dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Sat, Nov 29, 2008 at 04:19:46PM +0100, Martin Sandve Alnæs wrote:
> 2008/11/29 Anders Logg <logg@xxxxxxxxx>:
> > On Sat, Nov 29, 2008 at 03:09:53PM +0100, Martin Sandve Alnæs wrote:
> >> How do you intend to handle (sub)functions in a mixed space?
> >> Currently I don't see how the function space stuff generalizes
> >> to even simple mixed spaces.
> >>
> >> Take this simple example in a pure form language (FFC or UFL):
> >>     element1 = VectorElement("CG", "triangle", 2)
> >>     element2 = FiniteElement("CG", "triangle", 1)
> >>     mixed_element = element1 + element2
> >>     f, g = Functions(mixed_element)
> >>
> >> Now in PyDOLFIN, would a function space be defined by (reusing the elements):
> >>     space1 = FunctionSpace(mesh, element1)
> >>     space2 = FunctionSpace(mesh, element2)
> >>     mixed_space1 = space1 + space2
> >>
> >> or:
> >>     mixed_space2 = FunctionSpace(mesh, mixed_element)
> >>
> >> and would the functions in this space be
> >>     f, g = Functions(mixed_space)
> >> or
> >>     fg = Function(mixed_space)
> >>     f, g = fg.sub(0), fg.sub(1)
> >> ?
> >> Neither of these two definitions of (f, g) works out.
> >
> > It should be just as in your first example, but replace Element with
> > FunctionSpace:
> >
> >  V1 = VectorFunctionSpace(mesh, "CG", 2)
> >  V2 = FunctionSpace(mesh, "CG", 1)
> >  mixed_space = V1 + V2
> >  f, g = Functions(mixed_space)
> >
> >> The syntax
> >>     f, g = Functions(mixed_space)
> >> doesn't work, since ufl.Functions does not return ufl.Function objects,
> >> but ufl.Indexed objects that refer to subexpressions of ufl.Function objects.
> >>
> >> The syntax
> >>     fg = Function(mixed_space)
> >>     f, g = fg.sub(0), fg.sub(1)
> >> would require that sub returns something that is a subclass of what
> >> ufl.Functions returns (ufl.Indexed) and at the same time is a dolfin.Function.
> >
> > It should be enough to just define the following function:
> >
> > def Functions(V):
> >    v = Function(V)
> >    return tuple(v[i] for i in range(V.num_subspaces()))
> 
> In pure UFL, given
>     v = ufl.Function(mixed_element)
> then
>    v[i]
> is not subfunction i, but value component i of v.
>
> You can't override v[i] in dolfin.Function, then indexing of vector
> functions won't work.

Is it really necessary to have Functions()? It should be enough with
TestFunctions() and TrialFunctions().

For extraction of subfunctions from computed solutions, we need to use
what is already implemented in the C++. It is not necessary that what
comes back is a subclass of ufl.Functions. It will simply be a new
function (with copies of the values) just as in C++.

This means that there will be a difference between the following two
statements:

  w = Function(mixed_space)

  # Extract two independent Functions with their own vectors  
  (u, p) = w.split()
  
  # Extract UFL expressions, both sharing the same global vector
  u = w[0:2]
  p = w[2]

The first versions of u, p can be plotted and saved to file, but not
the second versions (for the same reason that we can't save grad(u)
directly to file).

-- 
Anders

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