dolfin team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

On Mon, 8 Sep 2008, Johan Hoffman wrote:

> > 2008/9/8 Dag Lindbo <dag@xxxxxxxxxx>:
> > > Anders Logg wrote:
> > > > There seems to be a problem (among many) with the current design of
> > > > the Function classes (see thread "evaluating higher order mesh
> > > > function").
> > > >
> > > > In particular, the finite element is missing in DiscreteFunction. My
> > > > suggestion would be to just add it and let a DiscreteFunction consist
> > > > of the following four items which are always available:
> > > >
> > > >   mesh, x, dof_map, finite_element
> > > >
> > > > Is this enough, and what other issues to we need to fix?
> > >
> > > I'm not sure I agree that the dof map and finite element should be owned
> > > by the discrete function. There was a great suggestion from Martin, in a
> > > thread "Abstraction idea" from 06/05/2008, to create a class
> > > FunctionSpace where the mesh, element and dof_map(s) are aggregated.
> > > Citing Martin:
> > > U = FunctionSpace(mesh, dofmapset, form, 0) # or something similar
> > > u = Function(U)
> > > v = Function(U)
> > >
> > > This seems a solid approach to me since it would provide a way of
> > > encapsulating the mathematical formulation of the problem, which is more
> > > or less const and likely to be reused by many discrete functions in a
> > > solver.
> > >
> > > It seems to me that there is an obvious risk that a lot of redundant
> > > initialization would occur if all discrete functions should own their
> > > own elements and dof maps. There seems to be consensus that the mesh
> > > should be "global" for efficiency reasons, so why not treat the function
> > > space the same way?
> > >
> > > Is there a problem with an approach where the funciton _always_ owns the
> > > vector and _never_ owns the function space (and mesh)? A very strict
> > > design would avoid shared/smart pointers, provide a comprehensible user
> > > interface and probably help the parallellization effort.
> > >
> > > /Dag
> >
> > If the Function always owns the vector, there are cases you'll have to
> > make unneccessary copies of a vector, in particular such scenarios
> > may occur when trying to combine dolfin with something else.
> >
> > If the Function never owns the function space, it must always be
> > constructed explicitly by the user. This may not be a bad thing.
> > However, if the Function is loaded from a file, nobody owns the
> > FunctionSpace.
> >
> > --
> > Martin
>
> Conceptually, I agree with Dag (and Martin?) that it is natural to have
> global function spaces. And if the explicit construction of such spaces
> can be made simple, it may not be a bad thing but a natural part in
> setting up the mathematical problem. And I do not really like that
> functions should be initialized from a form, which defines an equation.

I agree very much with this last sentence.

> I think one idea was to not force less mathematically oriented users to
> worry about function spaces. I guess there are (at least) 2 types of
> functions: (i) functions part of the form, and (ii) functions not part of
> the form, but used in pre/postprocessing etc.

Do you really think it is a huge leap for users to know what a function 
space is?  They don't need to know functional analysis.

> For (i) it may be natural to construct the function space from the form,
> and for (ii) it may be convenient in some cases, but it is not really
> obvious that this is the best solution.
>
> Maybe an explicit construction of a function space can come with a
> default, such as a nodal basis of piecewise linears?

Note: it must be possible to update the function space if the mesh 
changes.  I guess this would be automatic since the function space 
references the mesh.  Assuming the mesh does not change topology; then I 
guess there would be some interpolations happening, which could be done by 
a higher level module or the user.

This thread started from me trying to add a Function to the MeshGeometry 
class for use in higher order shaped elements.  Maybe it would be easier 
to change that, than the whole Function setup?  Unless the Function class 
needs to change anyway.

- Shawn