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=mesh_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 You received this question notification because you are a member of DOLFIN Team, which is an answer contact for DOLFIN. _______________________________________________ Mailing list: https://launchpad.net/~dolfin Post to : [email protected] Unsubscribe : https://launchpad.net/~dolfin More help : https://help.launchpad.net/ListHelp
