[petsc-dev] [petsc-maint #42811] TSPSEUDO and snes ex27

[Jed Brown]

Apparently I'm being excessively dense.  As long as the predictor for
the next step is just the old state, then we have

  \dot{x} = (x^{n+1}_{\text{predicted}}-x^n)/dt = (x^n - x^n)/dt = 0

so that

  f(x,\dot{x})

is in fact the steady state residual, in which case doing one Newton
step (with no line search, and no need to even check residual) is
equivalent to the algorithm described in the paper.  With respect to
ex27, this means that no code change is necessary to perform the
"correct" algorithm, and indeed the differences are minor.  Compared to
Figure 3.1, the DAE formulation converges in the same number of steps,
albeit with different residuals along the way, and the fully parabolized
form takes two extra steps (but both of these take many fewer linear
solves than when Newton is converged on the transient term at each
step).  I've put a note to this effect in the ex27 and TSPSEUDO
comments.

Jed