[petsc-users] snes parameter suggestions

[Barry Smith]

  Developing solver algorithms and software is easy, developing robust convergence test algorithms is difficult.

  
> On Mar 30, 2017, at 7:09 PM, Gideon Simpson <gideon.simpson at gmail.com> wrote:
> 
> 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
>