On 25/09/10 08:48, Renard Yves wrote: > Yes. If you set M to the identity, the value of the shape function will > be intrinsic to the edge in the case of Nedelec element, so the > connection to the degree of freedom of the neighbour element should be > ok, except the sign. I think, you have at least to keep the selection of > the direction which is made in the definition of the transformation > matrix M.
I have discovered that I need to understand the meaning of the different "vtype" that can be assigned, but didn't find it in the documentation. The Nedelec method uses vtype = VECTORIAL_DUAL_TYPE; RT0 uses vtype = VECTORIAL_PRIMAL_TYPE; A third type that seems to be possible is VECTORIAL_NOTRANSFORM_TYPE. I noticed that even when using M = Identity (is_equiv = true), the mass matrix elements for the Nedelec case scaled correctly when the thetrahedron size was varied. This was unexpected , and must be due to the vtype setting? If the tetrahedron side length is around h, the gradients of the hat functions are around 1/h. The Whitney edge elements are defined like lambda_ij = lambda_i grad lambda_j - lambda_j grad lambda_i ~ 1/h The correct mass matrix is therefore proportional to (1/h)^2 * h^3 ~ h. I confirmed this behaviour for the modified Nedelec method (my unfinished attempt at Whitney 1-forms), which does not use any M at the moment (is_equiv = true). So I'm guessing something is being taken care of "behind the scenes" due to the vtype setting? On the other hand, with vtype = VECTORIAL_NOTRANSFORM_TYPE, the mass matrix element scaling was not correct, but instead ~ h^3 as expected when one does not take account the vector transformation. When I understand this I need to understand how the cross product of gradients is to be treated for the Whitney 2-form case. Torquil _______________________________________________ Getfem-users mailing list [email protected] https://mail.gna.org/listinfo/getfem-users
