vertex, so you want 5. (I
>>> have no idea what is going on with block size set to 20).
>>>
>>> This is better but also smaller. 10 levels is a lot a levels.
>>>
>>> This is unsmoothed aggregation. I assume these are advection problems
>>> and smoothed aggregation does not work well. This is not in my wheelhouse.
>>> I think '-pc_gamg_square_graph 20' should reduce the number of levels and
>>> work better for you.
>>>
>>> Thanks,
>>> Mark
>>>
>>> On Wed, Oct 16, 2019 at 8:59 PM Mark Lohry <mlohry at gmail.com> wrote:
>>>
>>>> Hi Mark, are you referring to how on the coarser levels the coarsening
>>>> rate seems to nearly flatline? i.e. level 2 has 4,260 rows while level 1
>>>> has 4,240 rows? I was curious about that too...
>>>>
>>>> Not sure if this is the cause, but I have gone back and forth on what
>>>> blocksize I set; I'm doing high order elements with 5 coupled equations, so
>>>> the true block size in that case is 50x50. For that I had played with
>>>> setting block size to either 5 (number of equations) or 50 (actual block
>>>> size) and seemed to have seen a meager 20% improvement with the block size
>>>> at 5, so I kind of left it there.
>>>>
>>>> Running a much smaller variant of the same problem at lower order
>>>> (block size 20 instead of 50), the -info grep you asked for is below. I'll
>>>> get -info for the much larger case but it'll take a couple days.
>>>>
>>>> For options I'm running
>>>> -snes_lag_jacobian 10000 -ksp_gmres_restart 100 -pc_gamg_agg_nsmooths 0
>>>> -mg_levels_ksp_type richardson -mg_levels_pc_type asm -mg_levels_ksp_max_it
>>>> 1
>>>> -pc_mg_cycle_type v -snes_linesearch_type bt -snes_linesearch_order 3
>>>> -snes_linesearch_monitor -mg_levels_sub_pc_factor_in_place true -info
>>>>
>>>>
>>>> block size 5 :
>>>>
>>>> [0] PCSetUp_GAMG(): level 0) N=2006480, n data rows=5, n data cols=5,
>>>> nnz/row (ave)=100, np=16
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 20. nnz ave. (N=401296)
>>>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
>>>> [0] PCGAMGProlongator_AGG(): New grid 12947 nodes
>>>> [0] PCSetUp_GAMG(): 1) N=64735, n data cols=5, nnz/row (ave)=51, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 10.3351 nnz ave. (N=12947)
>>>> [0] PCGAMGProlongator_AGG(): New grid 2671 nodes
>>>> [0] PCSetUp_GAMG(): 2) N=13355, n data cols=5, nnz/row (ave)=66, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 12.5524 nnz ave. (N=2671)
>>>> [0] PCGAMGProlongator_AGG(): New grid 598 nodes
>>>> [0] PCSetUp_GAMG(): 3) N=2990, n data cols=5, nnz/row (ave)=65, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 12.7727 nnz ave. (N=598)
>>>> [0] PCGAMGProlongator_AGG(): New grid 178 nodes
>>>> [0] PCSetUp_GAMG(): 4) N=890, n data cols=5, nnz/row (ave)=52, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 8.28571 nnz ave. (N=178)
>>>> [0] PCGAMGProlongator_AGG(): New grid 80 nodes
>>>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 30 with simple
>>>> aggregation
>>>> [0] PCSetUp_GAMG(): 5) N=400, n data cols=5, nnz/row (ave)=34, 8 active
>>>> pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 5.77778 nnz ave. (N=80)
>>>> [0] PCGAMGProlongator_AGG(): New grid 50 nodes
>>>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 30 with simple
>>>> aggregation
>>>> [0] PCSetUp_GAMG(): 6) N=250, n data cols=5, nnz/row (ave)=25, 4 active
>>>> pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 4.76923 nnz ave. (N=50)
>>>> [0] PCGAMGProlongator_AGG(): New grid 36 nodes
>>>> [0] PCSetUp_GAMG(): 7) N=180, n data cols=5, nnz/row (ave)=18, 4 active
>>>> pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 3.75 nnz ave. (N=36)
>>>> [0] PCGAMGProlongator_AGG(): New grid 33 nodes
>>>> [0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=4,
>>>> neq(loc)=90
>>>> [0] PCSetUp_GAMG(): 8) N=165, n data cols=5, nnz/row (ave)=18, 4 active
>>>> pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 3.72222 nnz ave. (N=33)
>>>> [0] PCGAMGProlongator_AGG(): New grid 8 nodes
>>>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 35 with simple
>>>> aggregation
>>>> [0] PCSetUp_GAMG(): 9) N=40, n data cols=5, nnz/row (ave)=15, 1 active
>>>> pes
>>>> [0] PCSetUp_GAMG(): 10 levels, grid complexity = 1.02237
>>>>
>>>>
>>>>
>>>> block size 20:
>>>>
>>>> [0] PCSetUp_GAMG(): level 0) N=2006480, n data rows=20, n data cols=20,
>>>> nnz/row (ave)=100, np=16
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 5. nnz ave. (N=100324)
>>>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
>>>> [0] PCGAMGProlongator_AGG(): New grid 12948 nodes
>>>> [0] PCSetUp_GAMG(): 1) N=258960, n data cols=20, nnz/row (ave)=205, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 10.2857 nnz ave. (N=12948)
>>>> [0] PCGAMGProlongator_AGG(): New grid 2671 nodes
>>>> [0] PCSetUp_GAMG(): 2) N=53420, n data cols=20, nnz/row (ave)=266, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 12.5548 nnz ave. (N=2671)
>>>> [0] PCGAMGProlongator_AGG(): New grid 593 nodes
>>>> [0] PCSetUp_GAMG(): 3) N=11860, n data cols=20, nnz/row (ave)=264, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 10.8519 nnz ave. (N=593)
>>>> [0] PCGAMGProlongator_AGG(): New grid 181 nodes
>>>> [0] PCSetUp_GAMG(): 4) N=3620, n data cols=20, nnz/row (ave)=214, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 8.375 nnz ave. (N=181)
>>>> [0] PCGAMGProlongator_AGG(): New grid 79 nodes
>>>> [0] PCSetUp_GAMG(): 5) N=1580, n data cols=20, nnz/row (ave)=164, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 8. nnz ave. (N=79)
>>>> [0] PCGAMGProlongator_AGG(): New grid 43 nodes
>>>> [0] PCSetUp_GAMG(): 6) N=860, n data cols=20, nnz/row (ave)=100, 16
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 5. nnz ave. (N=43)
>>>> [0] PCGAMGProlongator_AGG(): New grid 15 nodes
>>>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 20 with simple
>>>> aggregation
>>>> [0] PCSetUp_GAMG(): 7) N=300, n data cols=20, nnz/row (ave)=81, 8
>>>> active pes
>>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
>>>> 2.66667 nnz ave. (N=15)
>>>> [0] PCGAMGProlongator_AGG(): New grid 1 nodes
>>>> [0] PCGAMGCreateLevel_GAMG(): Number of equations (loc) 0 with simple
>>>> aggregation
>>>> [0] PCSetUp_GAMG(): 8) N=20, n data cols=20, nnz/row (ave)=20, 1 active
>>>> pes
>>>> [0] PCSetUp_GAMG(): HARD stop of coarsening on level 7. Grid too
>>>> small: 1 block nodes
>>>> [0] PCSetUp_GAMG(): 9 levels, grid complexity = 1.35745
>>>>
>>>> On Wed, Oct 16, 2019 at 5:12 PM Mark Adams <mfadams at lbl.gov> wrote:
>>>>
>>>>> Thanks Barry,
>>>>> Sorry I missed this.
>>>>> Mark: this problem is going crazy. The (default) coarsening parameters
>>>>> are terrible for you. Can run with -info, grep for GAMG and send that? And
>>>>> please send me the gamg parameters that you are using.
>>>>> Thanks,
>>>>> Mark
>>>>>
>>>>> On Wed, Oct 16, 2019 at 9:01 AM Smith, Barry F. via petsc-users <
>>>>> petsc-users at mcs.anl.gov> wrote:
>>>>>
>>>>>>
>>>>>> barry/2019-10-15/bug-gamg-complexity/maint
>>>>>> https://gitlab.com/petsc/petsc/merge_requests/2179
>>>>>>
>>>>>>
>>>>>>
>>>>>> > On Oct 16, 2019, at 5:29 AM, Mark Lohry <mlohry at gmail.com> wrote:
>>>>>> >
>>>>>> > Well that was a quick late night bug fix. Thanks Barry, I'll try it
>>>>>> out.
>>>>>> >
>>>>>> > Just to confirm: You are running with with default double precision
>>>>>> numbers and have used the configure option --with-64-bit-indices ?
>>>>>> >
>>>>>> > Double precision floats, but 32 bit indices. I realize I'm playing
>>>>>> with fire here, but I'm bumping very close to available memory limits at
>>>>>> this scale and 64 bit indices tips me over. I figure integer index
>>>>>> overflows would probably show a catastrophic failure, but all output looks
>>>>>> sane.
>>>>>> >
>>>>>> > I see you are using MATMFFD as the operator and MPIAIJ as the
>>>>>> matrix from which to build the preconditioner? This is not suppose to cause
>>>>>> any difficulties since the complexity computation code uses the second
>>>>>> matrix, that is the MPAIJ matrix to get the complexity information.
>>>>>> >
>>>>>> > Right, I'm using MATMFFD for the operator, and using a
>>>>>> snes_lag_jacobian with SNESComputeJacobianDefaultColor for the matrix used
>>>>>> to build to preconditioner. The actual behavior is exactly what I'd expect
>>>>>> from smaller runs and the results look good, so it sounds like what you
>>>>>> describe.
>>>>>> >
>>>>>> > On Wed, Oct 16, 2019 at 12:17 AM Smith, Barry F. <
>>>>>> bsmith at mcs.anl.gov> wrote:
>>>>>> >
>>>>>> > I think I now see the bug: the code uses PetscInt lev,
>>>>>> nnz0 = -1; which will overflow. It should be using PetscLogDouble for nnz0
>>>>>> >
>>>>>> > You can try changing that one place in the code and see that it
>>>>>> now prints a reasonable value for complexity.
>>>>>> >
>>>>>> > I will prepare a MR for maint to fix the bug permanently.
>>>>>> >
>>>>>> > Barry
>>>>>> >
>>>>>> >
>>>>>> > static PetscErrorCode PCMGGetGridComplexity(PC pc, PetscReal *gc)
>>>>>> > {
>>>>>> > PetscErrorCode ierr;
>>>>>> > PC_MG *mg = (PC_MG*)pc->data;
>>>>>> > PC_MG_Levels **mglevels = mg->levels;
>>>>>> > PetscInt lev, nnz0 = -1;
>>>>>> > MatInfo info;
>>>>>> > PetscFunctionBegin;
>>>>>> > if (!mg->nlevels) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MG has
>>>>>> no levels");
>>>>>> > for (lev=0, *gc=0; lev<mg->nlevels; lev++) {
>>>>>> > Mat dB;
>>>>>> > ierr =
>>>>>> KSPGetOperators(mglevels[lev]->smoothd,NULL,&dB);CHKERRQ(ierr);
>>>>>> > ierr = MatGetInfo(dB,MAT_GLOBAL_SUM,&info);CHKERRQ(ierr); /*
>>>>>> global reduction */
>>>>>> > *gc += (PetscReal)info.nz_used;
>>>>>> > if (lev==mg->nlevels-1) nnz0 = info.nz_used;
>>>>>> > }
>>>>>> > if (nnz0) *gc /= (PetscReal)nnz0;
>>>>>> > else *gc = 0;
>>>>>> > PetscFunctionReturn(0);
>>>>>> > }
>>>>>> >
>>>>>> >
>>>>>> >
>>>>>> > > On Oct 15, 2019, at 11:11 PM, Smith, Barry F. <bsmith at mcs.anl.gov>
>>>>>> wrote:
>>>>>> > >
>>>>>> > >
>>>>>> > > Mark,
>>>>>> > >
>>>>>> > > It may be caused by some overflow in the calculations somewhere
>>>>>> due to your very large sizes and nonzeros but I could not see anything
>>>>>> based on a quick inspection of the code. We seem to use double to store the
>>>>>> counts which normally would be more than sufficient to hold the results
>>>>>> without overflow. Unless somewhere there is a mistaken use of int that
>>>>>> causes a problem.
>>>>>> > >
>>>>>> > > Just to confirm: You are running with with default double
>>>>>> precision numbers and have used the configure option --with-64-bit-indices
>>>>>> ?
>>>>>> > >
>>>>>> > > I see you are using MATMFFD as the operator and MPIAIJ as the
>>>>>> matrix from which to build the preconditioner? This is not suppose to cause
>>>>>> any difficulties since the complexity computation code uses the second
>>>>>> matrix, that is the MPAIJ matrix to get the complexity information.
>>>>>> > >
>>>>>> > > There is definitely a bug but I am hard pressed to suggest how
>>>>>> to find it since it seems only to be expressed in your giant runs.
>>>>>> > >
>>>>>> > > Barry
>>>>>> > >
>>>>>> > >
>>>>>> > >
>>>>>> > >
>>>>>> > >
>>>>>> > >> On Oct 15, 2019, at 9:16 PM, Mark Lohry via petsc-users <
>>>>>> petsc-users at mcs.anl.gov> wrote:
>>>>>> > >>
>>>>>> > >> I'm running some larger unsteady problems and trying to eek out
>>>>>> some better GAMG performance. As is, at very small time steps, ASM
>>>>>> preconditioner with ILU(0) is maybe 20% more efficient than my naive GAMG
>>>>>> setup, which gives me hope that some tuning of GAMG can give some
>>>>>> advantage. Convergence overall seems quite good, and light years better
>>>>>> than ASM/ILU at larger time steps.
>>>>>> > >>
>>>>>> > >> So looking through the manual and see a note that "grid
>>>>>> complexity should be well under 2.0 and preferably around 1.3 or lower". I
>>>>>> check ksp_view and see:
>>>>>> > >> Complexity: grid = -40.5483
>>>>>> > >>
>>>>>> > >> Is something funny happening here?
>>>>>> > >>
>>>>>> > >> Pasting whole -ksp_view below:
>>>>>> > >>
>>>>>> > >> KSP Object: 1920 MPI processes
>>>>>> > >> type: fgmres
>>>>>> > >> restart=100, using Classical (unmodified) Gram-Schmidt
>>>>>> Orthogonalization with no iterative refinement
>>>>>> > >> happy breakdown tolerance 1e-30
>>>>>> > >> maximum iterations=30, initial guess is zero
>>>>>> > >> tolerances: relative=0.0001, absolute=1e-06, divergence=10.
>>>>>> > >> right preconditioning
>>>>>> > >> using UNPRECONDITIONED norm type for convergence test
>>>>>> > >> PC Object: 1920 MPI processes
>>>>>> > >> type: gamg
>>>>>> > >> type is MULTIPLICATIVE, levels=20 cycles=v
>>>>>> > >> Cycles per PCApply=1
>>>>>> > >> Using externally compute Galerkin coarse grid matrices
>>>>>> > >> GAMG specific options
>>>>>> > >> Threshold for dropping small values in graph on each
>>>>>> level = 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
>>>>>> 0. 0. 0. 0. 0.
>>>>>> > >> Threshold scaling factor for each level not specified = 1.
>>>>>> > >> AGG specific options
>>>>>> > >> Symmetric graph false
>>>>>> > >> Number of levels to square graph 1
>>>>>> > >> Number smoothing steps 0
>>>>>> > >> Complexity: grid = -40.5483
>>>>>> > >> Coarse grid solver -- level -------------------------------
>>>>>> > >> KSP Object: (mg_coarse_) 1920 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: (mg_coarse_) 1920 MPI processes
>>>>>> > >> type: bjacobi
>>>>>> > >> number of blocks = 1920
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_coarse_sub_) 1 MPI processes
>>>>>> > >> type: preonly
>>>>>> > >> maximum iterations=1, initial guess is zero
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_coarse_sub_) 1 MPI processes
>>>>>> > >> type: lu
>>>>>> > >> out-of-place factorization
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> using diagonal shift on blocks to prevent zero pivot
>>>>>> [INBLOCKS]
>>>>>> > >> matrix ordering: nd
>>>>>> > >> factor fill ratio given 5., needed 1.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=15, cols=15, bs=5
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=175, allocated nonzeros=175
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 3 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=15, cols=15, bs=5
>>>>>> > >> total: nonzeros=175, allocated nonzeros=175
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 3 nodes, limit used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=15, cols=15, bs=5
>>>>>> > >> total: nonzeros=175, allocated nonzeros=175
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 3 nodes,
>>>>>> limit used is 5
>>>>>> > >> Down solver (pre-smoother) on level 1
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_1_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_1_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_1_sub_) 1 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: (mg_levels_1_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=4240, cols=4240
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=64800, allocated nonzeros=64800
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 848 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=4240, cols=4240
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=64800, allocated nonzeros=64800
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 848 nodes, limit used is
>>>>>> 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=4240, cols=4240, bs=5
>>>>>> > >> total: nonzeros=64800, allocated nonzeros=64800
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 848 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 2
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_2_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_2_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_2_sub_) 1 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: (mg_levels_2_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=4260, cols=4260
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=65200, allocated nonzeros=65200
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 852 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=4260, cols=4260
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=65200, allocated nonzeros=65200
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 852 nodes, limit used is
>>>>>> 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=4260, cols=4260, bs=5
>>>>>> > >> total: nonzeros=65200, allocated nonzeros=65200
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 852 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 3
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_3_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_3_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_3_sub_) 1 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: (mg_levels_3_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5440, cols=5440
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=90950, allocated nonzeros=90950
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1088 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5440, cols=5440
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=90950, allocated nonzeros=90950
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1088 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=5440, cols=5440, bs=5
>>>>>> > >> total: nonzeros=90950, allocated nonzeros=90950
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 1088 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 4
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_4_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_4_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_4_sub_) 1 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: (mg_levels_4_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5485, cols=5485
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=93075, allocated nonzeros=93075
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1097 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5485, cols=5485
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=93075, allocated nonzeros=93075
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1097 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=5485, cols=5485, bs=5
>>>>>> > >> total: nonzeros=93075, allocated nonzeros=93075
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 1097 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 5
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_5_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_5_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_5_sub_) 1 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: (mg_levels_5_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5685, cols=5685
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=98925, allocated nonzeros=98925
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1137 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5685, cols=5685
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=98925, allocated nonzeros=98925
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1137 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=5685, cols=5685, bs=5
>>>>>> > >> total: nonzeros=98925, allocated nonzeros=98925
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 1137 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 6
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_6_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_6_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_6_sub_) 1 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: (mg_levels_6_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5825, cols=5825
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=102325, allocated nonzeros=102325
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1165 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5825, cols=5825
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=102325, allocated nonzeros=102325
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1165 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=5825, cols=5825, bs=5
>>>>>> > >> total: nonzeros=102325, allocated nonzeros=102325
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 1165 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 7
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_7_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_7_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_7_sub_) 1 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: (mg_levels_7_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5925, cols=5925
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=104925, allocated nonzeros=104925
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1185 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=5925, cols=5925
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=104925, allocated nonzeros=104925
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1185 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=5925, cols=5925, bs=5
>>>>>> > >> total: nonzeros=104925, allocated nonzeros=104925
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 1185 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 8
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_8_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_8_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_8_sub_) 1 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: (mg_levels_8_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=6050, cols=6050
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=110200, allocated nonzeros=110200
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1210 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=6050, cols=6050
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=110200, allocated nonzeros=110200
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1210 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=6050, cols=6050, bs=5
>>>>>> > >> total: nonzeros=110200, allocated nonzeros=110200
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 1210 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 9
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_9_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_9_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_9_sub_) 1 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: (mg_levels_9_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=6890, cols=6890
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=153200, allocated nonzeros=153200
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1378 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=6890, cols=6890
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=153200, allocated nonzeros=153200
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1378 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=6890, cols=6890, bs=5
>>>>>> > >> total: nonzeros=153200, allocated nonzeros=153200
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 1378 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 10
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_10_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_10_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_10_sub_) 1 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: (mg_levels_10_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=7395, cols=7395
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=180025, allocated nonzeros=180025
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1479 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=7395, cols=7395
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=180025, allocated nonzeros=180025
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1479 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=7395, cols=7395, bs=5
>>>>>> > >> total: nonzeros=180025, allocated nonzeros=180025
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 1479 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 11
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_11_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_11_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_11_sub_) 1 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: (mg_levels_11_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=8960, cols=8960
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=259800, allocated nonzeros=259800
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 1792 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=8960, cols=8960
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=259800, allocated nonzeros=259800
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 1792 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=8960, cols=8960, bs=5
>>>>>> > >> total: nonzeros=259800, allocated nonzeros=259800
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 1792 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 12
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_12_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_12_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_12_sub_) 1 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: (mg_levels_12_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=1795, cols=1795
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=33275, allocated nonzeros=33275
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 359 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=1795, cols=1795
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=33275, allocated nonzeros=33275
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 359 nodes, limit used is
>>>>>> 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=11825, cols=11825, bs=5
>>>>>> > >> total: nonzeros=403125, allocated nonzeros=403125
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 359 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 13
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_13_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_13_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_13_sub_) 1 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: (mg_levels_13_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=340, cols=340
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=3500, allocated nonzeros=3500
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 68 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=340, cols=340
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=3500, allocated nonzeros=3500
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 68 nodes, limit used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=17210, cols=17210, bs=5
>>>>>> > >> total: nonzeros=696850, allocated nonzeros=696850
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 68 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 14
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_14_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_14_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_14_sub_) 1 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: (mg_levels_14_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=125, cols=125
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=625, allocated nonzeros=625
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 25 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=125, cols=125
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=625, allocated nonzeros=625
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 25 nodes, limit used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=29055, cols=29055, bs=5
>>>>>> > >> total: nonzeros=1475675, allocated nonzeros=1475675
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 25 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 15
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_15_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_15_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_15_sub_) 1 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: (mg_levels_15_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=45, cols=45
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=225, allocated nonzeros=225
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 9 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=45, cols=45
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=225, allocated nonzeros=225
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 9 nodes, limit used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=62935, cols=62935, bs=5
>>>>>> > >> total: nonzeros=3939025, allocated nonzeros=3939025
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 9 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 16
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_16_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_16_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_16_sub_) 1 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: (mg_levels_16_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=55, cols=55
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=725, allocated nonzeros=725
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 11 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=55, cols=55
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=725, allocated nonzeros=725
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 11 nodes, limit used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=205010, cols=205010, bs=5
>>>>>> > >> total: nonzeros=14780300, allocated nonzeros=14780300
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using scalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 11 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 17
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_17_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_17_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_17_sub_) 1 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: (mg_levels_17_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=360, cols=360
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=14350, allocated nonzeros=14350
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 72 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=360, cols=360
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=14350, allocated nonzeros=14350
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 72 nodes, limit used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=921310, cols=921310, bs=5
>>>>>> > >> total: nonzeros=63203300, allocated nonzeros=63203300
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using scalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 72 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 18
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_18_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_18_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_18_sub_) 1 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: (mg_levels_18_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=2130, cols=2130
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=87950, allocated nonzeros=87950
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 426 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=2130, cols=2130
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=87950, allocated nonzeros=87950
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 426 nodes, limit used is
>>>>>> 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=4473930, cols=4473930, bs=5
>>>>>> > >> total: nonzeros=232427300, allocated nonzeros=232427300
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using nonscalable MatPtAP() implementation
>>>>>> > >> using I-node (on process 0) routines: found 426 nodes,
>>>>>> limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> Down solver (pre-smoother) on level 19
>>>>>> -------------------------------
>>>>>> > >> KSP Object: (mg_levels_19_) 1920 MPI processes
>>>>>> > >> type: richardson
>>>>>> > >> damping factor=1.
>>>>>> > >> maximum iterations=1, nonzero initial guess
>>>>>> > >> tolerances: relative=1e-05, absolute=1e-50,
>>>>>> divergence=10000.
>>>>>> > >> left preconditioning
>>>>>> > >> using NONE norm type for convergence test
>>>>>> > >> PC Object: (mg_levels_19_) 1920 MPI processes
>>>>>> > >> type: asm
>>>>>> > >> total subdomain blocks = 1920, amount of overlap = 0
>>>>>> > >> restriction/interpolation type - RESTRICT
>>>>>> > >> Local solve is same for all blocks, in the following KSP
>>>>>> and PC objects:
>>>>>> > >> KSP Object: (mg_levels_19_sub_) 1 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: (mg_levels_19_sub_) 1 MPI processes
>>>>>> > >> type: ilu
>>>>>> > >> in-place factorization
>>>>>> > >> 0 levels of fill
>>>>>> > >> tolerance for zero pivot 2.22045e-14
>>>>>> > >> matrix ordering: natural
>>>>>> > >> factor fill ratio given 0., needed 0.
>>>>>> > >> Factored matrix follows:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=179050, cols=179050
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=42562500, allocated
>>>>>> nonzeros=42562500
>>>>>> > >> total number of mallocs used during MatSetValues
>>>>>> calls =0
>>>>>> > >> using I-node routines: found 35810 nodes, limit
>>>>>> used is 5
>>>>>> > >> linear system matrix = precond matrix:
>>>>>> > >> Mat Object: 1 MPI processes
>>>>>> > >> type: seqaij
>>>>>> > >> rows=179050, cols=179050
>>>>>> > >> package used to perform factorization: petsc
>>>>>> > >> total: nonzeros=42562500, allocated nonzeros=42562500
>>>>>> > >> total number of mallocs used during MatSetValues calls
>>>>>> =0
>>>>>> > >> using I-node routines: found 35810 nodes, limit used
>>>>>> is 5
>>>>>> > >> linear system matrix followed by preconditioner matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mffd
>>>>>> > >> rows=347149550, cols=347149550
>>>>>> > >> Matrix-free approximation:
>>>>>> > >> err=1.49012e-08 (relative error in function
>>>>>> evaluation)
>>>>>> > >> Using wp compute h routine
>>>>>> > >> Does not compute normU
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=347149550, cols=347149550, bs=5
>>>>>> > >> total: nonzeros=86758607500, allocated
>>>>>> nonzeros=86758607500
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 35810
>>>>>> nodes, limit used is 5
>>>>>> > >> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>> > >> linear system matrix followed by preconditioner matrix:
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mffd
>>>>>> > >> rows=347149550, cols=347149550
>>>>>> > >> Matrix-free approximation:
>>>>>> > >> err=1.49012e-08 (relative error in function evaluation)
>>>>>> > >> Using wp compute h routine
>>>>>> > >> Does not compute normU
>>>>>> > >> Mat Object: 1920 MPI processes
>>>>>> > >> type: mpiaij
>>>>>> > >> rows=347149550, cols=347149550, bs=5
>>>>>> > >> total: nonzeros=86758607500, allocated nonzeros=86758607500
>>>>>> > >> total number of mallocs used during MatSetValues calls =0
>>>>>> > >> using I-node (on process 0) routines: found 35810 nodes,
>>>>>> limit used is 5
>>>>>> > >> Line search: Using full step: fnorm 2.025875581923e+03
>>>>>> gnorm 2.801672254495e+00
>>>>>> > >> 1 SNES Function norm 2.801672254495e+00
>>>>>> > >
>>>>>> >
>>>>>>
>>>>>>
>
> --
> 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.cse.buffalo.edu/~knepley/>
>
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