[petsc-users] Disconnected domains and Poisson equation
Barry Smith
bsmith at petsc.dev
Thu Sep 30 09:39:25 CDT 2021
It looks like the initial solution (guess) is to round-off the solution to the linear system 9.010260489109e-14
0 KSP unpreconditioned resid norm 9.010260489109e-14 true resid norm 9.010260489109e-14 ||r(i)||/||b|| 2.021559024868e+00
0 KSP Residual norm 9.010260489109e-14 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
1 KSP unpreconditioned resid norm 4.918108339808e-15 true resid norm 4.918171792537e-15 ||r(i)||/||b|| 1.103450292594e-01
1 KSP Residual norm 4.918108339808e-15 % max 9.566256813737e-01 min 9.566256813737e-01 max/min 1.000000000000e+00
2 KSP unpreconditioned resid norm 1.443599554690e-15 true resid norm 1.444867143493e-15 ||r(i)||/||b|| 3.241731154382e-02
2 KSP Residual norm 1.443599554690e-15 % max 9.614019380614e-01 min 7.360950481750e-01 max/min 1.306083963538e+00
Thus the Krylov solver will not be able to improve the solution, it then gets stuck trying to improve the solution but cannot because of round off.
In other words the algorithm has converged (even at the initial solution (guess) and should stop immediately.
You can use -ksp_atol 1.e-12 to get it to stop immediately without iterating if the initial residual is less than 1e-12.
Barry
> On Sep 30, 2021, at 4:16 AM, Marco Cisternino <marco.cisternino at optimad.it> wrote:
>
> Hello Barry.
> This is the output of ksp_view using fgmres and gamg. It has to be said that the solution of the linear system should be a zero values field. As you can see both unpreconditioned residual and r/b converge at this iteration of the CFD solver. During the time integration of the CFD, I can observe pressure linear solver residuals behaving in a different way: unpreconditioned residual stil converges but r/b stalls. After the output of ksp_view I add the output of ksp_monitor_true_residual for one of these iteration where r/b stalls.
> Thanks,
>
> KSP Object: 1 MPI processes
> type: fgmres
> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=100, nonzero initial guess
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> right preconditioning
> using UNPRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: gamg
> type is MULTIPLICATIVE, levels=4 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 = 0.02 0.02
> Threshold scaling factor for each level not specified = 1.
> AGG specific options
> Symmetric graph true
> Number of levels to square graph 1
> Number smoothing steps 0
> Coarse grid solver -- level -------------------------------
> KSP Object: (mg_coarse_) 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_coarse_) 1 MPI processes
> type: bjacobi
> number of blocks = 1
> 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 DEFAULT norm type for convergence test
> PC Object: (mg_coarse_sub_) 1 MPI processes
> type: lu
> PC has not been set up so information may be incomplete
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
> matrix ordering: nd
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=18, cols=18
> total: nonzeros=104, allocated nonzeros=104
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=18, cols=18
> total: nonzeros=104, allocated nonzeros=104
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> Down solver (pre-smoother) on level 1 -------------------------------
> KSP Object: (mg_levels_1_) 1 MPI processes
> type: chebyshev
> eigenvalue estimates used: min = 0., max = 0.
> eigenvalues estimate via gmres min 0., max 0.
> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
> KSP Object: (mg_levels_1_esteig_) 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=10, initial guess is zero
> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
> left preconditioning
> using DEFAULT norm type for convergence test
> estimating eigenvalues using noisy right hand side
> maximum iterations=2, 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_) 1 MPI processes
> type: sor
> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=67, cols=67
> total: nonzeros=675, allocated nonzeros=675
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> Up solver (post-smoother) same as down solver (pre-smoother)
> Down solver (pre-smoother) on level 2 -------------------------------
> KSP Object: (mg_levels_2_) 1 MPI processes
> type: chebyshev
> eigenvalue estimates used: min = 0., max = 0.
> eigenvalues estimate via gmres min 0., max 0.
> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
> KSP Object: (mg_levels_2_esteig_) 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=10, initial guess is zero
> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
> left preconditioning
> using DEFAULT norm type for convergence test
> estimating eigenvalues using noisy right hand side
> maximum iterations=2, 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_) 1 MPI processes
> type: sor
> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=348, cols=348
> total: nonzeros=3928, allocated nonzeros=3928
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> Up solver (post-smoother) same as down solver (pre-smoother)
> Down solver (pre-smoother) on level 3 -------------------------------
> KSP Object: (mg_levels_3_) 1 MPI processes
> type: chebyshev
> eigenvalue estimates used: min = 0., max = 0.
> eigenvalues estimate via gmres min 0., max 0.
> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
> KSP Object: (mg_levels_3_esteig_) 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=10, initial guess is zero
> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
> left preconditioning
> using DEFAULT norm type for convergence test
> estimating eigenvalues using noisy right hand side
> maximum iterations=2, 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_) 1 MPI processes
> type: sor
> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=3584, cols=3584
> total: nonzeros=23616, allocated nonzeros=23616
> total number of mallocs used during MatSetValues calls =0
> has attached null space
> not using I-node routines
> Up solver (post-smoother) same as down solver (pre-smoother)
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=3584, cols=3584
> total: nonzeros=23616, allocated nonzeros=23616
> total number of mallocs used during MatSetValues calls =0
> has attached null space
> not using I-node routines
> Pressure system has reached convergence in 0 iterations with reason 3.
> 0 KSP unpreconditioned resid norm 4.798763170703e-16 true resid norm 4.798763170703e-16 ||r(i)||/||b|| 1.000000000000e+00
> 0 KSP Residual norm 4.798763170703e-16 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
> 1 KSP unpreconditioned resid norm 1.648749109132e-17 true resid norm 1.648749109132e-17 ||r(i)||/||b|| 3.435779284125e-02
> 1 KSP Residual norm 1.648749109132e-17 % max 9.561792537103e-01 min 9.561792537103e-01 max/min 1.000000000000e+00
> 2 KSP unpreconditioned resid norm 4.737880600040e-19 true resid norm 4.737880600040e-19 ||r(i)||/||b|| 9.873128619820e-04
> 2 KSP Residual norm 4.737880600040e-19 % max 9.828636644296e-01 min 9.293131521763e-01 max/min 1.057623753767e+00
> 3 KSP unpreconditioned resid norm 2.542212716830e-20 true resid norm 2.542212716830e-20 ||r(i)||/||b|| 5.297641551371e-05
> 3 KSP Residual norm 2.542212716830e-20 % max 9.933572357920e-01 min 9.158303248850e-01 max/min 1.084652046127e+00
> 4 KSP unpreconditioned resid norm 6.614510286263e-21 true resid norm 6.614510286269e-21 ||r(i)||/||b|| 1.378378146822e-05
> 4 KSP Residual norm 6.614510286263e-21 % max 9.950912550705e-01 min 6.296575800237e-01 max/min 1.580368896747e+00
> 5 KSP unpreconditioned resid norm 1.981505525281e-22 true resid norm 1.981505525272e-22 ||r(i)||/||b|| 4.129200493513e-07
> 5 KSP Residual norm 1.981505525281e-22 % max 9.984097962703e-01 min 5.316259535293e-01 max/min 1.878030577029e+00
> Linear solve converged due to CONVERGED_RTOL iterations 5
>
> Ksp_monitor_true_residual output for stalling r/b CFD iteration
> 0 KSP unpreconditioned resid norm 9.010260489109e-14 true resid norm 9.010260489109e-14 ||r(i)||/||b|| 2.021559024868e+00
> 0 KSP Residual norm 9.010260489109e-14 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
> 1 KSP unpreconditioned resid norm 4.918108339808e-15 true resid norm 4.918171792537e-15 ||r(i)||/||b|| 1.103450292594e-01
> 1 KSP Residual norm 4.918108339808e-15 % max 9.566256813737e-01 min 9.566256813737e-01 max/min 1.000000000000e+00
> 2 KSP unpreconditioned resid norm 1.443599554690e-15 true resid norm 1.444867143493e-15 ||r(i)||/||b|| 3.241731154382e-02
> 2 KSP Residual norm 1.443599554690e-15 % max 9.614019380614e-01 min 7.360950481750e-01 max/min 1.306083963538e+00
> 3 KSP unpreconditioned resid norm 6.623206616803e-16 true resid norm 6.654132553541e-16 ||r(i)||/||b|| 1.492933720678e-02
> 3 KSP Residual norm 6.623206616803e-16 % max 9.764112945239e-01 min 4.911485418014e-01 max/min 1.988016274960e+00
> 4 KSP unpreconditioned resid norm 6.551896936698e-16 true resid norm 6.646157296305e-16 ||r(i)||/||b|| 1.491144376933e-02
> 4 KSP Residual norm 6.551896936698e-16 % max 9.883425885532e-01 min 1.461270778833e-01 max/min 6.763582786091e+00
> 5 KSP unpreconditioned resid norm 6.222297644887e-16 true resid norm 1.720560536914e-15 ||r(i)||/||b|| 3.860282047823e-02
> 5 KSP Residual norm 6.222297644887e-16 % max 1.000409371755e+00 min 4.989767363560e-03 max/min 2.004921870829e+02
> 6 KSP unpreconditioned resid norm 6.496945794974e-17 true resid norm 2.031914800253e-14 ||r(i)||/||b|| 4.558842341106e-01
> 6 KSP Residual norm 6.496945794974e-17 % max 1.004914985753e+00 min 1.459258738706e-03 max/min 6.886475709192e+02
> 7 KSP unpreconditioned resid norm 1.965237342540e-17 true resid norm 1.684522207337e-14 ||r(i)||/||b|| 3.779425772373e-01
> 7 KSP Residual norm 1.965237342540e-17 % max 1.005737762541e+00 min 1.452603803766e-03 max/min 6.923689446035e+02
> 8 KSP unpreconditioned resid norm 1.627718951285e-17 true resid norm 1.958642967520e-14 ||r(i)||/||b|| 4.394448276241e-01
> 8 KSP Residual norm 1.627718951285e-17 % max 1.006364278765e+00 min 1.452081813014e-03 max/min 6.930492963590e+02
> 9 KSP unpreconditioned resid norm 1.616577677764e-17 true resid norm 2.019110946644e-14 ||r(i)||/||b|| 4.530115373837e-01
> 9 KSP Residual norm 1.616577677764e-17 % max 1.006648747131e+00 min 1.452031376577e-03 max/min 6.932692801059e+02
> 10 KSP unpreconditioned resid norm 1.285788988203e-17 true resid norm 2.065082694477e-14 ||r(i)||/||b|| 4.633258453698e-01
> 10 KSP Residual norm 1.285788988203e-17 % max 1.007469033514e+00 min 1.433291867068e-03 max/min 7.029057072477e+02
> 11 KSP unpreconditioned resid norm 5.490854431580e-19 true resid norm 1.798071628891e-14 ||r(i)||/||b|| 4.034187394623e-01
> 11 KSP Residual norm 5.490854431580e-19 % max 1.008058905554e+00 min 1.369401685301e-03 max/min 7.361309076612e+02
> 12 KSP unpreconditioned resid norm 1.371754802104e-20 true resid norm 1.965688920064e-14 ||r(i)||/||b|| 4.410256708163e-01
> 12 KSP Residual norm 1.371754802104e-20 % max 1.008409402214e+00 min 1.369243011779e-03 max/min 7.364721919624e+02
> Linear solve converged due to CONVERGED_RTOL iterations 12
>
>
>
> Marco Cisternino
>
> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
> Sent: mercoledì 29 settembre 2021 18:34
> To: Marco Cisternino <marco.cisternino at optimad.it <mailto:marco.cisternino at optimad.it>>
> Cc: petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] Disconnected domains and Poisson equation
>
>
>
>
> On Sep 29, 2021, at 11:59 AM, Marco Cisternino <marco.cisternino at optimad.it <mailto:marco.cisternino at optimad.it>> wrote:
>
> For sake of completeness, explicitly building the null space using a vector per sub-domain make s the CFD runs using BCGS and GMRES more stable, but still slower than FGMRES.
>
> Something is strange. Please run with -ksp_view and send the output on the solver details.
>
>
> I had divergence using BCGS and GMRES setting the null space with only one constant.
> Thanks
>
> Marco Cisternino
>
> From: Marco Cisternino
> Sent: mercoledì 29 settembre 2021 17:54
> To: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
> Cc: petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>
> Subject: RE: [petsc-users] Disconnected domains and Poisson equation
>
> Thank you Barry for the quick reply.
> About the null space: I already tried what you suggest, building 2 Vec (constants) with 0 and 1 chosen by sub-domain, normalizing them and setting the null space like this
> MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_FALSE,nconstants,constants,&nullspace);
> The solution is slightly different in values but it is still different in the two sub-domains.
> About the solver: I tried BCGS, GMRES and FGMRES. The linear system is a pressure system in a navier-stokes solver and only solving with FGMRES makes the CFD stable, with BCGS and GMRES the CFD solution diverges. Moreover, in the same case but with a single domain, CFD solution is stable using all the solvers, but FGMRES converges in much less iterations than the others.
>
> Marco Cisternino
>
> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
> Sent: mercoledì 29 settembre 2021 15:59
> To: Marco Cisternino <marco.cisternino at optimad.it <mailto:marco.cisternino at optimad.it>>
> Cc: petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] Disconnected domains and Poisson equation
>
>
> The problem actually has a two dimensional null space; constant on each domain but possibly different constants. I think you need to build the MatNullSpace by explicitly constructing two vectors, one with 0 on one domain and constant value on the other and one with 0 on the other domain and constant on the first.
>
> Separate note: why use FGMRES instead of just GMRES? If the problem is linear and the preconditioner is linear (no GMRES inside the smoother) then you can just use GMRES and it will save a little space/work and be conceptually clearer.
>
> Barry
>
>
> On Sep 29, 2021, at 8:46 AM, Marco Cisternino <marco.cisternino at optimad.it <mailto:marco.cisternino at optimad.it>> wrote:
>
> Good morning,
> I want to solve the Poisson equation on a 3D domain with 2 non-connected sub-domains.
> I am using FGMRES+GAMG and I have no problem if the two sub-domains see a Dirichlet boundary condition each.
> On the same domain I would like to solve the Poisson equation imposing periodic boundary condition in one direction and homogenous Neumann boundary conditions in the other two directions. The two sub-domains are symmetric with respect to the separation between them and the operator discretization and the right hand side are symmetric as well. It would be nice to have the same solution in both the sub-domains.
> Setting the null space to the constant, the solver converges to a solution having the same gradients in both sub-domains but different values.
> Am I doing some wrong with the null space? I’m not setting a block matrix (one block for each sub-domain), should I?
> I tested the null space against the matrix using MatNullSpaceTest and the answer is true. Can I do something more to have a symmetric solution as outcome of the solver?
> Thank you in advance for any comments and hints.
>
> Best regards,
>
> Marco Cisternino
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