[petsc-users] GAMG issue

John Mousel john.mousel at gmail.com
Thu Mar 29 13:40:28 CDT 2012


I'm attempting to solve a non-symmetric discretization of a 3D Poisson
problem. The problem is singular. I've attached the results of KSPView from
runs with ML and GAMG. When I run ML, I get convergence in 30 iterations.
When I attempt to use the same settings with GAMG, I'm not getting
convergence at all. The two things I notice are:

1. GAMG is using KSPType preonly, even though I've set it to be Richardson
in my command line options.
2. ML only coarsens down to 4 rows while GAMG coarsens to 2. My problem is
singular, and whenever I try to use LU, I get zero pivot problems. To
mitigate this, I've been using Richardson with SOR on the coarse matrix.
Could the smaller coarse grid size of GAMG be causing problems with SOR. If
so, is there a way to put a lower limit on the coarse grid size?

John

On Thu, Mar 29, 2012 at 11:03 AM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Thu, Mar 29, 2012 at 09:18, John Mousel <john.mousel at gmail.com> wrote:
>
>> [0]PETSC ERROR: Error in external library!
>> [0]PETSC ERROR: Cannot disable floating point exceptions!
>>
>
> Looks like something is strange with your environment because fesetenv()
> is returning an error. I have disabled the call if the trap mode is not
> changing.
>
> http://petsc.cs.iit.edu/petsc/petsc-dev/rev/352b4c19e451
>
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	[0]PCSetFromOptions_GAMG threshold set 1.000000e-02
	[0]PCSetUp_GAMG level 0 N=556240, n data rows=1, n data cols=1, nnz/row (ave)=27, np=4
	[0]PCGAMGFilterGraph 65.8687% nnz after filtering, with threshold 0.01, 27.0672 nnz ave.
	[0]maxIndSetAgg removed 0 of 556240 vertices. (0 local)  20114 selected.
		[0]PCGAMGProlongator_AGG New grid 20114 nodes
			PCGAMGOptprol_AGG smooth P0: max eigen=1.925528e+00 min=3.616018e-02 PC=jacobi
		[0]PCSetUp_GAMG 1) N=20114, n data cols=1, nnz/row (ave)=65, 4 active pes
	[0]PCGAMGFilterGraph 31.9285% nnz after filtering, with threshold 0.01, 65.3544 nnz ave.
	[0]maxIndSetAgg removed 0 of 20114 vertices. (0 local)  443 selected.
		[0]PCGAMGProlongator_AGG New grid 443 nodes
			PCGAMGOptprol_AGG smooth P0: max eigen=3.782372e+00 min=1.065309e-01 PC=jacobi
		[0]PCSetUp_GAMG 2) N=443, n data cols=1, nnz/row (ave)=113, 4 active pes
	[0]PCGAMGFilterGraph 11.1902% nnz after filtering, with threshold 0.01, 113.813 nnz ave.
	[0]maxIndSetAgg removed 0 of 443 vertices. (0 local)  20 selected.
		[0]PCGAMGProlongator_AGG New grid 20 nodes
			PCGAMGOptprol_AGG smooth P0: max eigen=2.141505e+00 min=5.132666e-03 PC=jacobi
	[0]createLevel aggregate processors: npe: 4 --> 1, neq=20
		[0]PCSetUp_GAMG 3) N=20, n data cols=1, nnz/row (ave)=20, 1 active pes
	[0]PCGAMGFilterGraph 45% nnz after filtering, with threshold 0.01, 20 nnz ave.
	[0]maxIndSetAgg removed 0 of 20 vertices. (0 local)  2 selected.
		[0]PCGAMGProlongator_AGG New grid 2 nodes
			PCGAMGOptprol_AGG smooth P0: max eigen=1.444685e+00 min=9.769929e-05 PC=jacobi
		[0]PCSetUp_GAMG 4) N=2, n data cols=1, nnz/row (ave)=2, 1 active pes
	[0]PCSetUp_GAMG 5 levels, grid complexity = 1.09069
  Residual norms for pres_ solve.
  0 KSP preconditioned resid norm 1.653389026762e+05 true resid norm 1.643826511377e+01 ||r(i)||/||b|| 1.000000000000e+00
  2 KSP preconditioned resid norm 3.498722572696e+04 true resid norm 1.676304035805e+01 ||r(i)||/||b|| 1.019757270128e+00
  4 KSP preconditioned resid norm 3.466542979714e+04 true resid norm 1.682142736387e+01 ||r(i)||/||b|| 1.023309165988e+00
  6 KSP preconditioned resid norm 3.544823492105e+04 true resid norm 2.096113365180e+01 ||r(i)||/||b|| 1.275142693388e+00
  8 KSP preconditioned resid norm 3.830052737912e+04 true resid norm 4.734563796599e+01 ||r(i)||/||b|| 2.880208929489e+00
 10 KSP preconditioned resid norm 4.928240285009e+04 true resid norm 1.505114395192e+02 ||r(i)||/||b|| 9.156163285936e+00
 12 KSP preconditioned resid norm 2.692615589856e+04 true resid norm 1.610600319827e+02 ||r(i)||/||b|| 9.797872881841e+00
 14 KSP preconditioned resid norm 3.258672961867e+04 true resid norm 3.930018988644e+01 ||r(i)||/||b|| 2.390774793717e+00
 16 KSP preconditioned resid norm 5.254695737537e+04 true resid norm 3.184054936988e+02 ||r(i)||/||b|| 1.936977482083e+01
 18 KSP preconditioned resid norm 4.664982713877e+04 true resid norm 2.267717910337e+02 ||r(i)||/||b|| 1.379536036584e+01
 20 KSP preconditioned resid norm 3.556402200695e+04 true resid norm 3.209651885839e+01 ||r(i)||/||b|| 1.952549045550e+00
 22 KSP preconditioned resid norm 3.751970755236e+04 true resid norm 6.277578808422e+01 ||r(i)||/||b|| 3.818881594241e+00
 24 KSP preconditioned resid norm 3.528015422621e+04 true resid norm 2.472314669019e+01 ||r(i)||/||b|| 1.503999754176e+00
 26 KSP preconditioned resid norm 3.520149611893e+04 true resid norm 2.349210422028e+01 ||r(i)||/||b|| 1.429110922454e+00
 28 KSP preconditioned resid norm 3.541077679608e+04 true resid norm 2.187432271791e+01 ||r(i)||/||b|| 1.330695335944e+00
 30 KSP preconditioned resid norm 3.517654266134e+04 true resid norm 2.171356997182e+01 ||r(i)||/||b|| 1.320916156391e+00
 32 KSP preconditioned resid norm 3.515900089315e+04 true resid norm 2.158840469643e+01 ||r(i)||/||b|| 1.313301893297e+00
 34 KSP preconditioned resid norm 3.559564844912e+04 true resid norm 2.273499576040e+01 ||r(i)||/||b|| 1.383053236035e+00
 36 KSP preconditioned resid norm 3.558002879717e+04 true resid norm 2.230901057983e+01 ||r(i)||/||b|| 1.357138994013e+00
 38 KSP preconditioned resid norm 3.536033027489e+04 true resid norm 2.255313539785e+01 ||r(i)||/||b|| 1.371990002702e+00
 40 KSP preconditioned resid norm 3.530445288118e+04 true resid norm 2.222344798566e+01 ||r(i)||/||b|| 1.351933907371e+00
 42 KSP preconditioned resid norm 3.531238381899e+04 true resid norm 2.203611003220e+01 ||r(i)||/||b|| 1.340537452078e+00
 44 KSP preconditioned resid norm 3.526814846743e+04 true resid norm 2.162375692510e+01 ||r(i)||/||b|| 1.315452499120e+00
 46 KSP preconditioned resid norm 3.549420786877e+04 true resid norm 2.658362282001e+01 ||r(i)||/||b|| 1.617179345632e+00
 48 KSP preconditioned resid norm 3.475902657029e+04 true resid norm 6.863778415755e+01 ||r(i)||/||b|| 4.175488330582e+00
 50 KSP preconditioned resid norm 3.455004242441e+04 true resid norm 8.709937353956e+01 ||r(i)||/||b|| 5.298574571997e+00
 52 KSP preconditioned resid norm 3.397528825543e+04 true resid norm 1.124159495041e+02 ||r(i)||/||b|| 6.838674806984e+00
 54 KSP preconditioned resid norm 3.312054456379e+04 true resid norm 1.290515134210e+02 ||r(i)||/||b|| 7.850677217321e+00
 56 KSP preconditioned resid norm 3.451647821637e+04 true resid norm 2.295572351071e+01 ||r(i)||/||b|| 1.396480915221e+00
 58 KSP preconditioned resid norm 3.415274707483e+04 true resid norm 1.478357632082e+02 ||r(i)||/||b|| 8.993392075441e+00
 60 KSP preconditioned resid norm 3.301948214819e+04 true resid norm 1.684691863247e+02 ||r(i)||/||b|| 1.024859893418e+01
 62 KSP preconditioned resid norm 3.312565770380e+04 true resid norm 1.525060310355e+02 ||r(i)||/||b|| 9.277501608592e+00
 64 KSP preconditioned resid norm 3.185347314326e+04 true resid norm 1.829054885160e+02 ||r(i)||/||b|| 1.112681218183e+01
 66 KSP preconditioned resid norm 3.171608219114e+04 true resid norm 1.875039031777e+02 ||r(i)||/||b|| 1.140655062319e+01
 68 KSP preconditioned resid norm 3.171847298154e+04 true resid norm 1.880370116219e+02 ||r(i)||/||b|| 1.143898156652e+01
 70 KSP preconditioned resid norm 3.178619322639e+04 true resid norm 1.860704776770e+02 ||r(i)||/||b|| 1.131935008890e+01
 72 KSP preconditioned resid norm 3.184456847066e+04 true resid norm 1.852753590050e+02 ||r(i)||/||b|| 1.127098010177e+01
 74 KSP preconditioned resid norm 3.189769214425e+04 true resid norm 1.842324138668e+02 ||r(i)||/||b|| 1.120753392111e+01
 76 KSP preconditioned resid norm 3.199081602250e+04 true resid norm 1.822782258561e+02 ||r(i)||/||b|| 1.108865349199e+01
 78 KSP preconditioned resid norm 3.102476484074e+04 true resid norm 2.097078712241e+02 ||r(i)||/||b|| 1.275729949436e+01
 80 KSP preconditioned resid norm 3.065784272235e+04 true resid norm 2.065139379058e+02 ||r(i)||/||b|| 1.256300080796e+01
 82 KSP preconditioned resid norm 2.394546049264e+04 true resid norm 4.274889221658e+02 ||r(i)||/||b|| 2.600572014182e+01
 84 KSP preconditioned resid norm 5.540308447940e+04 true resid norm 2.519566526625e+02 ||r(i)||/||b|| 1.532744793436e+01
 86 KSP preconditioned resid norm 8.474143362887e+05 true resid norm 1.261372272928e+04 ||r(i)||/||b|| 7.673390495884e+02
 88 KSP preconditioned resid norm 1.848633122514e+06 true resid norm 2.777035833045e+04 ||r(i)||/||b|| 1.689372822391e+03
 90 KSP preconditioned resid norm 7.565704677060e+05 true resid norm 1.143785512560e+04 ||r(i)||/||b|| 6.958067074863e+02
 92 KSP preconditioned resid norm 6.757814515708e+05 true resid norm 1.024954173515e+04 ||r(i)||/||b|| 6.235172424959e+02
 94 KSP preconditioned resid norm 6.614703098041e+05 true resid norm 1.004656691097e+04 ||r(i)||/||b|| 6.111695389652e+02
 96 KSP preconditioned resid norm 2.934757771515e+05 true resid norm 4.802602009791e+03 ||r(i)||/||b|| 2.921599071771e+02
 98 KSP preconditioned resid norm 2.585058956777e+05 true resid norm 4.004734942226e+03 ||r(i)||/||b|| 2.436227250570e+02
100 KSP preconditioned resid norm 2.309935778893e+05 true resid norm 4.002669905640e+03 ||r(i)||/||b|| 2.434971013022e+02
102 KSP preconditioned resid norm 2.015988421948e+05 true resid norm 4.016332928729e+03 ||r(i)||/||b|| 2.443282731439e+02
104 KSP preconditioned resid norm 2.045801533779e+05 true resid norm 4.000349066110e+03 ||r(i)||/||b|| 2.433559161154e+02
106 KSP preconditioned resid norm 2.264469374791e+05 true resid norm 3.893162890422e+03 ||r(i)||/||b|| 2.368353876445e+02
108 KSP preconditioned resid norm 3.080238001769e+05 true resid norm 3.906970507584e+03 ||r(i)||/||b|| 2.376753556743e+02
110 KSP preconditioned resid norm 2.793144888698e+05 true resid norm 4.313926252234e+03 ||r(i)||/||b|| 2.624319672652e+02
112 KSP preconditioned resid norm 2.403158281465e+05 true resid norm 5.534097030480e+03 ||r(i)||/||b|| 3.366594340813e+02
114 KSP preconditioned resid norm 1.045230913669e+06 true resid norm 2.054226795354e+04 ||r(i)||/||b|| 1.249661555606e+03
116 KSP preconditioned resid norm 1.059410089666e+06 true resid norm 2.765007218808e+04 ||r(i)||/||b|| 1.682055374865e+03
118 KSP preconditioned resid norm 7.620229766528e+05 true resid norm 2.851741985732e+04 ||r(i)||/||b|| 1.734819316999e+03
Linear solve did not converge due to DIVERGED_ITS iterations 118
KSP Object:(pres_) 4 MPI processes
  type: bcgsl
    BCGSL: Ell = 2
    BCGSL: Delta = 0
  maximum iterations=120
  tolerances:  relative=1e-08, absolute=1e-50, divergence=10000
  left preconditioning
  has attached null space
  using nonzero initial guess
  using PRECONDITIONED norm type for convergence test
PC Object:(pres_) 4 MPI processes
  type: gamg
    MG: type is MULTIPLICATIVE, levels=5 cycles=v
      Cycles per PCApply=1
      Using Galerkin computed coarse grid matrices
  Coarse grid solver -- level -------------------------------
    KSP Object:    (pres_mg_coarse_)     4 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:    (pres_mg_coarse_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 8, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=2, cols=2
        total: nonzeros=4, allocated nonzeros=4
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 1 nodes, limit used is 5
  Down solver (pre-smoother) on level 1 -------------------------------
    KSP Object:    (pres_mg_levels_1_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using NONE norm type for convergence test
    PC Object:    (pres_mg_levels_1_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=20, cols=20
        total: nonzeros=400, allocated nonzeros=400
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 4 nodes, limit used is 5
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 2 -------------------------------
    KSP Object:    (pres_mg_levels_2_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using NONE norm type for convergence test
    PC Object:    (pres_mg_levels_2_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=443, cols=443
        total: nonzeros=50419, allocated nonzeros=50419
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 3 -------------------------------
    KSP Object:    (pres_mg_levels_3_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using NONE norm type for convergence test
    PC Object:    (pres_mg_levels_3_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=20114, cols=20114
        total: nonzeros=1314538, allocated nonzeros=1314538
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 4 -------------------------------
    KSP Object:    (pres_mg_levels_4_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      has attached null space
      using nonzero initial guess
      using NONE norm type for convergence test
    PC Object:    (pres_mg_levels_4_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=556240, cols=556240
        total: nonzeros=15055870, allocated nonzeros=28055391
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Up solver (post-smoother) same as down solver (pre-smoother)
  linear system matrix = precond matrix:
  Matrix Object:   4 MPI processes
    type: mpiaij
    rows=556240, cols=556240
    total: nonzeros=15055870, allocated nonzeros=28055391
    total number of mallocs used during MatSetValues calls =0
      not using I-node (on process 0) routines
-------------- next part --------------

 Residual norms for pres_ solve.
  0 KSP preconditioned resid norm 2.993219493794e+03 true resid norm 1.643826511377e+01 ||r(i)||/||b|| 1.000000000000e+00
  2 KSP preconditioned resid norm 4.012627047075e+03 true resid norm 2.722662316913e+02 ||r(i)||/||b|| 1.656295416864e+01
  4 KSP preconditioned resid norm 7.152372463858e+02 true resid norm 3.245016507811e+01 ||r(i)||/||b|| 1.974062643078e+00
  6 KSP preconditioned resid norm 2.615419780458e+02 true resid norm 2.745979195842e+01 ||r(i)||/||b|| 1.670479930112e+00
  8 KSP preconditioned resid norm 1.626445578620e+02 true resid norm 8.455143190817e+00 ||r(i)||/||b|| 5.143573930885e-01
 10 KSP preconditioned resid norm 3.412604554263e+01 true resid norm 6.517443353179e-01 ||r(i)||/||b|| 3.964800000530e-02
 12 KSP preconditioned resid norm 4.448092876396e+01 true resid norm 2.990775751163e+00 ||r(i)||/||b|| 1.819398659448e-01
 14 KSP preconditioned resid norm 1.003757428948e+00 true resid norm 2.495627994699e-01 ||r(i)||/||b|| 1.518182105853e-02
 16 KSP preconditioned resid norm 6.831960905152e-01 true resid norm 2.110987118511e-02 ||r(i)||/||b|| 1.284190943449e-03
 18 KSP preconditioned resid norm 8.821616336254e-02 true resid norm 1.421049860455e-02 ||r(i)||/||b|| 8.644767867046e-04
 20 KSP preconditioned resid norm 2.018914933890e-02 true resid norm 1.749749201962e-03 ||r(i)||/||b|| 1.064436660349e-04
 22 KSP preconditioned resid norm 2.149723645607e-02 true resid norm 7.137329046115e-04 ||r(i)||/||b|| 4.341899219119e-05
 24 KSP preconditioned resid norm 1.085565650332e-03 true resid norm 9.250592958305e-05 ||r(i)||/||b|| 5.627475219728e-06
 26 KSP preconditioned resid norm 5.850921166024e-04 true resid norm 3.554584676434e-05 ||r(i)||/||b|| 2.162384322088e-06
 28 KSP preconditioned resid norm 2.636412182917e-04 true resid norm 8.740872361198e-06 ||r(i)||/||b|| 5.317393472305e-07
 30 KSP preconditioned resid norm 8.051486995446e-06 true resid norm 5.329776180424e-06 ||r(i)||/||b|| 3.242298468565e-07
KSP Object:(pres_) 4 MPI processes
  type: bcgsl
    BCGSL: Ell = 2
    BCGSL: Delta = 0
  maximum iterations=5000
  tolerances:  relative=1e-08, absolute=1e-50, divergence=10000
  left preconditioning
  has attached null space
  using nonzero initial guess
  using PRECONDITIONED norm type for convergence test
PC Object:(pres_) 4 MPI processes
  type: ml
    MG: type is MULTIPLICATIVE, levels=6 cycles=v
      Cycles per PCApply=1
      Using Galerkin computed coarse grid matrices
  Coarse grid solver -- level -------------------------------
    KSP Object:    (pres_mg_coarse_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using PRECONDITIONED norm type for convergence test
    PC Object:    (pres_mg_coarse_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 8, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=4, cols=4
        total: nonzeros=16, allocated nonzeros=16
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Down solver (pre-smoother) on level 1 -------------------------------
    KSP Object:    (pres_mg_levels_1_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using PRECONDITIONED norm type for convergence test
    PC Object:    (pres_mg_levels_1_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=23, cols=23
        total: nonzeros=481, allocated nonzeros=481
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 2 nodes, limit used is 5
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 2 -------------------------------
    KSP Object:    (pres_mg_levels_2_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using PRECONDITIONED norm type for convergence test
    PC Object:    (pres_mg_levels_2_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=204, cols=204
        total: nonzeros=19040, allocated nonzeros=19040
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 37 nodes, limit used is 5
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 3 -------------------------------
    KSP Object:    (pres_mg_levels_3_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using PRECONDITIONED norm type for convergence test
    PC Object:    (pres_mg_levels_3_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=2704, cols=2704
        total: nonzeros=277205, allocated nonzeros=277205
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 4 -------------------------------
    KSP Object:    (pres_mg_levels_4_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using nonzero initial guess
      using PRECONDITIONED norm type for convergence test
    PC Object:    (pres_mg_levels_4_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=52276, cols=52276
        total: nonzeros=5628023, allocated nonzeros=5628023
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Up solver (post-smoother) same as down solver (pre-smoother)
  Down solver (pre-smoother) on level 5 -------------------------------
    KSP Object:    (pres_mg_levels_5_)     4 MPI processes
      type: richardson
        Richardson: damping factor=1
      maximum iterations=1
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      has attached null space
      using nonzero initial guess
      using PRECONDITIONED norm type for convergence test
    PC Object:    (pres_mg_levels_5_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, omega = 1
      linear system matrix = precond matrix:
      Matrix Object:       4 MPI processes
        type: mpiaij
        rows=556240, cols=556240
        total: nonzeros=15055870, allocated nonzeros=28055391
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  Up solver (post-smoother) same as down solver (pre-smoother)
  linear system matrix = precond matrix:
  Matrix Object:   4 MPI processes
    type: mpiaij
    rows=556240, cols=556240
    total: nonzeros=15055870, allocated nonzeros=28055391
    total number of mallocs used during MatSetValues calls =0
      not using I-node (on process 0) routines






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