[petsc-users] PetscFE and TS

[Matthew Knepley]

On Mon, Nov 14, 2016 at 3:24 AM, Julian Andrej <juan at tf.uni-kiel.de> wrote:

> I think i'm understanding the concept now. Although i have another set
> of questions. If i am formulating a DAE (like in the linear stokes
> equation for example) it seems i am missing something to formulate the
> correct jacobian. The residual formulation with snes_mf or snes_fd
> works fine in terms of nonlinear convergence. If i use the hand coded
> jacobian the convergence is way slower, which is a reason for an
> incorrect jacobian formulation from my side (at least what i think
> right now). I should be able to test my jacobian with -snes_type test,
> even if i am using TS, right? This gives me a huge difference. I guess
> i am missing something in the formulation and thus in the
> implementation of the callbacks here.
>
> There is a small example attached.
>

I will look at it. It would be really helpful for me if you would include
the options you
run with, and perhaps a little output with the report.

  Thanks,

     Matt


> I appreciate your time and help.
>
> On Thu, Nov 10, 2016 at 4:45 PM, Matthew Knepley <knepley at gmail.com>
> wrote:
> > On Thu, Nov 10, 2016 at 9:38 AM, Jed Brown <jed at jedbrown.org> wrote:
> >>
> >> Matthew Knepley <knepley at gmail.com> writes:
> >>
> >> > On Thu, Nov 10, 2016 at 1:31 AM, Julian Andrej <juan at tf.uni-kiel.de>
> >> > wrote:
> >> >
> >> >> I'm getting the correct solution now, thanks! There are still a few
> >> >> open questions.
> >> >>
> >> >> 1. The mass term is necessary _and_ using the u_tShift value if i
> >> >> provide the jacobian. After reading the manual countless times, i
> >> >> still don't get what the u_tShift value tells me in this context. Are
> >> >> there any resources which you could point me to?
> >> >>
> >> >
> >> > The manual is always a lagging resource because we are trying things
> >> > out.
> >>
> >> This has been explained in the manual similarly to your email for
> >> several years.  If anyone has a suggestion for how to make it better,
> >> we'd like to hear.  The typical syndrome is that once you learn it, the
> >> description suddenly makes sense and you wonder why you were ever
> >> confused.  It takes feedback from people just learning the material to
> >> make the explanation more clear.
> >>
> >> > I learned about this by reading examples. The idea is the
> >> > following. We have an implicit definition of our timestepping method
> >> >
> >> >   F(u, grad u, u_t, x, t) = 0
> >>
> >> It doesn't make sense to write grad u as a separate argument here.
> >
> >
> > Sorry, that is just how I think of it, not the actual interface.
> >
> >>
> >> Also, is `x` meant to be coordinates or some other statically prescribed
> >
> >
> > Coordinates, as distinct from u. Again this is my fault.
> >
> >>
> >> data?  It can't be actively changing if you expect a generic TS to be
> >> convergent.  (It's not an argument to the function.)  So really, you
> >> have:
> >>
> >>   F(u, u_t, t) = 0
> >>
> >> > which is not unlike a Lagrangian description of a mechanical system.
> The
> >> > Jacobian can be considered
> >> > formally to have two parts,
> >> >
> >> >   dF/du and dF/du_t
> >> >
> >> > just as in the Lagrangian setting. The u_tShift variable is the
> >> > multiplier
> >> > for dF/du_t so that you actually
> >> > form
> >> >
> >> >   dF/du + u_tShift dF/du_t
> >>
> >> We're taking the total derivative of F with respect to u where u_t has
> >> been _defined_ as an affine function of u, i.e., shift*u+affine.
> >> u_tShift comes from the chain rule.  When computing the total
> >> derivative, we have
> >>
> >>   dF/du + dF/du_t du_t/du.
> >>
> >>
> >> >> 2. Is DMProjectFunction necessary _before_ TSSolve? This acts like an
> >> >> initial condition if i'm not mistaken.
> >> >>
> >> >
> >> > Yes, this is the initial condition.
> >> >
> >> >
> >> >> 3. A more in depth question i guess. Where is the "mass action"
> >> >> formed? As i could see by stepping through the debugger, there is
> just
> >> >> a formed action for the residual equation. It seems way over my
> >> >> understanding how this formulation works out. I'd also appreciate
> >> >> resources on that if thats possible.
> >> >>
> >> >
> >> > Jed is the only one who understands this completely.
> >>
> >> That's a stretch -- several other people have developed sophisticated TS
> >> implementations.
> >
> >
> > Matt does not understand this completely.
> >
> >>
> >>
> >> > However, I guess by "mass action" you mean the dF/du_t term. In the
> >> > explicit methods, you just have u_t + ..., so
> >> >
> >> >   dF/du_t = M
> >> >
> >> > for finite element methods. So you are putting that there in
> >> > FormIJacobian(). In the simplest
> >> > case of backwards Euler then u_tShift would be 1/dt.
> >>
> >> Specifically, for implicit methods, and many semi-implicit methods, we
> >> don't need M separate.
> >
> >
> > Yes.
> >
> >    Matt
> >
> > --
> > 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
>



-- 
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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