[petsc-users] Scaling GMRES residual

Jed Brown jedbrown at mcs.anl.gov
Mon Jul 9 14:53:14 CDT 2012

On Mon, Jul 9, 2012 at 11:23 AM, Colin McAuliffe <cjm2176 at columbia.edu>wrote:

> Ok thanks, I can see how introducing units to the residual is necessary,
> but when would it be necessary to introduce units to the state? I would
> imagine this would only be needed if a numerically differentiated jacobian
> was being used.

It depends if you care about symmetry and if you want the step tolerance to
be meaningful. It can also affect scaling of boundary conditions.

> Thanks
> Colin
> Quoting Jed Brown <jedbrown at mcs.anl.gov>:
>  On Tue, Jun 26, 2012 at 2:31 PM, Colin McAuliffe <cjm2176 at columbia.edu
>> >wrote:
>>  Hello,
>>> I would like to use GMRES for a monolithic solution of a multiphysics
>>> problem. There are drastically different units in the problem and so the
>>> residual norm is dominated by the terms with the largest units. Is there
>>> a
>>> way to tell petsc to scale the residual before taking the norm to avoid
>>> this?
>> You can "fix" it with preconditioning, but then you can only use the
>> preconditioned residual. You should really fix the units when formulating
>> the problem. (This does not require formal nondimensionalization, just
>> introduced units so that state and residuals are of order 1.)
> --
> Colin McAuliffe
> PhD Candidate
> Columbia University
> Department of Civil Engineering and Engineering Mechanics
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