[petsc-users] Problems with FBCGSR

[Elias Karabelas]

Hi,

I'm using petsc for solving a non symmetric block system with a 
field-split preconditioner. At the moment I use the fgmres as outer 
solver. I recently discovered that there is also a flexible BICG variant 
in petsc. So I wanted to give it a try. However I get strange behaviour 
when using it. With FGMRES i got the following residual history

   0 KSP unpreconditioned resid norm 8.632122370708e+00 true resid norm 
8.632122370708e+00 ||r(i)||/||b|| 1.000000000000e+00
   1 KSP unpreconditioned resid norm 5.881521061968e-04 true resid norm 
5.881521061969e-04 ||r(i)||/||b|| 6.813528364620e-05
   2 KSP unpreconditioned resid norm 6.142969823931e-05 true resid norm 
6.142969823933e-05 ||r(i)||/||b|| 7.116407252031e-06
   3 KSP unpreconditioned resid norm 4.110742198982e-05 true resid norm 
4.110742198982e-05 ||r(i)||/||b|| 4.762145417367e-06
   4 KSP unpreconditioned resid norm 2.628280876832e-05 true resid norm 
2.628280876817e-05 ||r(i)||/||b|| 3.044767861187e-06
   5 KSP unpreconditioned resid norm 1.293845872473e-05 true resid norm 
1.293845872450e-05 ||r(i)||/||b|| 1.498873413612e-06
   6 KSP unpreconditioned resid norm 6.930434272105e-06 true resid norm 
6.930434271781e-06 ||r(i)||/||b|| 8.028656191550e-07
   7 KSP unpreconditioned resid norm 4.654261998874e-06 true resid norm 
4.654261998975e-06 ||r(i)||/||b|| 5.391793349419e-07
   8 KSP unpreconditioned resid norm 3.370057395937e-06 true resid norm 
3.370057396119e-06 ||r(i)||/||b|| 3.904088996184e-07
   9 KSP unpreconditioned resid norm 2.540901076284e-06 true resid norm 
2.540901076192e-06 ||r(i)||/||b|| 2.943541538306e-07
  10 KSP unpreconditioned resid norm 2.039263657470e-06 true resid norm 
2.039263657746e-06 ||r(i)||/||b|| 2.362412822907e-07
  11 KSP unpreconditioned resid norm 1.583890355441e-06 true resid norm 
1.583890355170e-06 ||r(i)||/||b|| 1.834879404102e-07
  12 KSP unpreconditioned resid norm 1.184174171199e-06 true resid norm 
1.184174170742e-06 ||r(i)||/||b|| 1.371822733607e-07
  13 KSP unpreconditioned resid norm 8.493013125005e-07 true resid norm 
8.493013119686e-07 ||r(i)||/||b|| 9.838846989132e-08
  14 KSP unpreconditioned resid norm 5.905267399341e-07 true resid norm 
5.905267385984e-07 ||r(i)||/||b|| 6.841037617843e-08
  15 KSP unpreconditioned resid norm 4.160983692482e-07 true resid norm 
4.160983680083e-07 ||r(i)||/||b|| 4.820348347010e-08
  16 KSP unpreconditioned resid norm 2.929006184135e-07 true resid norm 
2.929006164636e-07 ||r(i)||/||b|| 3.393147176151e-08
  17 KSP unpreconditioned resid norm 2.085222908044e-07 true resid norm 
2.085222901282e-07 ||r(i)||/||b|| 2.415654935984e-08


Switching to FBCGSR however yielded the following results
   0 KSP unpreconditioned resid norm 8.632122370749e+00 true resid norm 
8.632122370749e+00 ||r(i)||/||b|| 1.000000000000e+00
   1 KSP unpreconditioned resid norm 6.155300069200e-05 true resid norm 
4.783918927770e+05 ||r(i)||/||b|| 5.541996188539e+04
   2 KSP unpreconditioned resid norm 5.203978464579e-05 true resid norm 
4.069231018620e+05 ||r(i)||/||b|| 4.714056223773e+04
   3 KSP unpreconditioned resid norm 4.124211335014e-05 true resid norm 
8.257465019947e+05 ||r(i)||/||b|| 9.565973077408e+04
   4 KSP unpreconditioned resid norm 2.735866558072e-05 true resid norm 
4.745745445186e+05 ||r(i)||/||b|| 5.497773596523e+04
   5 KSP unpreconditioned resid norm 1.234049073102e-05 true resid norm 
3.694211077995e+05 ||r(i)||/||b|| 4.279609254050e+04
   6 KSP unpreconditioned resid norm 7.813287928316e-06 true resid norm 
3.595303092238e+05 ||r(i)||/||b|| 4.165027947728e+04
   7 KSP unpreconditioned resid norm 3.221541950651e-06 true resid norm 
3.179392486707e+05 ||r(i)||/||b|| 3.683210629034e+04
   8 KSP unpreconditioned resid norm 1.777674826629e-06 true resid norm 
3.155842168872e+05 ||r(i)||/||b|| 3.655928441846e+04
   9 KSP unpreconditioned resid norm 1.698816021362e-06 true resid norm 
3.145809168718e+05 ||r(i)||/||b|| 3.644305575854e+04
  10 KSP unpreconditioned resid norm 1.577351929557e-06 true resid norm 
3.259758397382e+05 ||r(i)||/||b|| 3.776311615354e+04
  11 KSP unpreconditioned resid norm 1.613962504892e-06 true resid norm 
3.186021802487e+05 ||r(i)||/||b|| 3.690890450398e+04
  12 KSP unpreconditioned resid norm 4.564619465810e-07 true resid norm 
3.142082512956e+05 ||r(i)||/||b|| 3.639988380613e+04
  13 KSP unpreconditioned resid norm 3.413352474598e-07 true resid norm 
3.136609638739e+05 ||r(i)||/||b|| 3.633648254765e+04
  14 KSP unpreconditioned resid norm 2.914787162382e-07 true resid norm 
3.133747605150e+05 ||r(i)||/||b|| 3.630332692884e+04
  15 KSP unpreconditioned resid norm 3.607032335094e-07 true resid norm 
3.108398102641e+05 ||r(i)||/||b|| 3.600966215648e+04
  16 KSP unpreconditioned resid norm 7.653443566257e-08 true resid norm 
3.124857549918e+05 ||r(i)||/||b|| 3.620033887039e+04


So it seems to me something weird is going on here. Could you help me?

Kind regards
Elias