[petsc-dev] accuracy of solutions PETSc returns

[Jed Brown]

On Thu, 22 Apr 2010 15:59:18 -0500, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
>    The petsc-maint request titled "Question on setting rtol in KSP"  
> points to a HUGE deficiency in PETSc.

I don't recieve petsc-maint, what was the request?

>    When PETSc returns an answer to a linear or nonlinear solver it  
> returns no useful information about how accurate that solution is. In  
> any other field beside numerical computing this would be considered  
> disgraceful.  We should fix this for KSP and SNES and also make sure  
> that ALL the TS's allow proper error control (as some of them already  
> do?).

So TS error *control* is quite hard and generally expensive, even for
model problems.  It's more common to attempt to keep *local* truncation
error beneath a threshold and keep track of a posteriori estimates so
that the results can be meaningfully assessed.  A more reliable approach
is adjoint-based error estimation.  In any case, many popular
integrators don't come with any cheap error estimates, so even just
logging errors is not going to work for every TS implementation.

I just wanted to point out that this is a huge field, and is intimately
coupled with the spatial discretization, so I don't think it's feasible
to provide goal-oriented (global) error control throughout TS.  I do
intend to provide discrete and continuous adjoints (assuming the user
can provide an adjoint of the spatial discretization).

Jed