[petsc-users] Preconditioning systems of equations with complex numbers
Isaac, Tobin G
tisaac at cc.gatech.edu
Fri Feb 1 15:06:33 CST 2019
- Resuggesting a look at the max/min eigenvalues for as big a system as possible.
- I like doing fgmres with a monitored krylov method to see if the smoother is behaving very differently on the fine vs intermediate vs coarse levels
On February 1, 2019 3:53:21 PM EST, Justin Chang via petsc-users <petsc-users at mcs.anl.gov> wrote:
>I tried these options:
>
>-ksp_view
>-ksp_monitor_true_residual
>-ksp_type gmres
>-ksp_max_it 50
>-pc_type gamg
>-mg_coarse_pc_type sor
>-mg_levels_1_ksp_type richardson
>-mg_levels_2_ksp_type richardson
>-mg_levels_3_ksp_type richardson
>-mg_levels_4_ksp_type richardson
>-mg_levels_1_pc_type sor
>-mg_levels_2_pc_type sor
>-mg_levels_3_pc_type sor
>-mg_levels_4_pc_type sor
>
>And still have a non-converging solution:
>
> 0 KSP preconditioned resid norm 1.573625743885e+05 true resid norm
>1.207500000000e+08 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 7.150979785488e+00 true resid norm
>1.218223835173e+04 ||r(i)||/||b|| 1.008881022917e-04
> 2 KSP preconditioned resid norm 5.627140225062e+00 true resid norm
>1.209346465397e+04 ||r(i)||/||b|| 1.001529163889e-04
> 3 KSP preconditioned resid norm 5.077324098998e+00 true resid norm
>1.211293532189e+04 ||r(i)||/||b|| 1.003141641564e-04
> 4 KSP preconditioned resid norm 4.324840589068e+00 true resid norm
>1.213758867766e+04 ||r(i)||/||b|| 1.005183327342e-04
> 5 KSP preconditioned resid norm 4.107764194462e+00 true resid norm
>1.212180975158e+04 ||r(i)||/||b|| 1.003876583981e-04
> 6 KSP preconditioned resid norm 4.033152911227e+00 true resid norm
>1.216543340208e+04 ||r(i)||/||b|| 1.007489308660e-04
> 7 KSP preconditioned resid norm 3.944875788743e+00 true resid norm
>1.220023550040e+04 ||r(i)||/||b|| 1.010371470012e-04
> 8 KSP preconditioned resid norm 3.926562233824e+00 true resid norm
>1.220662039610e+04 ||r(i)||/||b|| 1.010900239842e-04
> 9 KSP preconditioned resid norm 3.912450246357e+00 true resid norm
>1.219755005917e+04 ||r(i)||/||b|| 1.010149073223e-04
> 10 KSP preconditioned resid norm 3.838058250285e+00 true resid norm
>1.218625848551e+04 ||r(i)||/||b|| 1.009213953251e-04
> 11 KSP preconditioned resid norm 3.779259857769e+00 true resid norm
>1.219659071592e+04 ||r(i)||/||b|| 1.010069624506e-04
> 12 KSP preconditioned resid norm 3.694467405997e+00 true resid norm
>1.223911592358e+04 ||r(i)||/||b|| 1.013591380834e-04
> 13 KSP preconditioned resid norm 3.693468937696e+00 true resid norm
>1.223724162745e+04 ||r(i)||/||b|| 1.013436159623e-04
> 14 KSP preconditioned resid norm 3.616103662529e+00 true resid norm
>1.221242236516e+04 ||r(i)||/||b|| 1.011380734175e-04
> 15 KSP preconditioned resid norm 3.604541982832e+00 true resid norm
>1.220338362332e+04 ||r(i)||/||b|| 1.010632184126e-04
> 16 KSP preconditioned resid norm 3.599588304412e+00 true resid norm
>1.219870618529e+04 ||r(i)||/||b|| 1.010244818657e-04
> 17 KSP preconditioned resid norm 3.581088429735e+00 true resid norm
>1.219098863716e+04 ||r(i)||/||b|| 1.009605684237e-04
> 18 KSP preconditioned resid norm 3.577183857191e+00 true resid norm
>1.219422257290e+04 ||r(i)||/||b|| 1.009873505002e-04
> 19 KSP preconditioned resid norm 3.576075374018e+00 true resid norm
>1.219687565514e+04 ||r(i)||/||b|| 1.010093221958e-04
> 20 KSP preconditioned resid norm 3.574659675290e+00 true resid norm
>1.219494681037e+04 ||r(i)||/||b|| 1.009933483260e-04
> 21 KSP preconditioned resid norm 3.555091405270e+00 true resid norm
>1.218714149002e+04 ||r(i)||/||b|| 1.009287079919e-04
> 22 KSP preconditioned resid norm 3.553181473875e+00 true resid norm
>1.218106845443e+04 ||r(i)||/||b|| 1.008784137012e-04
> 23 KSP preconditioned resid norm 3.552613734076e+00 true resid norm
>1.217794060488e+04 ||r(i)||/||b|| 1.008525101853e-04
> 24 KSP preconditioned resid norm 3.551632777626e+00 true resid norm
>1.218032078237e+04 ||r(i)||/||b|| 1.008722218001e-04
> 25 KSP preconditioned resid norm 3.545808514701e+00 true resid norm
>1.219292407751e+04 ||r(i)||/||b|| 1.009765969151e-04
> 26 KSP preconditioned resid norm 3.528978940908e+00 true resid norm
>1.219073670770e+04 ||r(i)||/||b|| 1.009584820513e-04
> 27 KSP preconditioned resid norm 3.527789136030e+00 true resid norm
>1.218958906209e+04 ||r(i)||/||b|| 1.009489777399e-04
> 28 KSP preconditioned resid norm 3.525383863095e+00 true resid norm
>1.218344768375e+04 ||r(i)||/||b|| 1.008981174637e-04
> 29 KSP preconditioned resid norm 3.521750505784e+00 true resid norm
>1.218775781359e+04 ||r(i)||/||b|| 1.009338121208e-04
> 30 KSP preconditioned resid norm 3.521656008348e+00 true resid norm
>1.218930075437e+04 ||r(i)||/||b|| 1.009465900983e-04
> 31 KSP preconditioned resid norm 3.521655969692e+00 true resid norm
>1.218928102429e+04 ||r(i)||/||b|| 1.009464267021e-04
> 32 KSP preconditioned resid norm 3.521654896823e+00 true resid norm
>1.218929084207e+04 ||r(i)||/||b|| 1.009465080088e-04
> 33 KSP preconditioned resid norm 3.521654041929e+00 true resid norm
>1.218930804845e+04 ||r(i)||/||b|| 1.009466505047e-04
> 34 KSP preconditioned resid norm 3.521652043655e+00 true resid norm
>1.218914044919e+04 ||r(i)||/||b|| 1.009452625192e-04
> 35 KSP preconditioned resid norm 3.521602884006e+00 true resid norm
>1.218810333491e+04 ||r(i)||/||b|| 1.009366735810e-04
> 36 KSP preconditioned resid norm 3.521535454292e+00 true resid norm
>1.218820358646e+04 ||r(i)||/||b|| 1.009375038215e-04
> 37 KSP preconditioned resid norm 3.521433576778e+00 true resid norm
>1.218859696943e+04 ||r(i)||/||b|| 1.009407616516e-04
> 38 KSP preconditioned resid norm 3.521349747881e+00 true resid norm
>1.218888798454e+04 ||r(i)||/||b|| 1.009431717146e-04
> 39 KSP preconditioned resid norm 3.521212709133e+00 true resid norm
>1.218882278104e+04 ||r(i)||/||b|| 1.009426317270e-04
> 40 KSP preconditioned resid norm 3.521168785360e+00 true resid norm
>1.218866389996e+04 ||r(i)||/||b|| 1.009413159416e-04
> 41 KSP preconditioned resid norm 3.521164077366e+00 true resid norm
>1.218868324624e+04 ||r(i)||/||b|| 1.009414761593e-04
> 42 KSP preconditioned resid norm 3.521101506147e+00 true resid norm
>1.218773304385e+04 ||r(i)||/||b|| 1.009336069884e-04
> 43 KSP preconditioned resid norm 3.521013554688e+00 true resid norm
>1.218675768694e+04 ||r(i)||/||b|| 1.009255294984e-04
> 44 KSP preconditioned resid norm 3.520820039115e+00 true resid norm
>1.218829726209e+04 ||r(i)||/||b|| 1.009382796032e-04
> 45 KSP preconditioned resid norm 3.520763991575e+00 true resid norm
>1.218776399191e+04 ||r(i)||/||b|| 1.009338632870e-04
> 46 KSP preconditioned resid norm 3.520501770928e+00 true resid norm
>1.218624167053e+04 ||r(i)||/||b|| 1.009212560706e-04
> 47 KSP preconditioned resid norm 3.519005707047e+00 true resid norm
>1.219233855078e+04 ||r(i)||/||b|| 1.009717478325e-04
> 48 KSP preconditioned resid norm 3.518379807717e+00 true resid norm
>1.218961932675e+04 ||r(i)||/||b|| 1.009492283788e-04
> 49 KSP preconditioned resid norm 3.517809415824e+00 true resid norm
>1.218777984143e+04 ||r(i)||/||b|| 1.009339945460e-04
> 50 KSP preconditioned resid norm 3.517617854442e+00 true resid norm
>1.219011629981e+04 ||r(i)||/||b|| 1.009533440978e-04
>KSP Object: 1 MPI processes
> type: gmres
>restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization
>with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=50, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
>PC Object: 1 MPI processes
> type: gamg
> type is MULTIPLICATIVE, levels=5 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.
> 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
> Complexity: grid = 1.31821
> 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: sor
> type = local_symmetric, iterations = 1, local iterations = 1, omega
>= 1.
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=17, cols=17
> total: nonzeros=163, allocated nonzeros=163
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 12 nodes, limit used is 5
> Down solver (pre-smoother) on level 1 -------------------------------
> KSP Object: (mg_levels_1_) 1 MPI processes
> type: richardson
> damping factor=1.
> 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=100, cols=100
> total: nonzeros=1240, allocated nonzeros=1240
> 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: richardson
> damping factor=1.
> 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=537, cols=537
> total: nonzeros=5291, allocated nonzeros=5291
> 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: richardson
> damping factor=1.
> 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=1541, cols=1541
> total: nonzeros=8039, allocated nonzeros=8039
> 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 4 -------------------------------
> KSP Object: (mg_levels_4_) 1 MPI processes
> type: richardson
> damping factor=1.
> 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_) 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=8541, cols=8541
> total: nonzeros=46299, allocated nonzeros=46299
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 5464 nodes, limit used is 5
> Up solver (post-smoother) same as down solver (pre-smoother)
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=8541, cols=8541
> total: nonzeros=46299, allocated nonzeros=46299
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 5464 nodes, limit used is 5
>
>Am I doing this right? Did I miss anything?
>
>
>
>On Fri, Feb 1, 2019 at 1:22 PM Matthew Knepley <knepley at gmail.com>
>wrote:
>
>> On Fri, Feb 1, 2019 at 3:05 PM Justin Chang <jychang48 at gmail.com>
>wrote:
>>
>>> Hi Mark,
>>>
>>> 1) So with these options:
>>>
>>> -ksp_type gmres
>>> -ksp_rtol 1e-15
>>> -ksp_monitor_true_residual
>>> -ksp_converged_reason
>>> -pc_type bjacobi
>>>
>>> This is what I get:
>>>
>>> 0 KSP preconditioned resid norm 1.900749341028e+04 true resid norm
>>> 1.603849239146e+07 ||r(i)||/||b|| 1.000000000000e+00
>>> 1 KSP preconditioned resid norm 1.363172190058e+03 true resid norm
>>> 8.144804150077e+05 ||r(i)||/||b|| 5.078285384488e-02
>>> 2 KSP preconditioned resid norm 1.744431536443e+02 true resid norm
>>> 2.668646207476e+04 ||r(i)||/||b|| 1.663900909350e-03
>>> 3 KSP preconditioned resid norm 2.798960448093e+01 true resid norm
>>> 2.142171349084e+03 ||r(i)||/||b|| 1.335643835343e-04
>>> 4 KSP preconditioned resid norm 2.938319245576e+00 true resid norm
>>> 1.457432872748e+03 ||r(i)||/||b|| 9.087093956061e-05
>>> 5 KSP preconditioned resid norm 1.539484356450e-12 true resid norm
>>> 6.667274739274e-09 ||r(i)||/||b|| 4.157045797412e-16
>>> Linear solve converged due to CONVERGED_RTOL iterations 5
>>>
>>> 2) With richardson/sor:
>>>
>>
>> Okay, its looks like Richardson/SOR solves this just fine. You can
>use
>> this as the smoother for GAMG instead
>> of Cheby/Jacobi, and probably see better results on the larger
>problems.
>>
>> Matt
>>
>>
>>> -ksp_type richardson
>>> -ksp_rtol 1e-15
>>> -ksp_monitor_true_residual
>>> -pc_type sor
>>>
>>> This is what I get:
>>>
>>> 0 KSP preconditioned resid norm 1.772935756018e+04 true resid norm
>>> 1.603849239146e+07 ||r(i)||/||b|| 1.000000000000e+00
>>> 1 KSP preconditioned resid norm 1.206881305953e+03 true resid norm
>>> 4.507533687463e+03 ||r(i)||/||b|| 2.810447252426e-04
>>> 2 KSP preconditioned resid norm 4.166906741810e+02 true resid norm
>>> 1.221098715634e+03 ||r(i)||/||b|| 7.613550487354e-05
>>> 3 KSP preconditioned resid norm 1.540698682668e+02 true resid norm
>>> 4.241154731706e+02 ||r(i)||/||b|| 2.644359973612e-05
>>> 4 KSP preconditioned resid norm 5.904921520051e+01 true resid norm
>>> 1.587778309916e+02 ||r(i)||/||b|| 9.899797756316e-06
>>> 5 KSP preconditioned resid norm 2.327938633860e+01 true resid norm
>>> 6.161476099609e+01 ||r(i)||/||b|| 3.841680345773e-06
>>> 6 KSP preconditioned resid norm 9.409043410169e+00 true resid norm
>>> 2.458600025207e+01 ||r(i)||/||b|| 1.532937114786e-06
>>> 7 KSP preconditioned resid norm 3.888365194933e+00 true resid norm
>>> 1.005868527582e+01 ||r(i)||/||b|| 6.271590265661e-07
>>> 8 KSP preconditioned resid norm 1.638018293396e+00 true resid norm
>>> 4.207888403975e+00 ||r(i)||/||b|| 2.623618418285e-07
>>> 9 KSP preconditioned resid norm 7.010639340830e-01 true resid norm
>>> 1.793827818698e+00 ||r(i)||/||b|| 1.118451644279e-07
>>> 10 KSP preconditioned resid norm 3.038491129050e-01 true resid norm
>>> 7.763187747256e-01 ||r(i)||/||b|| 4.840347557474e-08
>>> 11 KSP preconditioned resid norm 1.329641892383e-01 true resid norm
>>> 3.398137553975e-01 ||r(i)||/||b|| 2.118738763617e-08
>>> 12 KSP preconditioned resid norm 5.860142364318e-02 true resid norm
>>> 1.499670452314e-01 ||r(i)||/||b|| 9.350445264501e-09
>>> 13 KSP preconditioned resid norm 2.596075957908e-02 true resid norm
>>> 6.655772419557e-02 ||r(i)||/||b|| 4.149874101073e-09
>>> 14 KSP preconditioned resid norm 1.154254160823e-02 true resid norm
>>> 2.964959279341e-02 ||r(i)||/||b|| 1.848652109546e-09
>>> 15 KSP preconditioned resid norm 5.144785556436e-03 true resid norm
>>> 1.323918323132e-02 ||r(i)||/||b|| 8.254630739714e-10
>>> 16 KSP preconditioned resid norm 2.296969429446e-03 true resid norm
>>> 5.919889645162e-03 ||r(i)||/||b|| 3.691051191517e-10
>>> 17 KSP preconditioned resid norm 1.026615599876e-03 true resid norm
>>> 2.649106197813e-03 ||r(i)||/||b|| 1.651717713333e-10
>>> 18 KSP preconditioned resid norm 4.591391433184e-04 true resid norm
>>> 1.185874433977e-03 ||r(i)||/||b|| 7.393927091354e-11
>>> 19 KSP preconditioned resid norm 2.054186999728e-04 true resid norm
>>> 5.309080126683e-04 ||r(i)||/||b|| 3.310211456976e-11
>>> 20 KSP preconditioned resid norm 9.192021190159e-05 true resid norm
>>> 2.376701584665e-04 ||r(i)||/||b|| 1.481873437138e-11
>>> 21 KSP preconditioned resid norm 4.113417679473e-05 true resid norm
>>> 1.063822174067e-04 ||r(i)||/||b|| 6.632931251279e-12
>>> 22 KSP preconditioned resid norm 1.840693141405e-05 true resid norm
>>> 4.760872579965e-05 ||r(i)||/||b|| 2.968404051805e-12
>>> 23 KSP preconditioned resid norm 8.236207862555e-06 true resid norm
>>> 2.130217091325e-05 ||r(i)||/||b|| 1.328190355634e-12
>>> 24 KSP preconditioned resid norm 3.684941963736e-06 true resid norm
>>> 9.529827966741e-06 ||r(i)||/||b|| 5.941847733654e-13
>>> 25 KSP preconditioned resid norm 1.648500148983e-06 true resid norm
>>> 4.262645649931e-06 ||r(i)||/||b|| 2.657759561118e-13
>>> 26 KSP preconditioned resid norm 7.373967102970e-07 true resid norm
>>> 1.906404712490e-06 ||r(i)||/||b|| 1.188643337515e-13
>>> 27 KSP preconditioned resid norm 3.298179068243e-07 true resid norm
>>> 8.525291822193e-07 ||r(i)||/||b|| 5.315519447909e-14
>>> 28 KSP preconditioned resid norm 1.475043181061e-07 true resid norm
>>> 3.812420047527e-07 ||r(i)||/||b|| 2.377043898189e-14
>>> 29 KSP preconditioned resid norm 6.596561561066e-08 true resid norm
>>> 1.704561511399e-07 ||r(i)||/||b|| 1.062794101712e-14
>>> 30 KSP preconditioned resid norm 2.949954993990e-08 true resid norm
>>> 7.626396764524e-08 ||r(i)||/||b|| 4.755058379793e-15
>>> 31 KSP preconditioned resid norm 1.319299835423e-08 true resid norm
>>> 3.408580527641e-08 ||r(i)||/||b|| 2.125249957693e-15
>>> 32 KSP preconditioned resid norm 5.894082812579e-09 true resid norm
>>> 1.548343581158e-08 ||r(i)||/||b|| 9.653922222659e-16
>>> 33 KSP preconditioned resid norm 2.636703982134e-09 true resid norm
>>> 7.135606738493e-09 ||r(i)||/||b|| 4.449050798748e-16
>>> 34 KSP preconditioned resid norm 1.180985878209e-09 true resid norm
>>> 3.381752613021e-09 ||r(i)||/||b|| 2.108522752938e-16
>>> 35 KSP preconditioned resid norm 5.286215416700e-10 true resid norm
>>> 2.401714396480e-09 ||r(i)||/||b|| 1.497468925296e-16
>>> 36 KSP preconditioned resid norm 2.343627265669e-10 true resid norm
>>> 2.406695615135e-09 ||r(i)||/||b|| 1.500574715125e-16
>>> 37 KSP preconditioned resid norm 1.063481191780e-10 true resid norm
>>> 1.939409664821e-09 ||r(i)||/||b|| 1.209221925282e-16
>>> 38 KSP preconditioned resid norm 4.641441861184e-11 true resid norm
>>> 2.137293190758e-09 ||r(i)||/||b|| 1.332602303628e-16
>>> 39 KSP preconditioned resid norm 2.197549316276e-11 true resid norm
>>> 2.134629170008e-09 ||r(i)||/||b|| 1.330941286692e-16
>>> 40 KSP preconditioned resid norm 1.014465992249e-11 true resid norm
>>> 2.134073377634e-09 ||r(i)||/||b|| 1.330594750147e-16
>>> Linear solve converged due to CONVERGED_RTOL iterations 40
>>>
>>> 3) And lastly with chebyshev/jacobi:
>>>
>>> -ksp_type chebyshev
>>> -ksp_rtol 1e-15
>>> -ksp_monitor_true_residual
>>> -pc_type jacobi
>>>
>>> 0 KSP preconditioned resid norm 1.124259077563e+04 true resid norm
>>> 2.745522604971e+06 ||r(i)||/||b|| 1.711833343159e-01
>>> 1 KSP preconditioned resid norm 7.344319020428e+03 true resid norm
>>> 7.783641348970e+06 ||r(i)||/||b|| 4.853100378135e-01
>>> 2 KSP preconditioned resid norm 1.071669918360e+04 true resid norm
>>> 2.799860726937e+06 ||r(i)||/||b|| 1.745713162185e-01
>>> 3 KSP preconditioned resid norm 3.419051822673e+03 true resid norm
>>> 1.775069259453e+06 ||r(i)||/||b|| 1.106755682597e-01
>>> 4 KSP preconditioned resid norm 4.986468711193e+03 true resid norm
>>> 1.206925036347e+06 ||r(i)||/||b|| 7.525177597052e-02
>>> 5 KSP preconditioned resid norm 1.700832321100e+03 true resid norm
>>> 2.637405831602e+05 ||r(i)||/||b|| 1.644422535005e-02
>>> 6 KSP preconditioned resid norm 1.643529813686e+03 true resid norm
>>> 3.974328566033e+05 ||r(i)||/||b|| 2.477993859417e-02
>>> 7 KSP preconditioned resid norm 7.473371550560e+02 true resid norm
>>> 5.323098795195e+04 ||r(i)||/||b|| 3.318952096788e-03
>>> 8 KSP preconditioned resid norm 4.683110030109e+02 true resid norm
>>> 1.087414808661e+05 ||r(i)||/||b|| 6.780031327884e-03
>>> 9 KSP preconditioned resid norm 2.873339948815e+02 true resid norm
>>> 3.568238211189e+04 ||r(i)||/||b|| 2.224796523325e-03
>>> 10 KSP preconditioned resid norm 1.262071076718e+02 true resid norm
>>> 2.462817350416e+04 ||r(i)||/||b|| 1.535566617052e-03
>>> 11 KSP preconditioned resid norm 1.002027390320e+02 true resid norm
>>> 1.546159763209e+04 ||r(i)||/||b|| 9.640306117750e-04
>>> 12 KSP preconditioned resid norm 3.354594608285e+01 true resid norm
>>> 4.591691194787e+03 ||r(i)||/||b|| 2.862919458211e-04
>>> 13 KSP preconditioned resid norm 3.131257260705e+01 true resid norm
>>> 5.245042976548e+03 ||r(i)||/||b|| 3.270284293891e-04
>>> 14 KSP preconditioned resid norm 9.505226922340e+00 true resid norm
>>> 1.166368684616e+03 ||r(i)||/||b|| 7.272308744166e-05
>>> 15 KSP preconditioned resid norm 8.743145384463e+00 true resid norm
>>> 1.504382325425e+03 ||r(i)||/||b|| 9.379823793327e-05
>>> 16 KSP preconditioned resid norm 3.088859985366e+00 true resid norm
>>> 5.407763762347e+02 ||r(i)||/||b|| 3.371740703775e-05
>>> 17 KSP preconditioned resid norm 2.376841598522e+00 true resid norm
>>> 3.716033743805e+02 ||r(i)||/||b|| 2.316947037855e-05
>>> 18 KSP preconditioned resid norm 1.081970394434e+00 true resid norm
>>> 2.205852224893e+02 ||r(i)||/||b|| 1.375348861385e-05
>>> 19 KSP preconditioned resid norm 6.554707900903e-01 true resid norm
>>> 8.301134625673e+01 ||r(i)||/||b|| 5.175757435963e-06
>>> 20 KSP preconditioned resid norm 3.637023760759e-01 true resid norm
>>> 7.510650297359e+01 ||r(i)||/||b|| 4.682890457559e-06
>>> 21 KSP preconditioned resid norm 1.871804319271e-01 true resid norm
>>> 2.219347914083e+01 ||r(i)||/||b|| 1.383763423590e-06
>>> 22 KSP preconditioned resid norm 1.100146172732e-01 true resid norm
>>> 2.219515834389e+01 ||r(i)||/||b|| 1.383868121901e-06
>>> 23 KSP preconditioned resid norm 5.760669698705e-02 true resid norm
>>> 8.337640509358e+00 ||r(i)||/||b|| 5.198518854427e-07
>>> 24 KSP preconditioned resid norm 2.957448587725e-02 true resid norm
>>> 5.874493674310e+00 ||r(i)||/||b|| 3.662746803708e-07
>>> 25 KSP preconditioned resid norm 1.998893198438e-02 true resid norm
>>> 3.167578238976e+00 ||r(i)||/||b|| 1.974985030802e-07
>>> 26 KSP preconditioned resid norm 8.664848450375e-03 true resid norm
>>> 1.486849213225e+00 ||r(i)||/||b|| 9.270504838826e-08
>>> 27 KSP preconditioned resid norm 6.981883525312e-03 true resid norm
>>> 1.069480324023e+00 ||r(i)||/||b|| 6.668209816232e-08
>>> 28 KSP preconditioned resid norm 2.719053601907e-03 true resid norm
>>> 4.199959208195e-01 ||r(i)||/||b|| 2.618674564719e-08
>>> 29 KSP preconditioned resid norm 2.165577279425e-03 true resid norm
>>> 3.210144228918e-01 ||r(i)||/||b|| 2.001524925514e-08
>>> 30 KSP preconditioned resid norm 7.988525722643e-04 true resid norm
>>> 1.420960576866e-01 ||r(i)||/||b|| 8.859689191379e-09
>>> 31 KSP preconditioned resid norm 6.325404656692e-04 true resid norm
>>> 8.848430840431e-02 ||r(i)||/||b|| 5.516996625657e-09
>>> 32 KSP preconditioned resid norm 2.774874251260e-04 true resid norm
>>> 4.978943834544e-02 ||r(i)||/||b|| 3.104371478953e-09
>>> 33 KSP preconditioned resid norm 2.189482639986e-04 true resid norm
>>> 2.363450483074e-02 ||r(i)||/||b|| 1.473611375302e-09
>>> 34 KSP preconditioned resid norm 1.083040043835e-04 true resid norm
>>> 1.640956513288e-02 ||r(i)||/||b|| 1.023136385414e-09
>>> 35 KSP preconditioned resid norm 7.862356661381e-05 true resid norm
>>> 6.670818331105e-03 ||r(i)||/||b|| 4.159255226918e-10
>>> 36 KSP preconditioned resid norm 3.874849522187e-05 true resid norm
>>> 5.033219998314e-03 ||r(i)||/||b|| 3.138212667043e-10
>>> 37 KSP preconditioned resid norm 2.528412836894e-05 true resid norm
>>> 2.108237735582e-03 ||r(i)||/||b|| 1.314486227337e-10
>>> 38 KSP preconditioned resid norm 1.267202237267e-05 true resid norm
>>> 1.451831066002e-03 ||r(i)||/||b|| 9.052166691026e-11
>>> 39 KSP preconditioned resid norm 8.210280946453e-06 true resid norm
>>> 7.040263504011e-04 ||r(i)||/||b|| 4.389604292084e-11
>>> 40 KSP preconditioned resid norm 4.663490696194e-06 true resid norm
>>> 4.017228546553e-04 ||r(i)||/||b|| 2.504741997254e-11
>>> 41 KSP preconditioned resid norm 3.031143852348e-06 true resid norm
>>> 2.322717593194e-04 ||r(i)||/||b|| 1.448214418476e-11
>>> 42 KSP preconditioned resid norm 1.849864051869e-06 true resid norm
>>> 1.124281997627e-04 ||r(i)||/||b|| 7.009898250945e-12
>>> 43 KSP preconditioned resid norm 1.124434187023e-06 true resid norm
>>> 7.306110293564e-05 ||r(i)||/||b|| 4.555359765270e-12
>>> 44 KSP preconditioned resid norm 6.544412722416e-07 true resid norm
>>> 3.401751796431e-05 ||r(i)||/||b|| 2.120992243786e-12
>>> 45 KSP preconditioned resid norm 3.793047150173e-07 true resid norm
>>> 2.148969752882e-05 ||r(i)||/||b|| 1.339882640108e-12
>>> 46 KSP preconditioned resid norm 2.171588698514e-07 true resid norm
>>> 1.106350941000e-05 ||r(i)||/||b|| 6.898098112943e-13
>>> 47 KSP preconditioned resid norm 1.296462934907e-07 true resid norm
>>> 6.099370095521e-06 ||r(i)||/||b|| 3.802957252247e-13
>>> 48 KSP preconditioned resid norm 8.025171649527e-08 true resid norm
>>> 3.573262429072e-06 ||r(i)||/||b|| 2.227929123173e-13
>>> 49 KSP preconditioned resid norm 4.871794377896e-08 true resid norm
>>> 1.812080394338e-06 ||r(i)||/||b|| 1.129832125183e-13
>>> 50 KSP preconditioned resid norm 3.113615807350e-08 true resid norm
>>> 1.077814343384e-06 ||r(i)||/||b|| 6.720172426917e-14
>>> 51 KSP preconditioned resid norm 1.796713291999e-08 true resid norm
>>> 5.820635497903e-07 ||r(i)||/||b|| 3.629166230738e-14
>>> 52 KSP preconditioned resid norm 1.101194810402e-08 true resid norm
>>> 3.130702427551e-07 ||r(i)||/||b|| 1.951992962392e-14
>>> 53 KSP preconditioned resid norm 6.328675584656e-09 true resid norm
>>> 1.886022841038e-07 ||r(i)||/||b|| 1.175935240673e-14
>>> 54 KSP preconditioned resid norm 3.753197413786e-09 true resid norm
>>> 9.249216284944e-08 ||r(i)||/||b|| 5.766886350159e-15
>>> 55 KSP preconditioned resid norm 2.289205545523e-09 true resid norm
>>> 5.644941358874e-08 ||r(i)||/||b|| 3.519620935120e-15
>>> 56 KSP preconditioned resid norm 1.398041051045e-09 true resid norm
>>> 2.841582922959e-08 ||r(i)||/||b|| 1.771726951389e-15
>>> 57 KSP preconditioned resid norm 8.587888866230e-10 true resid norm
>>> 1.829052851330e-08 ||r(i)||/||b|| 1.140414452112e-15
>>> 58 KSP preconditioned resid norm 5.353939794444e-10 true resid norm
>>> 1.100004853784e-08 ||r(i)||/||b|| 6.858530259177e-16
>>> 59 KSP preconditioned resid norm 3.152419669065e-10 true resid norm
>>> 6.833334353224e-09 ||r(i)||/||b|| 4.260583966647e-16
>>> 60 KSP preconditioned resid norm 1.930837697706e-10 true resid norm
>>> 3.532215487724e-09 ||r(i)||/||b|| 2.202336355258e-16
>>> 61 KSP preconditioned resid norm 1.138921366053e-10 true resid norm
>>> 2.879312701518e-09 ||r(i)||/||b|| 1.795251468306e-16
>>> 62 KSP preconditioned resid norm 6.820698934300e-11 true resid norm
>>> 2.528012115752e-09 ||r(i)||/||b|| 1.576215553214e-16
>>> 63 KSP preconditioned resid norm 4.141390392052e-11 true resid norm
>>> 3.265136945688e-09 ||r(i)||/||b|| 2.035812884400e-16
>>> 64 KSP preconditioned resid norm 2.447449492240e-11 true resid norm
>>> 3.548082053472e-09 ||r(i)||/||b|| 2.212229158996e-16
>>> 65 KSP preconditioned resid norm 1.530621705437e-11 true resid norm
>>> 2.329307411648e-09 ||r(i)||/||b|| 1.452323170280e-16
>>> 66 KSP preconditioned resid norm 1.110145418759e-11 true resid norm
>>> 2.794373041066e-09 ||r(i)||/||b|| 1.742291590046e-16
>>> Linear solve converged due to CONVERGED_RTOL iterations 67
>>>
>>> Looks like neither of these ksp/pc combos are good? I also tried
>>> -pc_gamg_agg_nsmooths 0 but it didn't improve the solver at all.
>Here's the
>>> GAMG info I was able to grep from the out-of-box params:
>>>
>>> [0] PCSetUp_GAMG(): level 0) N=8541, n data rows=1, n data cols=1,
>>> nnz/row (ave)=5, np=1
>>> [0] PCGAMGFilterGraph(): 99.9114% nnz after filtering, with
>threshold
>>> 0., 5.42079 nnz ave. (N=8541)
>>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
>>> [0] PCGAMGProlongator_AGG(): New grid 1541 nodes
>>> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.587728e+00
>>> min=2.394056e-02 PC=jacobi
>>> [0] PCSetUp_GAMG(): 1) N=1541, n data cols=1, nnz/row (ave)=5, 1
>active
>>> pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 5.21674 nnz ave. (N=1541)
>>> [0] PCGAMGProlongator_AGG(): New grid 537 nodes
>>> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.939736e+00
>>> min=6.783380e-02 PC=jacobi
>>> [0] PCSetUp_GAMG(): 2) N=537, n data cols=1, nnz/row (ave)=9, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 9.85289 nnz ave. (N=537)
>>> [0] PCGAMGProlongator_AGG(): New grid 100 nodes
>>> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.521731e+00
>>> min=5.974776e-02 PC=jacobi
>>> [0] PCSetUp_GAMG(): 3) N=100, n data cols=1, nnz/row (ave)=12, 1
>active
>>> pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 12.4 nnz ave. (N=100)
>>> [0] PCGAMGProlongator_AGG(): New grid 17 nodes
>>> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.560264e+00
>>> min=4.842076e-01 PC=jacobi
>>> [0] PCSetUp_GAMG(): 4) N=17, n data cols=1, nnz/row (ave)=9, 1
>active pes
>>> [0] PCSetUp_GAMG(): 5 levels, grid complexity = 1.31821
>>>
>>> And the one with pc_gamg_agg_nsmooths 0
>>>
>>> [0] PCSetUp_GAMG(): level 0) N=8541, n data rows=1, n data cols=1,
>>> nnz/row (ave)=5, np=1
>>> [0] PCGAMGFilterGraph(): 99.9114% nnz after filtering, with
>threshold
>>> 0., 5.42079 nnz ave. (N=8541)
>>> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
>>> [0] PCGAMGProlongator_AGG(): New grid 1541 nodes
>>> [0] PCSetUp_GAMG(): 1) N=1541, n data cols=1, nnz/row (ave)=3, 1
>active
>>> pes
>>> [0] PCGAMGFilterGraph(): 99.7467% nnz after filtering, with
>threshold
>>> 0., 3.07398 nnz ave. (N=1541)
>>> [0] PCGAMGProlongator_AGG(): New grid 814 nodes
>>> [0] PCSetUp_GAMG(): 2) N=814, n data cols=1, nnz/row (ave)=3, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 3.02211 nnz ave. (N=814)
>>> [0] PCGAMGProlongator_AGG(): New grid 461 nodes
>>> [0] PCSetUp_GAMG(): 3) N=461, n data cols=1, nnz/row (ave)=3, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 3.00434 nnz ave. (N=461)
>>> [0] PCGAMGProlongator_AGG(): New grid 290 nodes
>>> [0] PCSetUp_GAMG(): 4) N=290, n data cols=1, nnz/row (ave)=3, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 3. nnz ave. (N=290)
>>> [0] PCGAMGProlongator_AGG(): New grid 197 nodes
>>> [0] PCSetUp_GAMG(): 5) N=197, n data cols=1, nnz/row (ave)=3, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 3. nnz ave. (N=197)
>>> [0] PCGAMGProlongator_AGG(): New grid 127 nodes
>>> [0] PCSetUp_GAMG(): 6) N=127, n data cols=1, nnz/row (ave)=2, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 2.98425 nnz ave. (N=127)
>>> [0] PCGAMGProlongator_AGG(): New grid 82 nodes
>>> [0] PCSetUp_GAMG(): 7) N=82, n data cols=1, nnz/row (ave)=2, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 2.97561 nnz ave. (N=82)
>>> [0] PCGAMGProlongator_AGG(): New grid 66 nodes
>>> [0] PCSetUp_GAMG(): 8) N=66, n data cols=1, nnz/row (ave)=2, 1
>active pes
>>> [0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold
>0.,
>>> 2.9697 nnz ave. (N=66)
>>> [0] PCGAMGProlongator_AGG(): New grid 36 nodes
>>> [0] PCSetUp_GAMG(): 9) N=36, n data cols=1, nnz/row (ave)=2, 1
>active pes
>>> [0] PCSetUp_GAMG(): 10 levels, grid complexity = 1.23689
>>>
>>>
>>> Thanks,
>>> Justin
>>>
>>> On Fri, Feb 1, 2019 at 7:13 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>
>>>>
>>>>
>>>>> Both GAMG and ILU are nice and dandy for this,
>>>>>
>>>>
>>>> I would test Richardson/SOR and Chebyshev/Jacobi on the tiny system
>and
>>>> converge it way down, say rtol = 1.e-12. See which one is better in
>the
>>>> early iteration and pick it. It would be nice to check that it
>solves the
>>>> problem ...
>>>>
>>>> The residual drops about 5 orders in the first iteration and then
>>>> flatlines. That is very bad. Check that the smoother can actually
>solve the
>>>> problem.
>>>>
>>>>
>>>>> but as soon as I look at a bigger system, like a network with 8500
>>>>> buses, the out-of-box gamg craps out. I am not sure where to start
>when it
>>>>> comes to tuning GAMG.
>>>>>
>>>>
>>>> First try -pc_gamg_nsmooths 0
>>>>
>>>> You can run with -info and grep on GAMG to see some diagnostic
>output.
>>>> Eigen estimates are fragile in practice and with this parameter and
>SOR
>>>> there are no eigen estimates needed. The max eigen values for all
>levels
>>>> should be between say 2 (or less) and say 3-4. Much higher is a
>sign of a
>>>> problem.
>>>>
>>>>
>>>>> Attached is the ksp monitor/view output for gamg on the
>unsuccessful
>>>>> solve
>>>>>
>>>>> I'm also attaching a zip file which contains the simple PETSc
>script
>>>>> that loads the binary matrix/vector as well as two test cases, if
>you guys
>>>>> are interested in trying it out. It only works if you have PETSc
>configured
>>>>> with complex numbers.
>>>>>
>>>>> Thanks
>>>>>
>>>>> Justin
>>>>>
>>>>> PS - A couple years ago I had asked if there was a paper/tutorial
>on
>>>>> using/tuning GAMG. Does such a thing exist today?
>>>>>
>>>>
>>>> There is a write up in the manual that is tutorial like.
>>>>
>>>>
>>>>>
>>>>> On Thu, Jan 31, 2019 at 5:00 PM Matthew Knepley
><knepley at gmail.com>
>>>>> wrote:
>>>>>
>>>>>> On Thu, Jan 31, 2019 at 6:22 PM Justin Chang
><jychang48 at gmail.com>
>>>>>> wrote:
>>>>>>
>>>>>>> Here's IMHO the simplest explanation of the equations I'm trying
>to
>>>>>>> solve:
>>>>>>>
>>>>>>>
>http://home.eng.iastate.edu/~jdm/ee458_2011/PowerFlowEquations.pdf
>>>>>>>
>>>>>>> Right now we're just trying to solve eq(5) (in section 1),
>inverting
>>>>>>> the linear Y-bus matrix. Eventually we have to be able to solve
>equations
>>>>>>> like those in the next section.
>>>>>>>
>>>>>>
>>>>>> Maybe I am reading this wrong, but the Y-bus matrix looks like an
>>>>>> M-matrix to me (if all the y's are positive). This means
>>>>>> that it should be really easy to solve, and I think GAMG should
>do it.
>>>>>> You can start out just doing relaxation, like SOR, on
>>>>>> small examples.
>>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>> Matt
>>>>>>
>>>>>>
>>>>>>> On Thu, Jan 31, 2019 at 1:47 PM Matthew Knepley
><knepley at gmail.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> On Thu, Jan 31, 2019 at 3:20 PM Justin Chang via petsc-users <
>>>>>>>> petsc-users at mcs.anl.gov> wrote:
>>>>>>>>
>>>>>>>>> Hi all,
>>>>>>>>>
>>>>>>>>> I'm working with some folks to extract a linear system of
>equations
>>>>>>>>> from an external software package that solves power flow
>equations in
>>>>>>>>> complex form. Since that external package uses serial direct
>solvers like
>>>>>>>>> KLU from suitesparse, I want a proof-of-concept where the same
>matrix can
>>>>>>>>> be solved in PETSc using its parallel solvers.
>>>>>>>>>
>>>>>>>>> I got mumps to achieve a very minor speedup across two MPI
>>>>>>>>> processes on a single node (went from solving a 300k dog
>system in 1.8
>>>>>>>>> seconds to 1.5 seconds). However I want to use iterative
>solvers and
>>>>>>>>> preconditioners but I have never worked with complex numbers
>so I am not
>>>>>>>>> sure what the "best" options are given PETSc's capabilities.
>>>>>>>>>
>>>>>>>>> So far I tried GMRES/BJACOBI and it craps out
>(unsurprisingly). I
>>>>>>>>> believe I also tried BICG with BJACOBI and while it did
>converge it
>>>>>>>>> converged slowly. Does anyone have recommendations on how one
>would go
>>>>>>>>> about preconditioning PETSc matrices with complex numbers? I
>was originally
>>>>>>>>> thinking about converting it to cartesian form: Declaring all
>voltages =
>>>>>>>>> sqrt(real^2+imaginary^2) and all angles to be something like a
>conditional
>>>>>>>>> arctan(imaginary/real) because all the papers I've seen in
>literature that
>>>>>>>>> claim to successfully precondition power flow equations
>operate in this
>>>>>>>>> form.
>>>>>>>>>
>>>>>>>>
>>>>>>>> 1) We really need to see the (simplified) equations
>>>>>>>>
>>>>>>>> 2) All complex equations can be converted to a system of real
>>>>>>>> equations twice as large, but this is not necessarily the best
>way to go
>>>>>>>>
>>>>>>>> Thanks,
>>>>>>>>
>>>>>>>> Matt
>>>>>>>>
>>>>>>>>
>>>>>>>>> Justin
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> 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/>
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>> --
>>>>>> 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/>
>>>>>>
>>>>>
>>
>> --
>> 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/>
>>
More information about the petsc-users
mailing list