[petsc-users] Preconditioning systems of equations with complex numbers
Abhyankar, Shrirang G
shrirang.abhyankar at pnnl.gov
Tue Feb 5 19:09:13 CST 2019
Hi Justin,
Typically, the power grid distribution systems have a radial structure (unless it is an urban area) that leads to a, more or less, staircase type matrix. So a MatLoad() or VecLoad() would presumably just just splits the stairs, akin to a 1-D PDE. However, as you pointed out, it may cause the phases for a bus to be split across processors, but I don’t think it would cause a big performance hit.
I’ve worked with OpenDSS recently and have created a C wrapper for it that you can use to query values from it. I can help out with your experimentations, if you need.
Shri
From: petsc-users <petsc-users-bounces at mcs.anl.gov> On Behalf Of Justin Chang via petsc-users
Sent: Tuesday, February 5, 2019 5:23 PM
To: Mark Adams <mfadams at lbl.gov>
Cc: petsc-users <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Preconditioning systems of equations with complex numbers
Hi all,
So I *think* I know what the problem is. I am modeling a a distribution system where each bus can have anywhere from 1 to 3 phases. In the smallest example I had, all four buses had 3 phases (hence 12 dofs), and this was very easy to decompose - each MPI process should have a specific set of complex voltages on their respective nodes/buses. The larger test cases have lots of single phase buses attached, so a naive decomposition of the matrix isn't trivial. Again we're only extracting the Y-bus matrices out of an external software (OpenDSS to be specific) so we have no a priori information on how they organize their degrees-of-freedom - we let MatLoad() and VecLoad() do the decomposition. So it's possible that during this decomposition, a single bus' phases are being split across two or more MPI processes, which I assume would mess up the algorithmic performance of GAMG/ASM when more than one MPI process is needed.
Yeah DMNetwork will fix this and ensure that all dofs per vertex do not get split across different MPI procs, but for now we're just trying to see if we can get a simple proof-of-concept working. We're trying to come up with a toy distribution system where everything is three-phase (hence very straightforward to decompose even with MatLoad().
Justin
On Tue, Feb 5, 2019 at 9:26 AM Mark Adams <mfadams at lbl.gov<mailto:mfadams at lbl.gov>> wrote:
I would stay away from eigen estimates in the solver (but give us the spectra to look at), so set -pc_gamg_agg_nsmooths 0 and use sor.
Applications that have lived on direct solvers can add sorts of crap like penalty terms.
sor seemed to work OK so I'd check the coarse grids in GAMG. Test with just two levels. That way you don't have to use sor on an internal MG grid, which can be bad and probably is here.
On Mon, Feb 4, 2019 at 10:59 PM Smith, Barry F. via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
> On Feb 4, 2019, at 1:56 PM, Justin Chang via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
>
> Thanks everyone for your suggestions/feedback. So a few things:
>
> 1) When I examined larger distribution networks (~150k buses) my eigenvalue estimates from the chebyshev method get enormous indeed. See below:
>
> [0] PCSetUp_GAMG(): level 0) N=320745, n data rows=1, n data cols=1, nnz/row (ave)=6, np=1
> [0] PCGAMGFilterGraph(): 98.5638% nnz after filtering, with threshold 0., 6.01293 nnz ave. (N=320745)
> [0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
> [0] PCGAMGProlongator_AGG(): New grid 44797 nodes
> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.403335e+00 min=4.639523e-02 PC=jacobi
> [0] PCSetUp_GAMG(): 1) N=44797, n data cols=1, nnz/row (ave)=7, 1 active pes
> [0] PCGAMGFilterGraph(): 99.9753% nnz after filtering, with threshold 0., 7.32435 nnz ave. (N=44797)
> [0] PCGAMGProlongator_AGG(): New grid 13043 nodes
> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=8.173298e+00 min=9.687506e-01 PC=jacobi
> [0] PCSetUp_GAMG(): 2) N=13043, n data cols=1, nnz/row (ave)=22, 1 active pes
> [0] PCGAMGFilterGraph(): 99.684% nnz after filtering, with threshold 0., 22.5607 nnz ave. (N=13043)
> [0] PCGAMGProlongator_AGG(): New grid 2256 nodes
> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=5.696594e+00 min=6.150856e-01 PC=jacobi
> [0] PCSetUp_GAMG(): 3) N=2256, n data cols=1, nnz/row (ave)=79, 1 active pes
> [0] PCGAMGFilterGraph(): 93.859% nnz after filtering, with threshold 0., 79.5142 nnz ave. (N=2256)
> [0] PCGAMGProlongator_AGG(): New grid 232 nodes
> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.454120e+00 min=6.780909e-01 PC=jacobi
> [0] PCSetUp_GAMG(): 4) N=232, n data cols=1, nnz/row (ave)=206, 1 active pes
> [0] PCGAMGFilterGraph(): 99.1729% nnz after filtering, with threshold 0., 206.379 nnz ave. (N=232)
> [0] PCGAMGProlongator_AGG(): New grid 9 nodes
> [0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=2.443612e+00 min=2.153627e-01 PC=jacobi
> [0] PCSetUp_GAMG(): 5) N=9, n data cols=1, nnz/row (ave)=9, 1 active pes
> [0] PCSetUp_GAMG(): 6 levels, grid complexity = 1.44058
>
> 2) I tried all the suggestions mentioned before: setting -pc_gamg_agg_nsmooths 0 -pc_gamg_square_graph 10 did not improve my convergence. Neither did explicitly setting -mg_coarse_pc_type lu or more iterations of richardson/sor.
>
> 3a) -pc_type asm works only if I set -sub_pc_type lu. Basically I'm just solving LU on the whole system.
>
> 3b)The problem is that I can't get it to even speedup across 2 MPI processes for my 150k bus case (~300k dofs) - and I already checked that this problem could in theory be parallelized by setting the -ksp_max_it to something low and observing that the KSPSolve time decreases as MPI concurrency increases. The potential speedup is countered by the fact that the algorithmic convergence rate blows up when either more MPI processes are added or when I tune the block_size/overlap parameters.
Yes, we just haven't gotten a scalable preconditioner yet for your matrix.
>
> Which leads me to one of two conclusions/questions:
>
> A) Is my 300 DOF problem still too small? Do I need to look at a problem with, say, 10 Million DOF or more to see that increasing the asm_block_size will have better performance (despite having more KSP iterations) than a single giant asm_block?
No, if you had a scalable preconditioner you would see good speed up with 300k unknowns, using 10 million won't help.
>
> B) Or is there something even more sinister about my system of equations in complex form?
There is a technical term for matrices for which both GAMG and ASM do very poorly on: nasty :-)
Have you tried using parallel LU (for example ./configure --download-superlu_dist). Direct LU is the last refuge of the unpreconditionable. How large will your matrices get?
Barry
>
> Thanks,
> Justin
>
> On Sat, Feb 2, 2019 at 1:41 PM Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> wrote:
> The coarse grid is getting set to SOR rather than LU.
>
> Matt
>
> On Fri, Feb 1, 2019 at 3:54 PM Justin Chang <jychang48 at gmail.com<mailto:jychang48 at gmail.com>> 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<mailto:knepley at gmail.com>> wrote:
> On Fri, Feb 1, 2019 at 3:05 PM Justin Chang <jychang48 at gmail.com<mailto: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<mailto: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<mailto:knepley at gmail.com>> wrote:
> On Thu, Jan 31, 2019 at 6:22 PM Justin Chang <jychang48 at gmail.com<mailto: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<mailto: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<mailto: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/
>
>
> --
> 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/
>
>
> --
> 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/
>
>
> --
> 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/
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