[petsc-users] Preconditioning systems of equations with complex numbers

Justin Chang jychang48 at gmail.com
Fri Feb 1 14:04:45 CST 2019 

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:

-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/>
>>>
>>
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