dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Tue, Aug 19, 2008 at 03:40:13PM +0200, Jed Brown wrote:
> On Tue 2008-08-19 14:06, Anders Logg wrote:
> > On Tue, Aug 19, 2008 at 01:49:22PM +0200, Jed Brown wrote:
> > > On Tue 2008-08-19 13:40, Anders Logg wrote:
> > > > On Tue, Aug 19, 2008 at 12:12:50PM +0200, Jed Brown wrote:
> > > > > On Tue 2008-08-19 11:59, Anders Logg wrote:
> > > > > > On Thu, Aug 14, 2008 at 10:10:03PM +0000, Jed Brown wrote:
> > > > > > > One way to implement this is to allocate a vector for Dirichlet values,
> > > > > > > a vector for Homogeneous values, and a Combined vector.  The Homogeneous
> > > > > > > vector is the only one that is externally visible.
> > > > > > 
> > > > > > Isn't this problematic? I want the entire vector visible externally
> > > > > > (and not the homogeneous part). It would make it difficult to plot
> > > > > > solutions, saving to file etc.
> > > > > > 
> > > > > > Maybe the Function class could handle the wrapping but it would involve a
> > > > > > complication.
> > > > > 
> > > > > Right, by `externally visible' I mean to the solution process, that is
> > > > > time-stepping, nonlinear solver, linear solvers, preconditioners.  The
> > > > > vector you are concerned about is the post-processed state which you can
> > > > > get with zero communication.  It is inherently tied to the mesh and
> > > > > anything you do with it likely needs to know mesh connectivity.  I don't
> > > > > think it is advantageous to lump this in with the global state vector.
> > > > > 
> > > > > Jed
> > > > 
> > > > I don't understand. What is the global state vector?
> > > 
> > > The global state vector is the vector that the solution process sees.
> > > Every entry in this vector is a real degree of freedom (Dirichlet
> > > conditions have been removed).  This is the vector used for computing
> > > norms, applying matrices, etc.  When writing a state to a file, this
> > > global vector is scattered to a local vector and boundary conditions are
> > > also scattered into the local vector.  The local vector is serialized
> > > according to ownership of the mesh (you have to do this anyway).
> > > 
> > > Jed
> > 
> > I'm only worried about how to create a simple interface. Now, one may
> > do
> > 
> >   u = Function(...);
> >   A = assemble(a, mesh)
> >   b = assemble(L, mesh)
> >   bc.apply(A, b)
> >   solve(A, u.x(), b)
> >   plot(u)
> > 
> > How would this look if we were to separate out Dirichlet dofs?
> 
> How about a FunctionSpace object which manages this distinction.
> Something like the following should work.
> 
>   V = FunctionSpace(mesh, bcs); // Is this name clearer?

We've discussed introducing a FunctionSpace concept earlier (on ufl-dev)
to handle boundary conditions, and to enable sharing of function space
data like meshes and dof maps. This might be a good idea, but it has
to be something like

  V = FunctionSpace(element, mesh, bcs)

>   u = V.function();

I think this should be

  u = Function(V)

>   A = V.matrix(a);
>   P = V.matrix(p);     // preconditioning matrix, optional [1]

What do these accomplish? Return a matrix of appropriate size? I don't
think that's necessary since the assembler can set the size.

>   solver = LinearSolver(A, P);
>   u0 = u.copy();       // if nonlinear, set initial guess
> 
>   V.assemble(A, a, u0); // builds Jacobian matrix [2]
>   V.assemble(P, p, u0); // preconditioning form, optional
>   V.assemble(b, L, u0); // the ``linear form'' (aka nonlinear residual)
>   solver.solve(u, b);

The problem here is that the solver needs to be aware of Functions.
Now, a solver only knows about linear algebra, which is nice.

> Note that u0 disappears if the problem is linear and P disappears if you
> use the real Jacobian as the preconditioning matrix.  The key point is
> that boundary conditions are built into the function space.  It is no
> more work, it just happens in a different place.
> 
> [1] It is essential that the test/trial spaces for the preconditioning
> matrix are the same as for the Jacobian.
> 
> [2] I don't like the implicit wiring of the state vector into
> assemble().  It is really hard to track dependencies and the current
> state is not a property of the Bilinear/Linear forms.

Maybe one could do

  (A, b) = assemble(a, L, mesh, bc)
  solve(A, u.dofs(), b)

This would be in addition to the current

  (A, b) = assemble(a, L, mesh)
  bc.apply(A, b)
  solve(A. u.vector(), b)

In the first version, the assembler knows about the boundary
conditions and in the second it doesn't. This would require having two
members in the Function class that return a Vector:

  u.vector() // Returns entire vector
  u.dofs()   // Returns non-Dirichlet dofs

-- 
Anders

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