[petsc-users] Can I use the direct solver without providing the analytical Jacobian?

[Jed Brown]

On Wed, Mar 23, 2011 at 20:07, Matthew Knepley <knepley at gmail.com> wrote:

> It looks like this FD derivative did not give any descent directions when
> factored. Possibly
> the FD Jacobian is too inaccurate, or the factorization was. These both
> mean your problem
> is very ill-conditioned. You should try to reformulate it.
>

Yes, it is often possible to reformulate to make the system better scaled.
You can also run with -snes_fd_type ds which uses a more robust method of
computing the step, sometimes this make a difference.

If you know the sparsity pattern of the Jacobian, you can use coloring to
"efficiently" assemble a sparse Jacobian using only residual evaluation.
There are many examples that do this.
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