[petsc-dev] Jacobian lag persist with ROSW method

[Jed Brown]

Mani Chandra <mc0710 at gmail.com> writes:

> 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.

Yes, that is fine.  Linearly implicit means that it only solves linear
problems.  RosW methods use an (approximate) Jacobian from the beginning
of the step for all subsequent stages.

> 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.

The solver convergence is a separate problem, for which error estimators
and higher order will not help.  Work out the solver issues with beuler
before doing anything else.

> 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.

You can try assembling a Jacobian for a first order method (no limiters)
and using TSROSW, but be very careful about stability.
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