[petsc-users] Convergence of AMG
Manav Bhatia
bhatiamanav at gmail.com
Sun Oct 28 16:12:05 CDT 2018
Var: 0,…,5 are the 6 variables that I am solving for: u, v, w, theta_x, theta_y, theta_z.
The norms identified in my email are the L2 norms of all dofs corresponding to each variable in the solution vector. So, var: 0: u: norm is the L2 norm of the dofs for u only, and so on.
I expect u, v, theta_z to be zero for the solution, which ends up being the case.
If I plot the solution, they look sensible, but the reduction of KSP norm is slow.
Thanks,
Manav
> On Oct 28, 2018, at 3:55 PM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
>
>
>
>> On Oct 28, 2018, at 12:16 PM, Manav Bhatia <bhatiamanav at gmail.com> wrote:
>>
>> Hi,
>>
>> I am attempting to solve a Mindlin plate bending problem with AMG solver in petsc. This test case is with a mesh of 300x300 elements and 543,606 dofs.
>>
>> The discretization includes 6 variables (u, v, w, tx, ty, tz), but only three are relevant for plate bending (w, tx, ty).
>>
>> I am calling the solver with the following options:
>>
>> -pc_type gamg -pc_gamg_threshold 0. --node-major-dofs -mat_block_size 6 -ksp_rtol 1.e-8 -ksp_monitor -ksp_converged_reason -ksp_view
>>
>> And the convergence behavior is shown below, along with the ksp_view information. Based on notes in the manual, this seems to be subpar convergence rate. At the end of the solution the norm of each variable is :
>>
>> var: 0: u : norm: 5.505909e-18
>> var: 1: v : norm: 7.639640e-18
>> var: 2: w : norm: 3.901464e-03
>> var: 3: tx : norm: 4.403576e-02
>> var: 4: ty : norm: 4.403576e-02
>> var: 5: tz : norm: 1.148409e-16
>
> What do you mean by var: 2: w : norm etc? Is this the norm of the error for that variable, the norm of the residual, something else? How exactly are you calculating it?
>
> Thanks
>
>
> Barry
>
>>
>> I tried different values of -ksp_rtol from 1e-1 to 1e-8 and this does not make a lot of difference in the norms of (w, tx, ty).
>>
>> I do provide the solver with 6 rigid-body vectors to approximate the null-space of the problem. Without these the solver shows very poor convergence.
>>
>> I would appreciate advice on possible strategies to improve this behavior.
>>
>> Thanks,
>> Manav
>>
>> 0 KSP Residual norm 1.696304497261e+00
>> 1 KSP Residual norm 1.120485505777e+00
>> 2 KSP Residual norm 8.324222302402e-01
>> 3 KSP Residual norm 6.477349534115e-01
>> 4 KSP Residual norm 5.080936471292e-01
>> 5 KSP Residual norm 4.051099646638e-01
>> 6 KSP Residual norm 3.260432664653e-01
>> 7 KSP Residual norm 2.560483838143e-01
>> 8 KSP Residual norm 2.029943986124e-01
>> 9 KSP Residual norm 1.560985741610e-01
>> 10 KSP Residual norm 1.163720702140e-01
>> 11 KSP Residual norm 8.488411085459e-02
>> 12 KSP Residual norm 5.888041729034e-02
>> 13 KSP Residual norm 4.027792209980e-02
>> 14 KSP Residual norm 2.819048087304e-02
>> 15 KSP Residual norm 1.904674196962e-02
>> 16 KSP Residual norm 1.289302447822e-02
>> 17 KSP Residual norm 9.162203296376e-03
>> 18 KSP Residual norm 7.016781679507e-03
>> 19 KSP Residual norm 5.399170865328e-03
>> 20 KSP Residual norm 4.254385887482e-03
>> 21 KSP Residual norm 3.530831740621e-03
>> 22 KSP Residual norm 2.946780747923e-03
>> 23 KSP Residual norm 2.339361361128e-03
>> 24 KSP Residual norm 1.815072489282e-03
>> 25 KSP Residual norm 1.408814185342e-03
>> 26 KSP Residual norm 1.063795714320e-03
>> 27 KSP Residual norm 7.828540233117e-04
>> 28 KSP Residual norm 5.683910750067e-04
>> 29 KSP Residual norm 4.131151010250e-04
>> 30 KSP Residual norm 3.065608221019e-04
>> 31 KSP Residual norm 2.634114273459e-04
>> 32 KSP Residual norm 2.198180137626e-04
>> 33 KSP Residual norm 1.748956510799e-04
>> 34 KSP Residual norm 1.317539710010e-04
>> 35 KSP Residual norm 9.790121566055e-05
>> 36 KSP Residual norm 7.465935386094e-05
>> 37 KSP Residual norm 5.689506626052e-05
>> 38 KSP Residual norm 4.413136619126e-05
>> 39 KSP Residual norm 3.512194236402e-05
>> 40 KSP Residual norm 2.877755408287e-05
>> 41 KSP Residual norm 2.340080556431e-05
>> 42 KSP Residual norm 1.904544450345e-05
>> 43 KSP Residual norm 1.504723478235e-05
>> 44 KSP Residual norm 1.141381950576e-05
>> 45 KSP Residual norm 8.206151384599e-06
>> 46 KSP Residual norm 5.911426091276e-06
>> 47 KSP Residual norm 4.233669089283e-06
>> 48 KSP Residual norm 2.898052944223e-06
>> 49 KSP Residual norm 2.023556779973e-06
>> 50 KSP Residual norm 1.459108043935e-06
>> 51 KSP Residual norm 1.097335545865e-06
>> 52 KSP Residual norm 8.440457332262e-07
>> 53 KSP Residual norm 6.705616854004e-07
>> 54 KSP Residual norm 5.404888680234e-07
>> 55 KSP Residual norm 4.391368084979e-07
>> 56 KSP Residual norm 3.697063014621e-07
>> 57 KSP Residual norm 3.021772094146e-07
>> 58 KSP Residual norm 2.479354520792e-07
>> 59 KSP Residual norm 2.013077841968e-07
>> 60 KSP Residual norm 1.553159612793e-07
>> 61 KSP Residual norm 1.400784224898e-07
>> 62 KSP Residual norm 9.707453662195e-08
>> 63 KSP Residual norm 7.263173080146e-08
>> 64 KSP Residual norm 5.593723572132e-08
>> 65 KSP Residual norm 4.448788809586e-08
>> 66 KSP Residual norm 3.613992590778e-08
>> 67 KSP Residual norm 2.946099051876e-08
>> 68 KSP Residual norm 2.408053564170e-08
>> 69 KSP Residual norm 1.945257374856e-08
>> 70 KSP Residual norm 1.572494535110e-08
>>
>>
>> KSP Object: 4 MPI processes
>> type: gmres
>> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
>> happy breakdown tolerance 1e-30
>> maximum iterations=10000, initial guess is zero
>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000.
>> left preconditioning
>> using PRECONDITIONED norm type for convergence test
>> PC Object: 4 MPI processes
>> type: gamg
>> type is MULTIPLICATIVE, levels=6 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.
>> 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 1
>> Coarse grid solver -- level -------------------------------
>> KSP Object: (mg_coarse_) 4 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_) 4 MPI processes
>> type: bjacobi
>> number of blocks = 4
>> 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=6, cols=6, bs=6
>> package used to perform factorization: petsc
>> total: nonzeros=36, allocated nonzeros=36
>> total number of mallocs used during MatSetValues calls =0
>> using I-node routines: found 2 nodes, limit used is 5
>> linear system matrix = precond matrix:
>> Mat Object: 1 MPI processes
>> type: seqaij
>> rows=6, cols=6, bs=6
>> total: nonzeros=36, allocated nonzeros=36
>> total number of mallocs used during MatSetValues calls =0
>> using I-node routines: found 2 nodes, limit used is 5
>> linear system matrix = precond matrix:
>> Mat Object: 4 MPI processes
>> type: mpiaij
>> rows=6, cols=6, bs=6
>> total: nonzeros=36, allocated nonzeros=36
>> total number of mallocs used during MatSetValues calls =0
>> using nonscalable MatPtAP() implementation
>> using I-node (on process 0) routines: found 2 nodes, limit used is 5
>> Down solver (pre-smoother) on level 1 -------------------------------
>> KSP Object: (mg_levels_1_) 4 MPI processes
>> type: chebyshev
>> eigenvalue estimates used: min = 0.099971, max = 1.09968
>> eigenvalues estimate via gmres min 0.154032, max 0.99971
>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>> KSP Object: (mg_levels_1_esteig_) 4 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 PRECONDITIONED 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_) 4 MPI processes
>> type: sor
>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>> linear system matrix = precond matrix:
>> Mat Object: 4 MPI processes
>> type: mpiaij
>> rows=54, cols=54, bs=6
>> total: nonzeros=2916, allocated nonzeros=2916
>> total number of mallocs used during MatSetValues calls =0
>> 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 2 -------------------------------
>> KSP Object: (mg_levels_2_) 4 MPI processes
>> type: chebyshev
>> eigenvalue estimates used: min = 0.171388, max = 1.88526
>> eigenvalues estimate via gmres min 0.0717873, max 1.71388
>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>> KSP Object: (mg_levels_2_esteig_) 4 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 PRECONDITIONED 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_) 4 MPI processes
>> type: sor
>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>> linear system matrix = precond matrix:
>> Mat Object: 4 MPI processes
>> type: mpiaij
>> rows=642, cols=642, bs=6
>> total: nonzeros=99468, allocated nonzeros=99468
>> total number of mallocs used during MatSetValues calls =0
>> using nonscalable MatPtAP() implementation
>> using I-node (on process 0) routines: found 47 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_) 4 MPI processes
>> type: chebyshev
>> eigenvalue estimates used: min = 0.164216, max = 1.80637
>> eigenvalues estimate via gmres min 0.0376323, max 1.64216
>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>> KSP Object: (mg_levels_3_esteig_) 4 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 PRECONDITIONED 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_) 4 MPI processes
>> type: sor
>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>> linear system matrix = precond matrix:
>> Mat Object: 4 MPI processes
>> type: mpiaij
>> rows=6726, cols=6726, bs=6
>> total: nonzeros=941796, allocated nonzeros=941796
>> total number of mallocs used during MatSetValues calls =0
>> using nonscalable MatPtAP() implementation
>> using I-node (on process 0) routines: found 552 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_) 4 MPI processes
>> type: chebyshev
>> eigenvalue estimates used: min = 0.163283, max = 1.79611
>> eigenvalues estimate via gmres min 0.0350306, max 1.63283
>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>> KSP Object: (mg_levels_4_esteig_) 4 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 PRECONDITIONED 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_4_) 4 MPI processes
>> type: sor
>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>> linear system matrix = precond matrix:
>> Mat Object: 4 MPI processes
>> type: mpiaij
>> rows=41022, cols=41022, bs=6
>> total: nonzeros=2852316, allocated nonzeros=2852316
>> total number of mallocs used during MatSetValues calls =0
>> using nonscalable MatPtAP() implementation
>> using I-node (on process 0) routines: found 3432 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_) 4 MPI processes
>> type: chebyshev
>> eigenvalue estimates used: min = 0.157236, max = 1.7296
>> eigenvalues estimate via gmres min 0.0317897, max 1.57236
>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>> KSP Object: (mg_levels_5_esteig_) 4 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 PRECONDITIONED 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_5_) 4 MPI processes
>> type: sor
>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>> linear system matrix = precond matrix:
>> Mat Object: () 4 MPI processes
>> type: mpiaij
>> rows=543606, cols=543606, bs=6
>> total: nonzeros=29224836, allocated nonzeros=29302596
>> total number of mallocs used during MatSetValues calls =0
>> has attached near null space
>> using I-node (on process 0) routines: found 45644 nodes, limit used is 5
>> Up solver (post-smoother) same as down solver (pre-smoother)
>> linear system matrix = precond matrix:
>> Mat Object: () 4 MPI processes
>> type: mpiaij
>> rows=543606, cols=543606, bs=6
>> total: nonzeros=29224836, allocated nonzeros=29302596
>> total number of mallocs used during MatSetValues calls =0
>> has attached near null space
>> using I-node (on process 0) routines: found 45644 nodes, limit used is 5
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