[dune-functions] New example for Taylor-Hood elements
graeser at mi.fu-berlin.de
Fri Apr 3 14:35:30 CEST 2015
Am 02.04.2015 um 14:28 schrieb Oliver Sander:
> Hi guys,
> I just added a second example file to our /examples directory. This one is intended
> to show how function space bases with non-trivial tree are used. The code discretizes
> the Stokes equation with a Taylor-Hood basis. The setting is the well-known driven-
> cavity problem: a unit square, no source term, homogeneneous Dirichlet boundary
> conditions on three sides of the square, constant (non-zero) Dirichlet bc on the forth side.
> Have a look at the example if you find the time. If you think that I did anything in
> a suboptimal way feel free to push patches.
> Unfortunately, when writing the example I found several situations where we are still
> lacking infrastructure:
> - Apparently there is no solver for such a problem in dune-istl. I'd volunteer to add
> such a solver, but I am unsure exactly what type of solver to implement. A preconditioned
> Uzawa? Please advice.
> - While the TaylorHoodBasis class is sufficient to assemble the algebraic problem,
> it is not sufficient for pre- and post-processing. How do you get the velocity
> part of a solution into a vtk file? Currently, the code instantiates a separate
> PQ2NodalBasis object for this, but what we really want is something like 'view objects'
> on given bases, that allow to extract subtrees and the corresponding coefficients.
> - Same for interpolation: To find the Dirichlet dofs I need to interpolate the identity
> function on the velocity basis. This is currently not possible.
I have the impression that the last two points could be addressed
by passing a TreePath to interpolate() or the Discrete...GridFunction
to select a single leaf. But I'm not sure because I've never used these
TypeTree features. I'll have a look (but this may take some time).
> Finally, there are some issues regarding the linear algebra.
> - The matrix data structure is now Matrix<BCRSMatrix<FieldMatrix<double,1,1> > >.
> This still ignores quite a bit of structure of the occupation pattern. This is
> unfortunate, because we claim that dune-functions and in particular dune-istl
> is all about using this structure.
> - The type for coefficient vectors is FieldVector<BlockVector<FieldVector> >.
> Strictly speaking this is against the rules, as FieldVectors are supposed
> to end recursion.
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