Re: [Libmesh-devel] [petsc-maint #141691] question about tolerances in SNES

[John P. <pet...@cf...>]

On Wed, Nov 28, 2012 at 2:08 PM, Barry Smith <bs...@mc...> wrote:
>
> On Nov 28, 2012, at 3:00 PM, Michael Povolotskyi <mpo...@pu...> wrote:
>
>> Thank you.
>> Looks like also others  treated this parameter erroneously as the absolute tolerance:
>>
>> For example, the Libmesh library:
>> http://libmesh.sourceforge.net/doxygen/classlibMesh_1_1PetscNonlinearSolver.php#a1d5ed777465c1f08785bc321c84c7c71
>>
>> 00486   // Set the tolerances for the non-linear solver.
>> 00487   ierr = SNESSetTolerances(_snes, this->absolute_residual_tolerance, this->relative_residual_tolerance,
>> 00488                            this->absolute_step_tolerance, this->max_nonlinear_iterations, this->max_function_evaluations);
>>
>> Am I right that they have a problem?
>
>    Based on the name of their variable yes it does appear to be wrong. The reason it is a relative tolerance (and not absolute)  is that one is computing
>
>     x  =   delta x   + x
>
> and once delta x is sufficiently smaller than x,   delta x + x   ==  x (in floating point) so we don't want to iterate past the point where x is not being changed.

So, if I'm interpreting everything correctly, it would be more correct
for the third argument to be

this->relative_step_tolerance

instead of

this->absolute_step_tolerance?

We could change this, but it might break backwards compatibility: some
users may not currently use relative_step_tolerance at all, etc.

--
John