[petsc-dev] Jacobian lag persist with ROSW method

[Mani Chandra]

Does linearly implicit mean that you can solve any nonlinear system with
the ROSW methods? I set my entire system using TSSetIFunction, without any
TSSetRHSFunction.

I wanted to try the ROSW methods because the THETA methods seems to want a
time step much much smaller than the courant time step for the nonlinear
solver to converge. I checked the validity of the solution and it is indeed
right, so the residual evaluation should be correct. I'm solving for the
general relativistic mhd equations in a fixed background spacetime (kerr
blackhole). There are large variations in the density and pressure  and I
use slope limiters.


On Sat, Mar 8, 2014 at 7:22 PM, Jed Brown <jed at jedbrown.org> wrote:

> Peter Brune <brune at mcs.anl.gov> writes:
>
> > You can control Jacobian lagging with -snes_lag_jacobian and
> > -snes_lag_jacobian_presists by setting the option
> > -ts_rosw_recompute_jacobian to true.  Otherwise it defaults to having it
> > recompute once per timestep by setting the SNES to do so, wiping out the
> > persistent lagging.  This will give you a rather odd pattern of Jacobian
> > assembly, and I don't recommend it at all.  Your Jacobian will often be
> > computed on the unconverged nonlinear solution, and may be garbage.  What
> > would be more reasonable is for us to add some option at the TS level to
> > lag the Jacobian by a number of steps.
>
> Rosenbrocks are linearly implicit and have to use the true Jacobian (so
> if you play games with lagging, the method is no longer consistent).
> The W methods can use an approximate Jacobian, but the method has no way
> to know how often the Jacobian needs to be updated (the method becomes
> unstable if you lag too much).  If you want to lag further than a step,
> I recommend writing a Rosenbrock (W) with more stages.  This way you
> have a consistent error estimator and don't need a special controller.
>
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