Hi I was wondering if someone could assist me with the following problem. I have a variational problem defined on some 3D mesh (let us say a unit cube for arguments sake) using Nedelec elements. The functional I have consists of 3 parts - one where integration takes place over the volume of the mesh and a second and third part that are constructed by integrating tangential components over two of the sides of the cube. In pydolfin terms:
=================== mesh = UnitCube(32, 32) V = FunctionSpace(mesh, "Nedelec", 1) # Define variational problem v = TestFunction(V) u = TrialFunction(V) # define the parts of the functional volume = (dot(curl(v), curl(u)) - dot(v, u))*dx surface_1 = (dot(*tangential*(v), *tangential*(u)) + dot(v, E))*dS_1 surface_2 = (dot(*tangential*(v), *tangential*(u)))*dS_2 =================== volume, surface_1, and surface_2 can then be assembled to obtain a matrix equation. E is a known source term and *tangential*() represents the component of the test or trial function tangential to the surface over which is being integrated. I have a couple of questions: Firstly, what would be a good way to implement the tangential operator - ie is is good enough to simply define a vector function normal to the surface and use the cross operator? and Secondly, how would I go about specifying the integration over the two different faces of the cube (ie dS_1 and dS_2)? Any assistance would be much appreciated. Evan
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