[petsc-users] Solving Linear Systems with Scalar Real and Complex
Mark Adams
mfadams at lbl.gov
Thu Aug 2 10:39:01 CDT 2018
It looks like ML and hypre are working well now. If you want to debug GAMG
you can run with -info, which is very noisy, and grep on GAMG or send the
whole output.
BTW, what equations are you solving?
On Thu, Aug 2, 2018 at 5:12 AM Pierpaolo Minelli <pierpaolo.minelli at cnr.it>
wrote:
> Thank you very much for the correction.
> By rebalancing the matrix coefficients, making them dimensionless, in my
> complex problem i managed to obtain a better result with both ML and HYPRE.
> GAMG instead seems to be unable to converge and in fact I get unexpected
> results. I report the outputs of the three simulations again (i tried to
> use also -pc_gamg_square_graph 20 without any improvement).
>
> Pierpaolo
>
> *-pc_type hypre -ksp_rtol 1.e-7 -ksp_monitor_true_residual*
>
> 0 KSP preconditioned resid norm 1.984853668904e-02 true resid norm
> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 1.924446712661e-04 true resid norm
> 1.204260204811e-04 ||r(i)||/||b|| 4.041323752460e-02
> 2 KSP preconditioned resid norm 5.161509100765e-06 true resid norm
> 2.810809726926e-06 ||r(i)||/||b|| 9.432672496933e-04
> 3 KSP preconditioned resid norm 9.297326931238e-08 true resid norm
> 4.474617977876e-08 ||r(i)||/||b|| 1.501617328625e-05
> 4 KSP preconditioned resid norm 1.910271882670e-09 true resid norm
> 9.637470658283e-10 ||r(i)||/||b|| 3.234196308186e-07
> 0 KSP preconditioned resid norm 2.157687745805e+04 true resid norm
> 3.182001523188e+03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 1.949268476386e+02 true resid norm
> 1.243419788627e+02 ||r(i)||/||b|| 3.907665598415e-02
> 2 KSP preconditioned resid norm 5.078054475792e+00 true resid norm
> 2.745355604400e+00 ||r(i)||/||b|| 8.627763325675e-04
> 3 KSP preconditioned resid norm 8.663802743529e-02 true resid norm
> 4.254290979292e-02 ||r(i)||/||b|| 1.336985839979e-05
> 4 KSP preconditioned resid norm 1.795605563039e-03 true resid norm
> 9.040507428245e-04 ||r(i)||/||b|| 2.841138623714e-07
> 0 KSP preconditioned resid norm 6.728304961395e+02 true resid norm
> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 2.190497539532e+01 true resid norm
> 4.630095820203e+02 ||r(i)||/||b|| 2.463500802413e+00
> 2 KSP preconditioned resid norm 8.425561564252e-01 true resid norm
> 7.012565302251e+01 ||r(i)||/||b|| 3.731123700223e-01
> 3 KSP preconditioned resid norm 3.029848345705e-02 true resid norm
> 4.379018464663e+00 ||r(i)||/||b|| 2.329911932795e-02
> 4 KSP preconditioned resid norm 7.374025528575e-04 true resid norm
> 1.337183702137e-01 ||r(i)||/||b|| 7.114654320570e-04
> 5 KSP preconditioned resid norm 3.009400175162e-05 true resid norm
> 7.731135032616e-03 ||r(i)||/||b|| 4.113447776459e-05
>
> *-pc_type ml -ksp_rtol 1.e-7 -ksp_monitor_true_residual*
>
> 0 KSP preconditioned resid norm 1.825767020538e-02 true resid norm
> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 6.495628259383e-04 true resid norm
> 3.739440526742e-04 ||r(i)||/||b|| 1.254902367550e-01
> 2 KSP preconditioned resid norm 4.971875712015e-05 true resid norm
> 2.118856024328e-05 ||r(i)||/||b|| 7.110575559127e-03
> 3 KSP preconditioned resid norm 3.726806462912e-06 true resid norm
> 1.370355844514e-06 ||r(i)||/||b|| 4.598716790303e-04
> 4 KSP preconditioned resid norm 2.496898447120e-07 true resid norm
> 9.494701893753e-08 ||r(i)||/||b|| 3.186285167645e-05
> 5 KSP preconditioned resid norm 1.541814409235e-08 true resid norm
> 6.216753346769e-09 ||r(i)||/||b|| 2.086252859898e-06
> 6 KSP preconditioned resid norm 1.153890845138e-09 true resid norm
> 5.290239857745e-10 ||r(i)||/||b|| 1.775328281039e-07
> 0 KSP preconditioned resid norm 1.961448048639e+04 true resid norm
> 3.182001523188e+03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 7.940694187370e+02 true resid norm
> 4.331011797078e+02 ||r(i)||/||b|| 1.361096707691e-01
> 2 KSP preconditioned resid norm 6.141876183555e+01 true resid norm
> 2.734346095946e+01 ||r(i)||/||b|| 8.593164007057e-03
> 3 KSP preconditioned resid norm 4.872887149917e+00 true resid norm
> 1.774255242955e+00 ||r(i)||/||b|| 5.575909470898e-04
> 4 KSP preconditioned resid norm 3.088357668927e-01 true resid norm
> 1.183728642343e-01 ||r(i)||/||b|| 3.720075662179e-05
> 5 KSP preconditioned resid norm 2.030016543073e-02 true resid norm
> 7.924623904393e-03 ||r(i)||/||b|| 2.490452580442e-06
> 6 KSP preconditioned resid norm 1.458276941086e-03 true resid norm
> 6.781128809522e-04 ||r(i)||/||b|| 2.131089114856e-07
> 0 KSP preconditioned resid norm 6.230592591466e+02 true resid norm
> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 3.825349376322e+01 true resid norm
> 7.755266613308e+02 ||r(i)||/||b|| 4.126287287931e+00
> 2 KSP preconditioned resid norm 4.321561767174e+00 true resid norm
> 2.170558998883e+02 ||r(i)||/||b|| 1.154873255992e+00
> 3 KSP preconditioned resid norm 2.806349660119e-01 true resid norm
> 2.931496742303e+01 ||r(i)||/||b|| 1.559739767247e-01
> 4 KSP preconditioned resid norm 1.707567397460e-02 true resid norm
> 2.684913551118e+00 ||r(i)||/||b|| 1.428542074383e-02
> 5 KSP preconditioned resid norm 1.741069717192e-03 true resid norm
> 2.914639372698e-01 ||r(i)||/||b|| 1.550770591410e-03
> 6 KSP preconditioned resid norm 1.460913620440e-04 true resid norm
> 3.460791330512e-02 ||r(i)||/||b|| 1.841357619965e-04
> 7 KSP preconditioned resid norm 1.741167177387e-05 true resid norm
> 3.396573365236e-03 ||r(i)||/||b|| 1.807189642642e-05
>
> *-pc_type gamg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true
> -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-7
> -ksp_max_it 30 -ksp_monitor_true_residual*
>
> 0 KSP preconditioned resid norm 1.244808265687e+15 true resid norm
> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 3.064535247522e+14 true resid norm
> 2.984544079484e-03 ||r(i)||/||b|| 1.001569995463e+00
> 2 KSP preconditioned resid norm 5.618140421534e+12 true resid norm
> 2.985603691163e-03 ||r(i)||/||b|| 1.001925585876e+00
> 3 KSP preconditioned resid norm 1.553607230691e+12 true resid norm
> 2.986068066312e-03 ||r(i)||/||b|| 1.002081423486e+00
> 4 KSP preconditioned resid norm 2.754119595329e+11 true resid norm
> 2.986119711375e-03 ||r(i)||/||b|| 1.002098754825e+00
> 5 KSP preconditioned resid norm 2.443949058171e+11 true resid norm
> 2.986120048522e-03 ||r(i)||/||b|| 1.002098867967e+00
> 6 KSP preconditioned resid norm 5.097094561118e+10 true resid norm
> 2.986121310105e-03 ||r(i)||/||b|| 1.002099291336e+00
> 7 KSP preconditioned resid norm 5.917979151193e+09 true resid norm
> 2.986121369446e-03 ||r(i)||/||b|| 1.002099311250e+00
> 8 KSP preconditioned resid norm 5.917672183458e+09 true resid norm
> 2.986121369424e-03 ||r(i)||/||b|| 1.002099311243e+00
> 9 KSP preconditioned resid norm 4.641300731865e+08 true resid norm
> 2.986121370475e-03 ||r(i)||/||b|| 1.002099311595e+00
> 10 KSP preconditioned resid norm 4.634203577645e+08 true resid norm
> 2.986121382852e-03 ||r(i)||/||b|| 1.002099315749e+00
> 11 KSP preconditioned resid norm 4.587254969048e+08 true resid norm
> 2.986121419848e-03 ||r(i)||/||b|| 1.002099328164e+00
> 12 KSP preconditioned resid norm 4.586269695339e+08 true resid norm
> 2.986121536662e-03 ||r(i)||/||b|| 1.002099367365e+00
> 13 KSP preconditioned resid norm 4.581015928356e+08 true resid norm
> 2.986122475198e-03 ||r(i)||/||b|| 1.002099682325e+00
> 14 KSP preconditioned resid norm 4.571106094607e+08 true resid norm
> 2.986124378604e-03 ||r(i)||/||b|| 1.002100321080e+00
> 15 KSP preconditioned resid norm 4.536929046842e+08 true resid norm
> 2.986134395719e-03 ||r(i)||/||b|| 1.002103682680e+00
> 16 KSP preconditioned resid norm 4.535016059345e+08 true resid norm
> 2.986135027367e-03 ||r(i)||/||b|| 1.002103894652e+00
> 17 KSP preconditioned resid norm 4.534978476038e+08 true resid norm
> 2.986135001016e-03 ||r(i)||/||b|| 1.002103885808e+00
> 18 KSP preconditioned resid norm 4.467301680293e+08 true resid norm
> 2.986152055223e-03 ||r(i)||/||b|| 1.002109608955e+00
> 19 KSP preconditioned resid norm 4.310227073192e+08 true resid norm
> 2.986506137056e-03 ||r(i)||/||b|| 1.002228433717e+00
> 20 KSP preconditioned resid norm 3.520200847767e+08 true resid norm
> 2.989053346159e-03 ||r(i)||/||b|| 1.003083240395e+00
> 21 KSP preconditioned resid norm 3.273563895836e+08 true resid norm
> 2.990009521982e-03 ||r(i)||/||b|| 1.003404119226e+00
> 22 KSP preconditioned resid norm 1.692012480634e+08 true resid norm
> 2.999909265923e-03 ||r(i)||/||b|| 1.006726330669e+00
> 23 KSP preconditioned resid norm 1.616841528495e+08 true resid norm
> 3.002594301034e-03 ||r(i)||/||b|| 1.007627389770e+00
> 24 KSP preconditioned resid norm 1.588031462511e+08 true resid norm
> 3.003789395992e-03 ||r(i)||/||b|| 1.008028446420e+00
> 25 KSP preconditioned resid norm 1.585650863283e+08 true resid norm
> 3.003987247746e-03 ||r(i)||/||b|| 1.008094842618e+00
> 26 KSP preconditioned resid norm 1.482994894928e+08 true resid norm
> 3.004024810257e-03 ||r(i)||/||b|| 1.008107448056e+00
> 27 KSP preconditioned resid norm 1.293588493466e+08 true resid norm
> 3.005576275194e-03 ||r(i)||/||b|| 1.008628097337e+00
> 28 KSP preconditioned resid norm 1.082178475680e+08 true resid norm
> 3.010519288328e-03 ||r(i)||/||b|| 1.010286901332e+00
> 0 KSP preconditioned resid norm 4.688654651573e+20 true resid norm
> 3.182001523188e+03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 4.673814485341e+20 true resid norm
> 3.182057223735e+03 ||r(i)||/||b|| 1.000017504878e+00
> 2 KSP preconditioned resid norm 1.203925723825e+19 true resid norm
> 3.185040065807e+03 ||r(i)||/||b|| 1.000954915514e+00
> 3 KSP preconditioned resid norm 3.042270671882e+18 true resid norm
> 3.187076078024e+03 ||r(i)||/||b|| 1.001594768198e+00
> 4 KSP preconditioned resid norm 5.678481873896e+17 true resid norm
> 3.187261697361e+03 ||r(i)||/||b|| 1.001653102343e+00
> 5 KSP preconditioned resid norm 4.462228267454e+17 true resid norm
> 3.187264158420e+03 ||r(i)||/||b|| 1.001653875774e+00
> 6 KSP preconditioned resid norm 9.314909592131e+16 true resid norm
> 3.187268102332e+03 ||r(i)||/||b|| 1.001655115218e+00
> 7 KSP preconditioned resid norm 8.843621410196e+15 true resid norm
> 3.187268285359e+03 ||r(i)||/||b|| 1.001655172737e+00
> 8 KSP preconditioned resid norm 8.214565462317e+15 true resid norm
> 3.187268286281e+03 ||r(i)||/||b|| 1.001655173027e+00
> 9 KSP preconditioned resid norm 4.525549868436e+14 true resid norm
> 3.187268287235e+03 ||r(i)||/||b|| 1.001655173327e+00
> 10 KSP preconditioned resid norm 4.522301211733e+14 true resid norm
> 3.187268289937e+03 ||r(i)||/||b|| 1.001655174176e+00
> 11 KSP preconditioned resid norm 4.295952793336e+14 true resid norm
> 3.187268328860e+03 ||r(i)||/||b|| 1.001655186408e+00
> 12 KSP preconditioned resid norm 4.294637249487e+14 true resid norm
> 3.187268422725e+03 ||r(i)||/||b|| 1.001655215907e+00
> 13 KSP preconditioned resid norm 4.285778654372e+14 true resid norm
> 3.187269536466e+03 ||r(i)||/||b|| 1.001655565920e+00
> 14 KSP preconditioned resid norm 4.162983479677e+14 true resid norm
> 3.187285280554e+03 ||r(i)||/||b|| 1.001660513777e+00
> 15 KSP preconditioned resid norm 4.162978556133e+14 true resid norm
> 3.187285288668e+03 ||r(i)||/||b|| 1.001660516326e+00
> 16 KSP preconditioned resid norm 4.161875124570e+14 true resid norm
> 3.187285309889e+03 ||r(i)||/||b|| 1.001660522996e+00
> 17 KSP preconditioned resid norm 4.117671313790e+14 true resid norm
> 3.187289951588e+03 ||r(i)||/||b|| 1.001661981731e+00
> 18 KSP preconditioned resid norm 4.103112320458e+14 true resid norm
> 3.187292327095e+03 ||r(i)||/||b|| 1.001662728276e+00
> 19 KSP preconditioned resid norm 4.032611123108e+14 true resid norm
> 3.187463967167e+03 ||r(i)||/||b|| 1.001716669191e+00
> 20 KSP preconditioned resid norm 3.432105733172e+14 true resid norm
> 3.189686334937e+03 ||r(i)||/||b|| 1.002415087389e+00
> 21 KSP preconditioned resid norm 3.125440416815e+14 true resid norm
> 3.191137543657e+03 ||r(i)||/||b|| 1.002871155278e+00
> 22 KSP preconditioned resid norm 2.214281952780e+14 true resid norm
> 3.198766855775e+03 ||r(i)||/||b|| 1.005268800931e+00
> 23 KSP preconditioned resid norm 2.205574806871e+14 true resid norm
> 3.198012835064e+03 ||r(i)||/||b|| 1.005031836647e+00
> 24 KSP preconditioned resid norm 2.202202974538e+14 true resid norm
> 3.197792157500e+03 ||r(i)||/||b|| 1.004962484838e+00
> 25 KSP preconditioned resid norm 2.188941573096e+14 true resid norm
> 3.197631986560e+03 ||r(i)||/||b|| 1.004912148300e+00
> 26 KSP preconditioned resid norm 1.811445509155e+14 true resid norm
> 3.201511171410e+03 ||r(i)||/||b|| 1.006131250435e+00
> 27 KSP preconditioned resid norm 1.333006235872e+14 true resid norm
> 3.207865456494e+03 ||r(i)||/||b|| 1.008128196394e+00
> 28 KSP preconditioned resid norm 1.290269724722e+14 true resid norm
> 3.209026547700e+03 ||r(i)||/||b|| 1.008493089747e+00
> 29 KSP preconditioned resid norm 8.645848930695e+13 true resid norm
> 3.216715733004e+03 ||r(i)||/||b|| 1.010909551603e+00
> 30 KSP preconditioned resid norm 7.051095175336e+13 true resid norm
> 3.219405322929e+03 ||r(i)||/||b|| 1.011754802589e+00
> 0 KSP preconditioned resid norm 4.970534641714e+02 true resid norm
> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 9.825390294838e+01 true resid norm
> 6.304087699909e+03 ||r(i)||/||b|| 3.354169267824e+01
> 2 KSP preconditioned resid norm 1.317425630977e+01 true resid norm
> 1.659038483292e+03 ||r(i)||/||b|| 8.827123224947e+00
> 3 KSP preconditioned resid norm 1.267331175258e+00 true resid norm
> 3.723773819327e+02 ||r(i)||/||b|| 1.981280765700e+00
> 4 KSP preconditioned resid norm 1.451198865319e-01 true resid norm
> 6.113281457366e+01 ||r(i)||/||b|| 3.252648403059e-01
> 5 KSP preconditioned resid norm 2.428012832580e-02 true resid norm
> 9.525516489005e+00 ||r(i)||/||b|| 5.068171032587e-02
> 6 KSP preconditioned resid norm 3.273131599046e-03 true resid norm
> 1.693121214500e+00 ||r(i)||/||b|| 9.008464689439e-03
> 7 KSP preconditioned resid norm 3.629020564958e-04 true resid norm
> 1.937921370699e-01 ||r(i)||/||b|| 1.031095475584e-03
> 8 KSP preconditioned resid norm 4.303742583350e-05 true resid norm
> 2.733022203972e-02 ||r(i)||/||b|| 1.454138889117e-04
>
> *-pc_type gamg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true
> -pc_gamg_square_graph 20 -pc_gamg_threshold 0. -ksp_rtol 1.e-7
> -ksp_max_it 30 -ksp_monitor_true_residual*
>
> 0 KSP preconditioned resid norm 3.031864566839e+14 true resid norm
> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 1.212883161649e+14 true resid norm
> 2.982229202367e-03 ||r(i)||/||b|| 1.000793156052e+00
> 2 KSP preconditioned resid norm 5.312941731712e+12 true resid norm
> 2.985627671175e-03 ||r(i)||/||b|| 1.001933633223e+00
> 3 KSP preconditioned resid norm 3.602406845592e+12 true resid norm
> 2.985818915765e-03 ||r(i)||/||b|| 1.001997812152e+00
> 4 KSP preconditioned resid norm 6.891073564923e+10 true resid norm
> 2.986120881484e-03 ||r(i)||/||b|| 1.002099147497e+00
> 5 KSP preconditioned resid norm 1.267096776171e+09 true resid norm
> 2.986121018547e-03 ||r(i)||/||b|| 1.002099193494e+00
> 6 KSP preconditioned resid norm 5.130735430694e+08 true resid norm
> 2.986121020564e-03 ||r(i)||/||b|| 1.002099194170e+00
> 7 KSP preconditioned resid norm 5.122457469991e+08 true resid norm
> 2.986121025937e-03 ||r(i)||/||b|| 1.002099195974e+00
> 8 KSP preconditioned resid norm 5.115042446514e+08 true resid norm
> 2.986121044146e-03 ||r(i)||/||b|| 1.002099202084e+00
> 9 KSP preconditioned resid norm 5.103842476065e+08 true resid norm
> 2.986121084005e-03 ||r(i)||/||b|| 1.002099215460e+00
> 10 KSP preconditioned resid norm 5.103414725629e+08 true resid norm
> 2.986121151167e-03 ||r(i)||/||b|| 1.002099237999e+00
> 11 KSP preconditioned resid norm 5.103050707318e+08 true resid norm
> 2.986121488999e-03 ||r(i)||/||b|| 1.002099351370e+00
> 12 KSP preconditioned resid norm 5.101511376685e+08 true resid norm
> 2.986123179301e-03 ||r(i)||/||b|| 1.002099918611e+00
> 13 KSP preconditioned resid norm 5.101218154297e+08 true resid norm
> 2.986123839891e-03 ||r(i)||/||b|| 1.002100140296e+00
> 14 KSP preconditioned resid norm 5.095285470767e+08 true resid norm
> 2.986138347067e-03 ||r(i)||/||b|| 1.002105008695e+00
> 15 KSP preconditioned resid norm 5.082373114330e+08 true resid norm
> 2.986170368742e-03 ||r(i)||/||b|| 1.002115754708e+00
> 16 KSP preconditioned resid norm 5.079055966450e+08 true resid norm
> 2.986178765357e-03 ||r(i)||/||b|| 1.002118572491e+00
> 17 KSP preconditioned resid norm 4.278159855635e+08 true resid norm
> 2.989173921061e-03 ||r(i)||/||b|| 1.003123703595e+00
> 18 KSP preconditioned resid norm 3.704767561598e+08 true resid norm
> 2.991993992919e-03 ||r(i)||/||b|| 1.004070079082e+00
> 19 KSP preconditioned resid norm 3.690160215681e+08 true resid norm
> 2.992090282533e-03 ||r(i)||/||b|| 1.004102392489e+00
> 20 KSP preconditioned resid norm 3.135406273863e+08 true resid norm
> 2.996344554486e-03 ||r(i)||/||b|| 1.005530064867e+00
> 21 KSP preconditioned resid norm 1.938459923255e+08 true resid norm
> 3.005844334042e-03 ||r(i)||/||b|| 1.008718054025e+00
> 22 KSP preconditioned resid norm 1.827826394560e+08 true resid norm
> 3.007605246670e-03 ||r(i)||/||b|| 1.009308990933e+00
> 23 KSP preconditioned resid norm 1.108660460314e+08 true resid norm
> 3.020965814060e-03 ||r(i)||/||b|| 1.013792604867e+00
> 24 KSP preconditioned resid norm 1.051235646374e+08 true resid norm
> 3.021541389078e-03 ||r(i)||/||b|| 1.013985759551e+00
> 25 KSP preconditioned resid norm 7.173044522784e+07 true resid norm
> 3.024254088703e-03 ||r(i)||/||b|| 1.014896102464e+00
> 26 KSP preconditioned resid norm 6.350860057272e+07 true resid norm
> 3.023434854983e-03 ||r(i)||/||b|| 1.014621179430e+00
> 27 KSP preconditioned resid norm 5.267152287984e+07 true resid norm
> 3.022203752421e-03 ||r(i)||/||b|| 1.014208039146e+00
> 28 KSP preconditioned resid norm 4.650599761568e+07 true resid norm
> 3.022093139351e-03 ||r(i)||/||b|| 1.014170918994e+00
> 29 KSP preconditioned resid norm 3.141941642480e+07 true resid norm
> 3.023444082486e-03 ||r(i)||/||b|| 1.014624276047e+00
> 30 KSP preconditioned resid norm 2.065598123858e+07 true resid norm
> 3.024498453617e-03 ||r(i)||/||b|| 1.014978107808e+00
> 0 KSP preconditioned resid norm 4.257133849062e+20 true resid norm
> 3.182001523188e+03 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 2.793742274994e+19 true resid norm
> 3.184922256681e+03 ||r(i)||/||b|| 1.000917891922e+00
> 2 KSP preconditioned resid norm 1.137325629643e+19 true resid norm
> 3.185147137826e+03 ||r(i)||/||b|| 1.000988564781e+00
> 3 KSP preconditioned resid norm 7.164960007703e+18 true resid norm
> 3.186117509159e+03 ||r(i)||/||b|| 1.001293521056e+00
> 4 KSP preconditioned resid norm 1.109461464210e+17 true resid norm
> 3.187268097356e+03 ||r(i)||/||b|| 1.001655113654e+00
> 5 KSP preconditioned resid norm 1.984768045830e+15 true resid norm
> 3.187268427639e+03 ||r(i)||/||b|| 1.001655217451e+00
> 6 KSP preconditioned resid norm 7.354105789290e+14 true resid norm
> 3.187268429720e+03 ||r(i)||/||b|| 1.001655218105e+00
> 7 KSP preconditioned resid norm 6.662738391887e+14 true resid norm
> 3.187268442496e+03 ||r(i)||/||b|| 1.001655222120e+00
> 8 KSP preconditioned resid norm 5.358556594776e+14 true resid norm
> 3.187268479547e+03 ||r(i)||/||b|| 1.001655233764e+00
> 9 KSP preconditioned resid norm 5.055368509046e+14 true resid norm
> 3.187268491131e+03 ||r(i)||/||b|| 1.001655237405e+00
> 10 KSP preconditioned resid norm 5.050370080533e+14 true resid norm
> 3.187268557074e+03 ||r(i)||/||b|| 1.001655258129e+00
> 11 KSP preconditioned resid norm 5.049526065770e+14 true resid norm
> 3.187269209319e+03 ||r(i)||/||b|| 1.001655463108e+00
> 12 KSP preconditioned resid norm 5.048442087580e+14 true resid norm
> 3.187270145328e+03 ||r(i)||/||b|| 1.001655757265e+00
> 13 KSP preconditioned resid norm 5.048317293084e+14 true resid norm
> 3.187270420057e+03 ||r(i)||/||b|| 1.001655843604e+00
> 14 KSP preconditioned resid norm 5.046339848740e+14 true resid norm
> 3.187276012517e+03 ||r(i)||/||b|| 1.001657601133e+00
> 15 KSP preconditioned resid norm 5.036574780195e+14 true resid norm
> 3.187304228896e+03 ||r(i)||/||b|| 1.001666468627e+00
> 16 KSP preconditioned resid norm 5.033948448037e+14 true resid norm
> 3.187311929535e+03 ||r(i)||/||b|| 1.001668888688e+00
> 17 KSP preconditioned resid norm 4.374073117273e+14 true resid norm
> 3.190248474209e+03 ||r(i)||/||b|| 1.002591749552e+00
> 18 KSP preconditioned resid norm 3.454318321770e+14 true resid norm
> 3.195991944291e+03 ||r(i)||/||b|| 1.004396736143e+00
> 19 KSP preconditioned resid norm 3.438483821871e+14 true resid norm
> 3.196113376292e+03 ||r(i)||/||b|| 1.004434898287e+00
> 20 KSP preconditioned resid norm 3.090011643835e+14 true resid norm
> 3.199125186774e+03 ||r(i)||/||b|| 1.005381412756e+00
> 21 KSP preconditioned resid norm 1.976112359751e+14 true resid norm
> 3.209202875553e+03 ||r(i)||/||b|| 1.008548503879e+00
> 22 KSP preconditioned resid norm 1.874048396302e+14 true resid norm
> 3.210733816807e+03 ||r(i)||/||b|| 1.009029629122e+00
> 23 KSP preconditioned resid norm 1.086663247242e+14 true resid norm
> 3.224219602770e+03 ||r(i)||/||b|| 1.013267774787e+00
> 24 KSP preconditioned resid norm 1.036005882413e+14 true resid norm
> 3.224749127723e+03 ||r(i)||/||b|| 1.013434187326e+00
> 25 KSP preconditioned resid norm 6.943244220256e+13 true resid norm
> 3.227732423395e+03 ||r(i)||/||b|| 1.014371740514e+00
> 26 KSP preconditioned resid norm 6.064453821356e+13 true resid norm
> 3.227303114420e+03 ||r(i)||/||b|| 1.014236822611e+00
> 27 KSP preconditioned resid norm 5.237876331038e+13 true resid norm
> 3.226320811775e+03 ||r(i)||/||b|| 1.013928116710e+00
> 28 KSP preconditioned resid norm 4.407157490353e+13 true resid norm
> 3.226123552298e+03 ||r(i)||/||b|| 1.013866124447e+00
> 29 KSP preconditioned resid norm 3.691867703712e+13 true resid norm
> 3.226578266524e+03 ||r(i)||/||b|| 1.014009026398e+00
> 0 KSP preconditioned resid norm 4.105203293801e+02 true resid norm
> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 1.404700393158e+02 true resid norm
> 5.941722233814e+03 ||r(i)||/||b|| 3.161368157187e+01
> 2 KSP preconditioned resid norm 3.849004101235e+01 true resid norm
> 3.456178528017e+03 ||r(i)||/||b|| 1.838903320294e+01
> 3 KSP preconditioned resid norm 8.384263059954e+00 true resid norm
> 1.401839902990e+03 ||r(i)||/||b|| 7.458665781386e+00
> 4 KSP preconditioned resid norm 1.363029002549e+00 true resid norm
> 3.612540200618e+02 ||r(i)||/||b|| 1.922097517753e+00
> 5 KSP preconditioned resid norm 3.734525206097e-01 true resid norm
> 1.272038960182e+02 ||r(i)||/||b|| 6.768043515285e-01
> 6 KSP preconditioned resid norm 8.146021124788e-02 true resid norm
> 3.196642795661e+01 ||r(i)||/||b|| 1.700814064749e-01
> 7 KSP preconditioned resid norm 2.110568459516e-02 true resid norm
> 6.793208791728e+00 ||r(i)||/||b|| 3.614412305757e-02
> 8 KSP preconditioned resid norm 4.044708317961e-03 true resid norm
> 1.976363197299e+00 ||r(i)||/||b|| 1.051548933644e-02
> 9 KSP preconditioned resid norm 9.154675861687e-04 true resid norm
> 3.458820713849e-01 ||r(i)||/||b|| 1.840309128547e-03
> 10 KSP preconditioned resid norm 2.106487039520e-04 true resid norm
> 1.064965566696e-01 ||r(i)||/||b|| 5.666283442018e-04
> 11 KSP preconditioned resid norm 5.145654020522e-05 true resid norm
> 2.436255895394e-02 ||r(i)||/||b|| 1.296240636532e-04
> 12 KSP preconditioned resid norm 1.223910887488e-05 true resid norm
> 4.954689842368e-03 ||r(i)||/||b|| 2.636205140533e-05
>
> Il giorno 01 ago 2018, alle ore 15:41, Matthew Knepley <knepley at gmail.com>
> ha scritto:
>
> On Wed, Aug 1, 2018 at 9:02 AM Pierpaolo Minelli <pierpaolo.minelli at cnr.it>
> wrote:
>
>> Il giorno 27 lug 2018, alle ore 18:32, Smith, Barry F. <
>> bsmith at mcs.anl.gov> ha scritto:
>>
>> On Jul 27, 2018, at 3:26 AM, Pierpaolo Minelli <pierpaolo.minelli at cnr.it>
>> wrote:
>>
>>
>> Finally, I have a question. In my simulation I solve the two systems at
>> each step of the calculation, and it was my habit to use the following
>> option after the first resolution and before solving the system in the
>> second time step:
>>
>> call KSPSetInitialGuessNonzero(ksp,PETSC_TRUE,ierr)
>>
>> Since this option was incompatible with the use of MUMPS or SuperLU_Dist,
>> I commented on it and noticed, to my surprise, that iterative methods were
>> not affected by this comment, rather they were slightly faster. Is this
>> normal? Or do I use this command incorrectly?
>>
>>
>> Presuming this is a linear problem?
>>
>>
>> You should run with -ksp_monitor_true_residual and compare the final
>> residual norms (at linear system convergence). Since KSP uses a relative
>> decrease in the residual norm to declare convergence what you have told us
>> isn't enough to determine if one is converging "faster" to the solution
>> then the other.
>>
>> Barry
>>
>>
>> Yes, there are two linear problems. The first in the field of complex
>> numbers (which I divided into two problems in the field of real numbers as
>> suggested by Matthew) and the second in the field of real numbers.
>>
>> These are the results obtained using the option
>> -ksp_monitor_true_residual:
>>
>> *-pc_type gamg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true
>> -pc_gamg_square_graph 1 -pc_gamg_threshold 0. -ksp_rtol 1.e-7
>> -ksp_monitor_true_residual*
>>
>> 0 KSP preconditioned resid norm 1.324344286254e-02 true resid norm
>> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 3.399266083153e-03 true resid norm
>> 1.196951495628e+05 ||r(i)||/||b|| 4.016796777391e+07
>> 2 KSP preconditioned resid norm 6.287919852336e-04 true resid norm
>> 4.429876706490e+04 ||r(i)||/||b|| 1.486602802524e+07
>> 3 KSP preconditioned resid norm 8.836547690039e-05 true resid norm
>> 1.182383826632e+04 ||r(i)||/||b|| 3.967909778970e+06
>> 4 KSP preconditioned resid norm 1.291370058561e-05 true resid norm
>> 2.801893692950e+03 ||r(i)||/||b|| 9.402751571421e+05
>> 5 KSP preconditioned resid norm 2.073922228951e-06 true resid norm
>> 6.312112895919e+02 ||r(i)||/||b|| 2.118254150770e+05
>> 6 KSP preconditioned resid norm 3.283811876800e-07 true resid norm
>> 8.777865833701e+01 ||r(i)||/||b|| 2.945725313178e+04
>> 7 KSP preconditioned resid norm 5.414680273500e-08 true resid norm
>> 1.610127004050e+01 ||r(i)||/||b|| 5.403354258448e+03
>> 8 KSP preconditioned resid norm 9.645834363683e-09 true resid norm
>> 3.006444251909e+00 ||r(i)||/||b|| 1.008919377818e+03
>> 9 KSP preconditioned resid norm 1.915420455785e-09 true resid norm
>> 6.672996533262e-01 ||r(i)||/||b|| 2.239361500298e+02
>> 10 KSP preconditioned resid norm 3.334928638696e-10 true resid norm
>> 1.185976397497e-01 ||r(i)||/||b|| 3.979965929219e+01
>>
>
> You can see from the "true resid norm" that your complex problem is not
> actually being solved. ML and Hypre have similar results.
> I would guess that your coarse grid is near singular.
>
> The real problem is being solved correctly, although you are still 100x
> off the true residual so the preconditioner is not great.
> Have you tested with a manufactured solution?
>
> Thanks,
>
> Matt
>
>
>
>
>
>
>
>
>
>
>> 0 KSP preconditioned resid norm 1.416256896904e+04 true resid norm
>> 6.623626291881e+05 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 3.781264980774e+03 true resid norm
>> 1.283809201228e+11 ||r(i)||/||b|| 1.938227104995e+05
>> 2 KSP preconditioned resid norm 7.392413714593e+02 true resid norm
>> 4.990467508600e+10 ||r(i)||/||b|| 7.534343407504e+04
>> 3 KSP preconditioned resid norm 1.087641767696e+02 true resid norm
>> 1.367263690390e+10 ||r(i)||/||b|| 2.064222270610e+04
>> 4 KSP preconditioned resid norm 1.627726591174e+01 true resid norm
>> 3.451534923895e+09 ||r(i)||/||b|| 5.210944536719e+03
>> 5 KSP preconditioned resid norm 2.564636460142e+00 true resid norm
>> 7.980525032990e+08 ||r(i)||/||b|| 1.204857381941e+03
>> 6 KSP preconditioned resid norm 4.252626820180e-01 true resid norm
>> 1.151817528111e+08 ||r(i)||/||b|| 1.738953070953e+02
>> 7 KSP preconditioned resid norm 6.758292325957e-02 true resid norm
>> 2.065701091779e+07 ||r(i)||/||b|| 3.118686050134e+01
>> 8 KSP preconditioned resid norm 1.099617201063e-02 true resid norm
>> 3.470561062696e+06 ||r(i)||/||b|| 5.239669192917e+00
>> 9 KSP preconditioned resid norm 2.195352537111e-03 true resid norm
>> 7.056823048483e+05 ||r(i)||/||b|| 1.065401750871e+00
>> 10 KSP preconditioned resid norm 4.380752631896e-04 true resid norm
>> 1.440377395627e+05 ||r(i)||/||b|| 2.174605468598e-01
>>
>> 0 KSP preconditioned resid norm 4.970534641714e+02 true resid norm
>> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 9.825390294838e+01 true resid norm
>> 6.304087699909e+03 ||r(i)||/||b|| 3.354169267824e+01
>> 2 KSP preconditioned resid norm 1.317425630977e+01 true resid norm
>> 1.659038483292e+03 ||r(i)||/||b|| 8.827123224947e+00
>> 3 KSP preconditioned resid norm 1.267331175258e+00 true resid norm
>> 3.723773819327e+02 ||r(i)||/||b|| 1.981280765700e+00
>> 4 KSP preconditioned resid norm 1.451198865319e-01 true resid norm
>> 6.113281457366e+01 ||r(i)||/||b|| 3.252648403059e-01
>> 5 KSP preconditioned resid norm 2.428012832580e-02 true resid norm
>> 9.525516489005e+00 ||r(i)||/||b|| 5.068171032587e-02
>> 6 KSP preconditioned resid norm 3.273131599046e-03 true resid norm
>> 1.693121214500e+00 ||r(i)||/||b|| 9.008464689439e-03
>> 7 KSP preconditioned resid norm 3.629020564958e-04 true resid norm
>> 1.937921370699e-01 ||r(i)||/||b|| 1.031095475584e-03
>> 8 KSP preconditioned resid norm 4.303742583350e-05 true resid norm
>> 2.733022203972e-02 ||r(i)||/||b|| 1.454138889117e-04
>>
>> *-pc_type ml -ksp_rtol 1.e-7 -ksp_monitor_true_residual*
>>
>> 0 KSP preconditioned resid norm 1.825767020537e-02 true resid norm
>> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 6.495628259378e-04 true resid norm
>> 1.373525306349e+04 ||r(i)||/||b|| 4.609353047603e+06
>> 2 KSP preconditioned resid norm 4.971875712010e-05 true resid norm
>> 2.154150315236e+03 ||r(i)||/||b|| 7.229018114651e+05
>> 3 KSP preconditioned resid norm 3.726806462903e-06 true resid norm
>> 3.000693510070e+02 ||r(i)||/||b|| 1.006989511706e+05
>> 4 KSP preconditioned resid norm 2.496898447113e-07 true resid norm
>> 3.004338446358e+01 ||r(i)||/||b|| 1.008212699813e+04
>> 5 KSP preconditioned resid norm 1.541814409235e-08 true resid norm
>> 2.256927674575e+00 ||r(i)||/||b|| 7.573924125705e+02
>> 6 KSP preconditioned resid norm 1.153890845088e-09 true resid norm
>> 2.007294077611e-01 ||r(i)||/||b|| 6.736189738408e+01
>> 0 KSP preconditioned resid norm 1.961448048638e+04 true resid norm
>> 6.623626291881e+05 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 7.940694187362e+02 true resid norm
>> 1.483756468402e+10 ||r(i)||/||b|| 2.240096894085e+04
>> 2 KSP preconditioned resid norm 6.141876183549e+01 true resid norm
>> 2.581042149104e+09 ||r(i)||/||b|| 3.896720671376e+03
>> 3 KSP preconditioned resid norm 4.872887149903e+00 true resid norm
>> 3.544664743366e+08 ||r(i)||/||b|| 5.351547003355e+02
>> 4 KSP preconditioned resid norm 3.088357668912e-01 true resid norm
>> 3.689655474675e+07 ||r(i)||/||b|| 5.570446326655e+01
>> 5 KSP preconditioned resid norm 2.030016543101e-02 true resid norm
>> 2.847019997470e+06 ||r(i)||/||b|| 4.298279933093e+00
>> 6 KSP preconditioned resid norm 1.458276940703e-03 true resid norm
>> 2.567051860886e+05 ||r(i)||/||b|| 3.875598875547e-01
>>
>> 0 KSP preconditioned resid norm 6.230592591466e+02 true resid norm
>> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 3.825349376322e+01 true resid norm
>> 7.755266613308e+02 ||r(i)||/||b|| 4.126287287931e+00
>> 2 KSP preconditioned resid norm 4.321561767174e+00 true resid norm
>> 2.170558998883e+02 ||r(i)||/||b|| 1.154873255992e+00
>> 3 KSP preconditioned resid norm 2.806349660119e-01 true resid norm
>> 2.931496742303e+01 ||r(i)||/||b|| 1.559739767247e-01
>> 4 KSP preconditioned resid norm 1.707567397460e-02 true resid norm
>> 2.684913551118e+00 ||r(i)||/||b|| 1.428542074383e-02
>> 5 KSP preconditioned resid norm 1.741069717192e-03 true resid norm
>> 2.914639372698e-01 ||r(i)||/||b|| 1.550770591410e-03
>> 6 KSP preconditioned resid norm 1.460913620440e-04 true resid norm
>> 3.460791330512e-02 ||r(i)||/||b|| 1.841357619965e-04
>> 7 KSP preconditioned resid norm 1.741167177387e-05 true resid norm
>> 3.396573365236e-03 ||r(i)||/||b|| 1.807189642642e-05
>>
>> *-pc_type hypre -ksp_rtol 1.e-7 -ksp_monitor_true_residual*
>>
>> 0 KSP preconditioned resid norm 1.984853668903e-02 true resid norm
>> 2.979865703850e-03 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 1.924446712660e-04 true resid norm
>> 8.461145171168e+03 ||r(i)||/||b|| 2.839438421750e+06
>> 2 KSP preconditioned resid norm 5.161509100761e-06 true resid norm
>> 4.501007519328e+02 ||r(i)||/||b|| 1.510473278548e+05
>> 3 KSP preconditioned resid norm 9.297326931235e-08 true resid norm
>> 1.474595580807e+01 ||r(i)||/||b|| 4.948530327732e+03
>> 4 KSP preconditioned resid norm 1.910271882618e-09 true resid norm
>> 3.603243780988e-01 ||r(i)||/||b|| 1.209196701829e+02
>> 0 KSP preconditioned resid norm 2.157687745804e+04 true resid norm
>> 6.623626291881e+05 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 1.949268476385e+02 true resid norm
>> 8.974916757495e+09 ||r(i)||/||b|| 1.354985375382e+04
>> 2 KSP preconditioned resid norm 5.078054475786e+00 true resid norm
>> 4.502684440161e+08 ||r(i)||/||b|| 6.797914377626e+02
>> 3 KSP preconditioned resid norm 8.663802743525e-02 true resid norm
>> 1.432117031381e+07 ||r(i)||/||b|| 2.162134408362e+01
>> 4 KSP preconditioned resid norm 1.795605563041e-03 true resid norm
>> 3.389868548833e+05 ||r(i)||/||b|| 5.117843911255e-01
>>
>> 0 KSP preconditioned resid norm 6.728304961395e+02 true resid norm
>> 1.879478105170e+02 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 2.190497539532e+01 true resid norm
>> 4.630095820203e+02 ||r(i)||/||b|| 2.463500802413e+00
>> 2 KSP preconditioned resid norm 8.425561564252e-01 true resid norm
>> 7.012565302251e+01 ||r(i)||/||b|| 3.731123700223e-01
>> 3 KSP preconditioned resid norm 3.029848345705e-02 true resid norm
>> 4.379018464663e+00 ||r(i)||/||b|| 2.329911932795e-02
>> 4 KSP preconditioned resid norm 7.374025528575e-04 true resid norm
>> 1.337183702137e-01 ||r(i)||/||b|| 7.114654320570e-04
>> 5 KSP preconditioned resid norm 3.009400175162e-05 true resid norm
>> 7.731135032616e-03 ||r(i)||/||b|| 4.113447776459e-05
>>
>> Thanks
>>
>> Pierpaolo
>>
>>
>> Thanks
>>
>> Pierpaolo
>>
>> Il giorno 23 lug 2018, alle ore 15:43, Mark Adams <mfadams at lbl.gov> ha
>> scritto:
>>
>> Note, as Barry said, GAMG works with native complex numbers. You can
>> start with your original complex build and use '-pc_type gamg'.
>> Mark
>>
>> On Mon, Jul 23, 2018 at 6:52 AM Pierpaolo Minelli <
>> pierpaolo.minelli at cnr.it> wrote:
>>
>>
>> Il giorno 20 lug 2018, alle ore 19:58, Smith, Barry F. <
>> bsmith at mcs.anl.gov> ha scritto:
>>
>>
>>
>> On Jul 20, 2018, at 7:01 AM, Pierpaolo Minelli <pierpaolo.minelli at cnr.it>
>> wrote:
>>
>> Hi,
>>
>> in my code I have to solve both a system in the field of real numbers and
>> in the field of complex numbers.
>> My approach has been as follows.
>> First I configured PETSc with the --with-scalar-type=complex option.
>> Using this option I have unfortunately lost the possibility to use the
>> two preconditioners ML and Hypre.
>>
>>
>> You should still be able to use the PETSc PCGAMG algebraic multigrid
>> solver. Have you tried that? If there are issues let us know because we
>> would like to continue to improve the performance of PCGAMG to get it to be
>> closer to as good as ML and hypre.
>>
>> Barry
>>
>>
>> I will try to convert, as suggested by Matthew, my complex system in a
>> system twice as large in real numbers. When i finish, i will try to use ML,
>> Hypre and GAMG and i let you know if there are any performance differences.
>>
>> Thanks
>>
>> Pierpaolo
>>
>>
>> I later created two subspaces of Krylov and tried to solve the two
>> systems as I used to when solving the only equation in the real numbers
>> field.
>> In order to correctly solve the system in the field of real numbers I had
>> to transform the coefficients from real to complex with an imaginary part
>> equal to zero.
>>
>> Is there a possibility to use a different and better approach to solve my
>> problem?
>>
>> Perhaps an approach where you can continue to use ML and Hypre for system
>> solving in the real numbers field or where you don't need to use complex
>> numbers when real numbers would actually suffice?
>>
>> Thanks in advance
>>
>> Pierpaolo
>>
>>
>>
>>
>>
>>
>>
>
> --
> 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.caam.rice.edu/~mk51/>
>
>
>
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