dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Fri, Nov 04, 2005 at 09:01:48AM +0100, Johan Hoffman wrote:

> >> (2) Semidiscreization space->time: this would be along the lines what
> >> Johan is doing now; computing f(u) to use in the ODE solver (for dot u =
> >> f(u)). We would then still declare a space element:
> >>
> >> space_discretization = FiniteElement("Lagrange", "tetrahedron", 1)
> >>
> >> but the time derivative Dt(u) would not be discretized by FFC, but
> >> instead
> >> would an output file for the ODE solver in DOLFIN be created that
> >> contain
> >> the evaluation of f(u).
> >
> > This is the most convenient. The ODE solver wants an ODE.
>
> I understand that this is the most convenient for the ODE solver. I'm just
> saying that one approach would be to able to generate FFC output suitable
> for both the ODE solver (2) and the PDE solver (1) (= solving system of
> algebraic equations). We should probably not retire the PDE functionality
> until we know that the ODE solver is capable to also solve all PDE
> problems efficiently.

We just need to allow the specification of a time derivative in the
form. If none is specified, we generate PDE code as usual, and if the
form contains a time derivative, we generate code suitable for the ODE
solver.

> >> (3) We also might like to generate the vector F(u) for using the non
> >> linear solver on F(u)=0, although this can be done already today with
> >> FFC
> >> defining an L in this form. For Newton we would also like to generate
> >> the
> >> Jacobian automatically, which will demand some new functionality.
> >>
> >> (4) A next step is moving meshes. Johan is doing this for elasticity I
> >> guess in a pure Lagrangian framework, but we also want to allow for ALE
> >> methods where the mesh is moving independetly from the solution. This
> >> corresponds to a coordinate transformation so that the derivatives and
> >> integrals (dx,ds etc.) needs to be modified according to a specified
> >> map.
> >> This would probably be quite easy to do in FFC by implementing
> >> map-dependent operators, where derivatives and integrals are interpreted
> >> using the chain rule wrt a given mapping.
> >
> > I think we should be able to get this working with alternative (2),
> > but we need to think about the details.
> >
> > /Anders
> 
> I think alterntive (1) is also worth considering. Then we would be able to
> write a PDE closer to the mathematical formulation in the form-file.

I think semi-discretization in space ("method of lines") is also
pretty close to the mathematical formulation. At least it's the way I
always write it.

/Anders