[petsc-users] Preconditioning systems of equations with complex numbers
Dave May
dave.mayhem23 at gmail.com
Fri Feb 1 16:32:24 CST 2019
I'd suggest
1) using LU on the coarse grid (you have 1 application of SOR) and
2) do more Richardson iterations on each level (you have the default of 2).
Try 4 or 6
Thanks,
Dave
On Fri, 1 Feb 2019 at 22:18, Mark Adams via petsc-users <
petsc-users at mcs.anl.gov> wrote:
> We do need the equations and discretization, this not a Laplacian or
> something is not working out-of-th-box.
>
> For pc_gamg_agg_nsmooths 0 you want -pc_gamg_square_graph 10
>
> The info output snows the size of the systems on each level and the number
> of non-zeros. with pc_gamg_agg_nsmooths 0 in 2D it courses very slowly. You
> want a reduction factor between grids of say 4 - 10 between grids.
>
> And here is shorthand for r/sor on all levels:
>
> -mg_levels_ksp_type richardson
> -mg_levels_pc_type sor
>
> On Fri, Feb 1, 2019 at 4:07 PM Isaac, Tobin G via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>> - 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/>
>> >>
>>
>
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