About a month ago, I mentioned that I was trying to set up a projected
integration scheme within petsc, where I use a classical integrator (i.e.,
RK4), at each time step, and then correct my prediction dependent variable, yp,
by solving a nonlinear equation g(y + lambda * f(yp)) =0 for a scalar parameter
lambda. Out of stubbornness, I did this entirely within the confines of petsc,
using a SNES. Following up on a comment of Barry’s, about the solver taking an
excessive number of function evaluations, I realized that, in fact, the SNES
was failing to converge (algorithmically), even though it was giving reasonable
answers. In particular, I see output like what is displayed below.
I am using the default snes/ksp solvers with default tolerances. It would seem
to me that I should have been quite happy after 1 SNES iteration, given that
this is a scalar problem. This can obviously be done by setting the atol to
something like 1e-12, but I was curious if people had other thoughts on this.
0 SNES Function norm 5.142950291311e-10
0 KSP Residual norm 6.057087103783e-11
1 KSP Residual norm 1.681179391195e-26
Line search: Using full step: fnorm 5.142950291311e-10 gnorm
5.783398860650e-14
1 SNES Function norm 5.783398860650e-14
0 KSP Residual norm 5.520053977167e-15
1 KSP Residual norm 1.370372252609e-30
Line search: gnorm after quadratic fit 5.728578676879e-14
Line search: Quadratically determined step, lambda=3.9611360239162957e-01
2 SNES Function norm 5.728578676879e-14
0 KSP Residual norm 5.024285935857e-15
1 KSP Residual norm 2.789038964144e-31
Line search: gnorm after quadratic fit 4.278033777465e-14
Line search: Quadratically determined step, lambda=2.4691358024691357e-01
3 SNES Function norm 4.278033777465e-14
0 KSP Residual norm 3.520343148370e-15
1 KSP Residual norm 5.527264229234e-31
Line search: gnorm after quadratic fit 2.842170943040e-14
Line search: Quadratically determined step, lambda=2.5438596491228038e-01
4 SNES Function norm 2.842170943040e-14
0 KSP Residual norm 2.016428211944e-15
1 KSP Residual norm 2.238685028403e-31
Line search: gnorm after quadratic fit 5.695433295430e-14
Line search: Cubic step no good, shrinking lambda, current gnorm
4.278033777465e-14 lambda=1.0000000000000002e-02
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.0000000000000002e-03
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=5.0000000000000012e-04
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=2.1132486540518717e-04
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=9.2196144189362134e-05
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=4.0004514620095227e-05
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.7374756353482527e-05
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=7.5449506476837614e-06
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=3.2764733594125655e-06
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.4228354923470249e-06
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=6.1787855254724169e-07
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=2.6831903567985152e-07
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.1651983473611860e-07
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=5.0599733967314922e-08
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=2.1973366898757625e-08
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=9.5421223580158174e-09
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=4.1437481801087470e-09
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.7994580593128418e-09
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=7.8143004026450871e-10
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=3.3934267301617141e-10
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.4736245574944127e-10
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=6.3993405755577026e-11
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=2.7789683331288042e-11
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=1.2067907474762995e-11
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=5.2405919521750200e-12
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=2.2757718408626572e-12
Line search: Cubic step no good, shrinking lambda, current gnorm
2.842170943040e-14 lambda=9.8827337043745462e-13
Line search: unable to find good step length! After 27 tries
Line search: fnorm=2.8421709430404007e-14, gnorm=2.8421709430404007e-14,
ynorm=2.0164282119435693e-15, minlambda=9.9999999999999998e-13,
lambda=9.8827337043745462e-13, initial slope=-8.0779356694631465e-28
-gideon
