[petsc-users] KSP convergence problem

[John Mousel]

Jed,

I've wanted to scrap this approach for a long time, but moving away from
these GFM-type treatments is not a choice that I've been allowed to follow
through on for various reasons which are out of my control.


On Wed, Mar 20, 2013 at 4:55 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

>
> On Wed, Mar 20, 2013 at 4:51 PM, John Mousel <john.mousel at gmail.com>wrote:
>
>> Right now, Mehrdad and I are just passing the constant vector. The
>> problem is that the null space is extremely expensive to compute. Something
>> like 5-20 times the cost of solving the Poisson equation itself depending
>> on the problem size. What we have tried in the past is to find a single
>> solution to Atrans*n = 0 and pass this as the nullspace. It's had success
>> at making the true residual drop in unison with the preconditioned
>> residual. However, because we are working with moving boundary problems,
>> the null space is changing each time step. In order to get around this, we
>> have decided to try to avoid giving the null space, and see if we get an
>> accurate answer, and we do get pretty much the same answer when we only
>> require preconditioned residual convergence. This is obviously less than
>> robust, but we've yet to find a way to get the null space in an efficient
>> manner. I tried programming up a GASM type algorithm where BiCG/ILU is used
>> near the interface where the solution is not smooth, and GAMG is used far
>> away where the changes in the null vector are very very small, but that
>> didn't have much success.
>
>
> It's not usually a good idea to choose a spatial discretization that is
> singular with a complicated null space. Proving that an iteration remains
> in the benign space is one of the first things demanded from such
> discretizations. If you can't find a way to iterate in the null space or
> otherwise project it out, then I would seriously reconsider your choice of
> this discretization.
>
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