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. <bsm...@mcs.anl.gov> wrote: > > > >> On Oct 28, 2018, at 12:16 PM, Manav Bhatia <bhatiama...@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