On Thu, Mar 30, 2017 at 7:09 PM, Gideon Simpson <[email protected]> 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. > I think its possible that your Jacobian is not accurate enough to converge below 1e-13, or that your residual evaluation is no longer accurate below that. I would set the atol as you suggest. Matt > 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 > > -- 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
