dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Sun, Dec 07, 2008 at 07:59:40PM +0100, Johan Hake wrote:
> On Sunday 07 December 2008 16:42:02 Anders Logg wrote:
> > On Sun, Dec 07, 2008 at 02:57:01PM +0100, Martin Sandve Alnæs wrote:
> > > 2008/12/6 Johan Hake <hake@xxxxxxxxx>:
> > > > On Saturday 06 December 2008 20:54:34 Anders Logg wrote:
> > > >> On Sat, Dec 06, 2008 at 04:03:25PM +0100, Johan Hake wrote:
> > > >> > On Saturday 06 December 2008 15:43:13 Anders Logg wrote:
> > > >> > > On Sat, Dec 06, 2008 at 03:34:40PM +0100, Johan Hake wrote:
> > > >> > > > On Saturday 06 December 2008 14:56:59 Anders Logg wrote:
> > > >> > > > > On Sat, Dec 06, 2008 at 12:05:41PM +0100, DOLFIN wrote:
> > > >> > > > > > One or more new changesets pushed to the primary dolfin
> > > >> > > > > > repository. A short summary of the last three changesets is
> > > >> > > > > > included below.
> > > >> > > > > >
> > > >> > > > > > changeset:   5262:0e349fbe09ce4179252652fe5c1d58725951bc3f
> > > >> > > > > > tag:         tip
> > > >> > > > > > user:        "Johan Hake <hake@xxxxxxxxx>"
> > > >> > > > > > date:        Sat Dec 06 12:05:42 2008 +0100
> > > >> > > > > > files:       demo/pde/stokes/taylor-hood/python/demo.py
> > > >> > > > > > dolfin/function/SpecialFunctions.h
> > > >> > > > > > dolfin/swig/dolfin_function_pre.i
> > > >> > > > > > site-packages/dolfin/function.py description:
> > > >> > > > > > Added support for f.split()
> > > >> > > > > >  - Renamed operator[] to f._sub instead of f.sub
> > > >> > > > > >  - f.sub(i) now returns an instantiated sub function
> > > >> > > > > >  - f.split() uses f.sub() to return a tuple of all sub
> > > >> > > > > > functions - stoke/taylor-hood demo now runs.
> > > >> > > > >
> > > >> > > > > Excellent!
> > > >> > > > >
> > > >> > > > > It runs now but the solution looks completely crazy. The
> > > >> > > > > problem is that the boundary conditions are not set correctly
> > > >> > > > > since we use V and Q to set the boundary conditions for the
> > > >> > > > > sub systems and they don't know the offsets
> > > >> > > > > (DofMap::offset()).
> > > >> > > >
> > > >> > > > The problem here is that these spaces need to be SubSpaces?
> > > >> > >
> > > >> > > Yes.
> > > >> > >
> > > >> > > > If that is the case, we could extract the subspaces after a
> > > >> > > > MixedFunctionSpace is created and then store these in the spaces
> > > >> > > > attribute, either as pure cpp.SubSpaces or add another python
> > > >> > > > class, SubSpace, which is a cpp.SubSpace and stores the original
> > > >> > > > ffc.element too, or something?
> > > >> > >
> > > >> > > I was thinking something like this:
> > > >> > >
> > > >> > > W = VectorFunctionSpace(mesh, "triangle", 2) + FunctionSpace(mesh,
> > > >> > > "triangle", 1) V, Q = W.split()
> > > >> >
> > > >> > Doesn't look too nice, and it will create a non intuitive work flow.
> > > >> > Combining two interfaces aren't easy!
> > > >> >
> > > >> > > The split function needs to both create SubSpaces (which will lead
> > > >> > > to DofMaps with correct offsets) and set the element correctly,
> > > >> > > which can be done by looking at the spaces attribute in
> > > >> > > MixedFunctionSpace.
> > > >> > >
> > > >> > > It's a bit weird since what we really do is
> > > >> > >
> > > >> > > V = VectorFunctionSpace(mesh, "triangle", 2)
> > > >> > > Q = FunctionSpace(mesh, "triangle", 1)
> > > >> > > W = V + Q
> > > >> > > V, Q = W.split()
> > > >> > >
> > > >> > > First, we put V and Q together to create a mixed function space.
> > > >> > > Then we split W again into V and Q. After the split V and Q know
> > > >> > > that they are part of the bigger space (at least they know the
> > > >> > > offset into the bigger space).
> > > >> >
> > > >> > Yes I see this. Instead, or in addition, of using split, we could
> > > >> > implement W.sub(i) that returns a subspace, which is then used when
> > > >> > setting the bc, and other relevant places.
> > > >> >
> > > >> > > The other option would be to let + have a side effect on V and Q
> > > >> > > but that does not seem to be a good solution.
> > > >> >
> > > >> > I thought of this too. But I cannot se how we could do it with the
> > > >> > present implementation of FunctionSpace/Subspace.
> > > >>
> > > >> If we can get make_subspace working as you suggest below, then it
> > > >> would be easy to modify __add__ for FunctionSpaceBase:
> > > >>
> > > >>   W = MixedFunctionSpace([self, other])
> > > >>   self.make_subspace(W, 0)
> > > >>   other.make_subspace(W, 1)
> > > >>   return W
> > > >
> > > > Yes something like that.
> > > >
> > > >> This would make the interface look nice but someone (you know who you
> > > >> are) might think we are insane... :-)
> > > >
> > > > *laugh*
> > > >
> > > > I am not very happy with it either, as the __add__ operator should not
> > > > do such a thing. What we are saying is that V and Q are individual
> > > > FunctionSpaces before we make make the add. After we have made it they
> > > > are suddenly subspaces of the result of an addition. Not very
> > > > intuitive.
> > > >
> > > > One slution could be to remove the __add__ operator and instead force
> > > > the user to instantiate the Mixed space with a constructor, e.g.
> > > >
> > > >   W = MixedFunctionSpace(V,Q)
> > > >
> > > > With this it is easier to justify that we are doing somthing with V and
> > > > Q.
> > >
> > > No it isn't.
> > >
> > > This isn't a matter of taste, it just doesn't scale outside a minimal
> > > example.
> > >
> > > What will happen here?
> > >   W0 = MixedFunctionSpace(V0,V1) # or V0 + V1, same thing
> > >   W1 = MixedFunctionSpace(V1,V2)
> > >   W2 = MixedFunctionSpace(V2,V3)
> > >
> > > >> > If we could just call a member function in a FunctionSpace, let say
> > > >> > V.make_subspace(W,i), and this would then create the needed stuff in
> > > >> > V, to make it SubSpaceable. But now SubSpace is a subclass which
> > > >> > effectively prevents this approach.
> > > >> >
> > > >> > This approach is abit intrucive too. But what difference would it
> > > >> > make for the user, i.e., if V in addition to be a FunctionSpace now
> > > >> > also is a> >> > subspace of W?
> > > >>
> > > >> The only reason we need this is to be able to set boundary conditions
> > > >> for sub systems. For that we need two things: the offset into the
> > > >> global system vector and the DofMap for the subsystem in question.
> > > >> There might be other ways to define the interface for DirichletBC,
> > > >> for example:
> > > >>
> > > >>   bc = DirichletBC(W, 0, ...)
> > > >
> > > > This is maybee the best one? The DirichletBC operates at the global
> > > > vector from the mixed space, and then it is more intuitive to actually
> > > > use the mixed space to set the BC.
> > >
> > > Agree.
> >
> > I'm still not convinced. The thing is that the C++ implementation of
> > DirichletBC assumes that it gets a FunctionSpace. Sometimes, this may
> > be a SubSpace (which is a subclass of FunctionSpace) but DirichletBC
> > doesn't care, it just sets the bcs for the FunctionSpace. Before, in
> > 0.8.1, there were 6 different constructors and an extra SubSystem
> > argument was required, but the introduction of SubSpace simplified the
> > implementation.
> >
> > This all works very fine in C++, but only because we don't see the
> > initial FunctionSpaces V and Q that are used to create the
> > MixedFunctionSpace W. We just get the MixedFunctionSpace W directly
> > and then it's natural to define V and Q from W. The problem in Python
> > is that we see the original V and Q, so it becomes awkward to put them
> > together and then split them:
> >
> >   W = V + Q
> >   (V, Q) = W.split()
> >
> > How about the following (just renaming the variables):
> >
> >   W = V + Q
> >   (W0, W1) = W.split()
> >
> >   bc0 = DirichletBC(W0, domain, u0)
> >   bc1 = DirichletBC(W1, domain, p0)
> 
> If we implement this as we did with the Function.split(), we could also 
> support:
> 
>    W = V + Q
> 
>    bc0 = DirichletBC(u0, W.sub(0), domain)
>    bc1 = DirichletBC(p0, W.sub(1), domain)

Looks good.

What about the order of the arguments? Should the value be first, or
the FunctionSpace?

> It is a bit fragile though, as the user can potentially send in the wrong 
> FunctionSpace. The only difference between V and W.sub(0), as I understand 
> it, is that the latter includes information about the offset into the global 
> vector.

Yes.

> Would it be possible to add a check in DirichletBC.apply (or/and in 
> BoundaryCondition.apply) that check the number of dofs in the vector it is 
> acting on and compare that with the number of dofs in the FunctionSpace? 
> 
> If the number of dofs in the vector is larger, then the FuncitonSpace have to 
> be a SubSpace, and issue an error or arning if it is not?

Yes, that would be good to add. Using dynamic_cast?

-- 
Anders

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