> On Feb 2, 2025, at 1:09 PM, Daniel.Abele--- via petsc-users
> <petsc-users@mcs.anl.gov> wrote:
>
> Hi,
> we are solving a time dependent problem with a single KSP in every time step.
> We are debating which convergence criterion to use. Is there general guidance
> around when to use one of the norms with initial residual
> (ksp_converged_use_initial_residual_norm or
> ksp_converged_use_min_initial_residual_norm) over the default norm?
> If I understand the formulas correctly, the initial residual norm “norm(b – A
> * x0)” (maybe add preconditioning) means that if you have a very good initial
> guess (as is often the case in time dependent problems if you can use the
> result if the last time step as initial guess), the norm is much stricter
> than the default norm “norm(b)”.
The above statement is correct.
> Is this meant as a way to control error accumulation over time? Or does it
> have some other purpose?
> Thanks and Regards,
> Daniel
For splitting-type methods, you want the error in the linear system solve,
e, to be on the same order as the maximum error from the splitting, the
explicit time-step discretization, and the implicit time-step discretization.
So you need some estimate of that value.
Now
|| e ||_2 < || B(b - Ax) ||_2
-------------------
\lambda_min(BA).
For this you need a handle on \lambda_min(BA) which you can obtain with
Lanczo using -ksp_monitor_singular_values. So the converge criteria should
really depend on setting the -ksp_atol using the required bound on || e ||_2
and \lambda_min(BA).
PETSc should provide this convergence test but no one has gotten around to
adding it.
Barry
