dolfin team mailing list archive

["Evan Lezar" <evanlezar@xxxxxxxxx>]

On Tue, Jun 3, 2008 at 11:37 PM, Evan Lezar <evanlezar@xxxxxxxxx> 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.
>
> Thanks
> Evan
>
> --
> visit http://randomestrandom.blogspot.com
>

OK

I feel as if I am making some progress.

I have now been able to use a Dirichlet BC to zero the entries in the
matrices that correspond to the edges on the boundary - to achieve
this I use a mesh SubDomain.

Is there no way to pass a mesh SubDomain to the assemble function - or
an interior mesh function similar to BoundaryMesh - that would allow
me to only assemble the matrix over the required degrees of freedom.
Alternatively, how could I remove the new zero entries from the matrix
returned from DirichletBC.zero()?

Thanks
Evan