For nonlinear problems the linesearch may very well fail if the linear
update is a bad descent direction
(usually indicating a nonconvexity of the corresponding energy functional,
if it exists;  is this a p-Laplacian problem? To the best of my knowledge
it is convex for p > 1, albeit the PDE is not uniformly elliptic for p \neq
2).

Additionally, the linesearch logic has changed a bit since petsc-3.3 to
make it more robust in the presence of small (in norm) current solutions
and linear updates.  There may still be problems with trying to
"overconverge" a system where the linesearch cannot make any more progress
and declares failure.  See this email thread to that end:
http://lists.mcs.anl.gov/pipermail/petsc-users/2012-October/015502.html

It is quite possible that LU without pivoting is unstable, as John is
suggesting. How big is the problem?  I would suggest running a small
version of the proble with -pc_type svd -pc_svd_monitor to get an idea of
the extreme singular values, to see if the system is (nearly) degenerate.

Dmitry.

On Thu, Mar 7, 2013 at 11:33 AM, John Peterson <[email protected]> wrote:

> On Thu, Mar 7, 2013 at 9:31 AM, Subramanya Gautam Sadasiva <
> [email protected]> wrote:
>
> > Yes, that is right... my bad..
> >
>
>
> Nevertheless, I think you are correct that there is *something* wrong with
> his Jacobian.  Maybe it's "good enough" to work with non-direct solvers but
> fails on LU?
>
> --
> John
>
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