[petsc-users] Simultaneously compute Residual+Jacobian in SNES

[Derek Gaston]

On Mon, Dec 12, 2016 at 11:43 AM Jed Brown <jed at jedbrown.org> wrote:

> I still don't understand your many field case. The geometric overhead is
> amortized and the Jacobian contribution typically grows quadratically in
> the number of fields, so I would expect it to increase the
> Jacobian:residual cost ratio, not reduce it.
>

It depends on how things are coupled... but I do agree that with many
fields the Jacobian tends to get even more expensive to produce.

However, the point is just about reusing an expensive computation: the
field values on every element.  Regardless of how expensive the
Jacobian/Residual are to compute... cutting the time in half for computing
the values of many fields could be worthwhile.

But I suppose your point is that if you are blindly computing Jacobians
with residuals... then you're going to waste a few Jacobians (at least one
every timestep for instance).  If that Jacobian is incredibly expensive to
produce then it's wiped out any gains made in not recomputing variable
values.

I can see that.

How about this: what if SNES only called this optional R+J interface when
it knew _for sure_ it needed both?  For instance... for the first linear
solve.

But anyway - the gains seem pretty small and not worth it.  I'm pretty
convinced this idea is foolhardy ;-)

Derek
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20161212/5449f06c/attachment.html>