flexible TS implementation for user-defined timestepping

[Matthew Knepley]

I think this example demonstrates my major problem with the current TS
implementation. I have had this problem since I was in grad school. We
would like to abstract different "methods" like CN for timestepping. This
is really abstracting the process of temporal discretization, and so far we
choose finite difference type discretizations. When these are combined
with FEM in space, this becomes difficult since we have no prescription for
constructing the operators we might need (like the identity in the FEM
space). Moreover, even when I added methods allowing the user to specify
these, the computation is not optimal since the parts are distended.

Thus, as I have maintained for a while, I think the way forward is to give PETSc
some measure of control over not just the discretization, but the equation
handling. So far, I can only see how this might have in FEM, although FD is
probably not any harder. For each method, the provided weak form would be
altered to accomodate the time discretization. Eventually, I believe the right
thing to do is use Galerkin time discretizations as well since this allows local
optimization of the time steps, crucial to adaptivity.

  Matt

On 9/17/07, Lisandro Dalcin <dalcinl at gmail.com> wrote:
> Current TS implementations never fited my needs. Why? My target
> application is solving incompressible NS equations with FEM and fully
> implicit schemes (trapezoidal rule with theta in [0.5, 1.0] ) and
> residual-based stabilization (SUPG/PSPG). Then I need to solve at each
> time step a nonlinear problem like F(t, u, t0, u0), where F is
> nonlinear in u. I'm surelly naive, and I could not accomodate my
> function and Jacobian code for the beuler/cn TS implementations.
>
> Futhermore, I've recently convinced some coworkers to take advance of
> SNES/TS features and my Python wrappers (petsc4py) to manage the the
> time evolution of some problems related to fluid-structure interaction
> and mesh movement (formulated as an optimization problem, only nodal
> positions change, not remeshing needed for many timesteps).
>
> In order to support those applications setups, I've wrote a new TS
> implemetation, which enables users to (almost) completely define the
> temporal evolution of their problems, with  pre/post solve/step
> methods and support for accept/reject steps and implementing timestep
> size control. Some of these features are available in some TS types,
> but not all-in-one.
>
> This code is available for review in petsc4py SVN repo (link below),
> an python example of this in action (very simple, just for testing all
> is working) is attached. Currently it only support implicit schemes
> and nonlinear problems, but I believe it can be extended to support
> explicit schemes and linear problems.
>
> http://petsc4py.googlecode.com/svn/trunk/petsc/lib/ext/src/ts/impls/implicit/user/
>
> I want to know the opinion of PETSc core developers and potential
> users ot this, and I hope anyone can provide suggestions for
> improvements. After that, I can push this to petsc-dev for general
> availability (in fact, the code is almost ready to be integrated in
> petsc).
>
> Perhaps in the long term, all this can be integrated in the generic TS
> interface if that is appropriate. Of course, this would require some
> (I hope minor) changes in TS interface, some additions, and a
> reimplementation of some default TS types
>
> Regards, and I'm waiting for your comments.
>
>
> --
> Lisandro Dalcín
> ---------------
> Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
> Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
> Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
> PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> Tel/Fax: +54-(0)342-451.1594
>
>


-- 
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