flexible TS implementation for user-defined timestepping

[Barry Smith]

  Yes, TS sucks and always has. I believe it sucks because

1) it has gotten little thought and been built up piece-meal over the years;
   plus none of the PETSc developers has a proper grounding in ODE/differential 
   algebraic equations. Yes we've taken classes and used them but we have
   not devoted our lives to them.

2) it has been used very little and so has not evolved well according 
   to users needs.

  I think I disagree with Matt, in that I think a solid, flexible framework
can be developed that is essentially still only algebraic (like SNES/KSP/PC).
I would like to see the equation/discretization features "overlaid" the 
algebraic framework and not "protube" into the lower "algebraic" level.


   Barry


On Mon, 17 Sep 2007, Matthew Knepley wrote:

> 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
> >
> >
> 
> 
>