[petsc-users] Preconditioning systems of equations with complex numbers
Dave May
dave.mayhem23 at gmail.com
Sat Feb 2 04:44:40 CST 2019
On Sat, 2 Feb 2019 at 04:05, Mark Adams <mfadams at lbl.gov> wrote:
>
>
> On Fri, Feb 1, 2019 at 5:32 PM Dave May <dave.mayhem23 at gmail.com> wrote:
>
>> I'd suggest
>> 1) using LU on the coarse grid (you have 1 application of SOR) and
>>
>
> Ah, good catch!
>
> By setting every level KSP/PC explicitly you seemed to have overroad the
> coarse grid LU solver that is set by default in GAMG.
>
Not really - there was an explicit option provided specifying the coarse pc
to use SOR.
>
>> 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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