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[Anders Logg <logg@xxxxxxxxx>]

On Thu, Jun 05, 2008 at 11:10:58AM +0200, Johan Hoffman wrote:
> > On Tue, Jun 3, 2008 at 11:31 PM, Anders Logg <logg@xxxxxxxxx> wrote:
> >> On Tue, Jun 03, 2008 at 11:24:54PM +0200, Evan Lezar wrote:
> >>> The problem is that I am not quite sure how to use it ...
> >>> The code I have at the moment is as follows:
> >>>     mesh = UnitSquare(1,1)
> >>>     mesh.refine()
> >>>     mesh.refine()
> >>>     element = FiniteElement("Nedelec", "triangle", order);
> >>>     v = TestFunction(element)
> >>>     u = TrialFunction(element)
> >>>     # assemble the mass and stiffness matrices
> >>>     # the bilinear form is defined as the transverse curl since it is
> >>> a two dimensional problem
> >>>     # a = dot(curl(v), curl(u))
> >>>     a = (vec(v.dx(0))[1] - vec(v.dx(1))[0])*(vec(u.dx(0))[1] -
> >>> vec(u.dx(1))[0])
> >>>     (S) = assemble(a*dx, mesh)
> >>>     (T) = assemble(dot(v, u)*dx, mesh)
> >>> I then use S and T to solve the eigenvalue system S x = lambda T x The
> reason I am having trouble is that this does not use the pde class and
> I have not found an example that uses the DirichletBC class to specify
> the boundary conditions for matrix assembly.
> >>> Thanks for the quick reply
> >>> Evan
> >> Hmm... I realize now I don't know how to set boundary conditions for an
> eigenvalue problem (other than by eliminating unknowns). For
> homogeneous boundary conditions, I guess one could zero out a row in S,
> insert a 1 on the diagonal and zero out the corresponding row in T.
> There is an example of applying boundary conditions in
> >>  demo/pde/convection-diffusion/python/demo.py
> >> but it is for a linear system Ax = b. There is also a function zero()
> in DirichletBC which can be used to zero out a row in a matrix. --
> >> Anders
> >> _______________________________________________
> >> DOLFIN-dev mailing list
> >> DOLFIN-dev@xxxxxxxxxx
> >> http://www.fenics.org/mailman/listinfo/dolfin-dev
> >
> > Well, eliminating unknowns is exactly what I need to do.  Typically in
> my own code I would not even create matrix entries for the edges on the
> boundary, thus eliminating the rows and columns associated with those
> degrees of freedom.  I think I did come across the zero()
> > function in my search, but how would I actually remove the rows or not
> have them assembled in the first place?
> >
> > I will have a look at the demo and see where that takes me.
> 
> Maybe you can solve this by using the subDomain classes?
> See the thread: "FFC implementation over a subdomain of \Omega" on the
> dolfin-dev mailing list.
> 
> /Johan

This doesn't help. The big problem here is we can't eliminate degrees
of freedom. This is something we should add at some point, along with
static condensation. I haven't thought much about it but it's
basically the same problem: express some degrees of freedom in terms
of others or given values, eliminate, solve, then add back the values
(or we might directly assemble the smaller system).

Until this has been implemented, you have to live with how we handle
Dirichlet conditions currently in DOLFIN, which is to zero out the
row, insert 1 on the diagonal and put the Dirichlet value in the
right-hand side. This is all handled by the DirichletBC class.

-- 
Anders

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