[petsc-users] force KSP to perform at least a single iteration

[Jed Brown]

Anush Krishnan <anush at bu.edu> writes:

> Hi Jed,
>
> Is there any reason why ATOL needs to be set for transient problems? 

If the solution does not change for a step, the initial algebraic
residual will be as small as it was at convergence on the last time
step.  If you solve to an RTOL, the solve will be much more accurate
than it needs to be.  With ATOL, you solve only as accurately as needed
and know when to exit early from slowly-changing solutions.  Similarly,
when the solution changes rapidly on a time step (e.g., from 1 to 1e10),
a very accurate relative tolerance might be needed.

In general, it's best to non-dimensionalize your problem and understand
the scales so that you can write a suitable absolute tolerance.

> Are there any references you can point me to? I've been experiencing
> some issues with transient problems where sometimes the flow stops
> evolving and the linear solvers exit after zero iterations, and was
> wondering if this might help.

Exiting after 0 iterations might be correct.  Check the converged
reason.
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