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[David Maxwell <question133939@xxxxxxxxxxxxxxxxxxxxx>]

Question #133939 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/133939

    Status: Answered => Open

David Maxwell is still having a problem:
This would be too easy. I'm looking for  a function defined on (a part
of) the boundary, not just its average value.

-David

On Nov 15, 2010, at 8:33 AM, Johan Hake wrote:

> Your question #133939 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/133939
> 
>    Status: Open => Answered
> 
> Johan Hake proposed the following answer:
> Couldn't you just assemble the boundary condition directly from the
> solution?
> 
>  neuman_vector = assemble(u*vv*ds(bottom),\
>                  exterior_facet_domains=mesh_function)
> 
> If this is what you want you can preassemble a boundary mass matrix:
> 
>  Mb = assemble(uu*vv*ds(bottom), exterior_facet_domains=mesh_function)
> 
> and then each times step:
> 
>  neuman_vector = Mb*u.vector()
> 
> Johan
> 
> On Saturday November 13 2010 12:58:06 David Maxwell wrote:
>> New question #133939 on DOLFIN:
>> https://answers.launchpad.net/dolfin/+question/133939
>> 
>> I'd like to extract Neumann data from a solution to an elliptic PDE.
>> 
>> For example, if u is a weak solution of -Laplacian(u) = f, then its Neumann
>> data (\partial_n u) on the boundary is well defined as follows:
>> 
>> Given sufficiently regular v defined on the boundary, extend v to a
>> function in H^1 in the domain.  Then
>> 
>> <\partial_n u, v> = \int_\Omega \nabla u \nabla v - f v
>> 
>> Since v belongs to L^2 of the boundary, I can interpret \partial_n as an
>> element of L^2 of the boundary.
>> 
>> In truth, I really only want the Neumann data on part of the boundary.
>> 
>> I thought I might proceed as follows.  In the following, 'u' is the
>> solution of the PDE in function space V, and mesh_function is a mesh
>> function on the edges that equals 1 on the 'top' boundary, 2 on the
>> remainder of the boundary, and 0 on all other edges.
>> 
>> My first attempt went something like:
>> 
>> uu = TestFunction(V)
>> vv = TrialFunction(V)
>> 
>> inside=0; top=1; bottom=2
>> 
>> a = uu*vv*ds(bottom)
>> rhs = inner(grad(u),grad(vv))*dx - vv*f*dx
>> 
>> top_bc = DirichletBC(V,Constant(0),mesh_function,top)
>> interior_bc = DirichletBC(V,Constant(0),mesh_function,inside) # I thought I
>> was being clever here!
>> 
>> u_n =
>> VariationalProblem(a,rhs,bcs=[top_bc,interior_bc],exterior_facet_domains=m
>> esh_function).solve()
>> 
>> This crashes on applying the boundary conditions using 'ident', so I tried
>> setting the 'use_ident' parameter to False on the boundary conditions.
>> 
>> This still doesn't work because the interior_bc is (rightfully) too
>> enthusiastic -- every vertex is joined to some interior edge and so I pick
>> up the zero solution.
>> 
>> I tried some other tacts, but they are perhaps too foolish to describe
>> here.
>> 
>> And I have the sense that I really ought to be solving a problem on a
>> BoundaryMesh (rather than a highly constrained problem on the original
>> mesh) but I don't know how to extend Functions on a boundary mesh to
>> Functions on the original mesh.
>> 
>> Help!
>> 
>> David Maxwell
>> 
>> 
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>> 
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