[petsc-dev] [petsc-maint] Petsc KSP options that provide the most 'robust' solve possible

[Matthew Knepley]

On Fri, Feb 3, 2017 at 11:41 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> > On Feb 3, 2017, at 12:59 AM, Mark McClure <mark.w.mccl at gmail.com> wrote:
> >
> > Hi, Jed and Matt.
> >
> > To close the loop, it turns out that the condition number issue had a
> simple explanation. The BC equation that I had added to the system had very
> different units from the other equations. Multiplying that row by a
> constant (effectively, modifying the units of the equation) improved the
> condition number of the matrix by many orders of magnitude. Big picture,
> this did not have an apparent effect on any of the numerical performance -
> the linear solver still had nonconvergence in the same places (when I used
> a large number of processes) and when I use a smaller number of processors
> so that the linear solve always converges, the overall numerical scheme is
> unaffected by whether or not I scale the extra BC equation. I hadn't
> realized how important it is to make sure the equations are scaled
> consistently/nondimensionalized when using the convergence number to
> evaluate whether a system is singular. Interesting experience.
> >
> > Thanks again for the help. I'll use the direct solver you suggested as a
> backup and send the user a warning if they try to use too many processors
> on a small problem.
> >
> > An aside, at first, when I saw that my overall numerical scheme was
> failing, I didn't realize the problem was that the linear solver was not
> converging. I spent a fair amount time debugging until I found the issue
> and learned how to use KSPConvergedReason. Because if KSP doesn't converge,
> it merely returns incorrect numbers. Without knowing to run
> KSPConvergedReason, an inexperienced user (like me) many not know about the
> nonconvergence in the linear solve and could spend a lot of time checking
> for other issues. It might be worth changing the default behavior for
> nonconvergence to be that it returns an nan so that the user gets a clear
> signal that the values coming out of KSP cannot be used.
>
>    Because the linear solvers in PETSc are usually used by the nonlinear
> solvers and ODE integrators that have recovery methods for failure in a
> linear solve we moved away from the "crash and burn" on failed linear
> solver approach; since that makes the recovery more difficult.
>
>     We could consider the following; if the KSP is not created by a SNES
> or TS it defaults to "crash and burn" on failed linear solve this would
> help newbies who are only solving linear systems and expecting a "crash and
> burn" on failure.
>

I am for that.

  Matt


>    What do people think?
>
>    Barry
>
> >
> > Regards,
> > Mark
> >
> >
> >
> > On Thu, Feb 2, 2017 at 7:48 AM, Jed Brown <jed at jedbrown.org> wrote:
> > Mark McClure <mark.w.mccl at gmail.com> writes:
> >
> > > I think you are right that I have an issue with how the BC is
> implemented.
> > > It is a pipe flow simulation that is solving mass and momentum balance
> > > simultaneously (corresponding unknowns are pressure and flow rate). I
> am
> > > applying a constant mass flow rate boundary condition. Upon further
> > > consideration, it may be that I am not properly providing a boundary
> > > condition for the momentum balance equation at the inlet. If I did, the
> > > inlet pressure could be readily calculated standalone,
> >
> > Momentum inflow is common, but if you also have momentum outflow (i.e.,
> > all Dirichlet conditions for momentum) then there is a null space of
> > constant pressure -- pressure is only determined up to a constant.
> > See the user manual section on solving singular equations.
> >
> > > outside the system of equations, and the problematic equation would be
> > > removed.
> >
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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