Interpolation of a finite element method on non-matching meshes

A special finite element method is defined in getfem/getfem_interpolated_fem.h which is not a real finite element method, but a pseudo-fem which interpolates a finite element method defined on another mesh. If you need to assemble a matrix with finite element methods defined on different meshes, you may use the “interpolated fem” for that purpose:

getfem::new_interpolated_fem(getfem::mesh_fem mf, getfem::mesh_im mim);

Because each base function of the finite element method has to be interpolated, such a computation can be a heavy procedure. By default, the interpolated fem object store the interpolation data.

The interpolation is made on each Gauss point of the integration methods of mim, so that you have to use these integration methods in the assembling procedures.

For instance if you need to compute the mass matrix between two different finite element methods defined on two different meshes, this is an example of code which interpolate the second FEM. on the mesh of the first FEM., assuming that mf describes the finite element method and mim is the chosen integration method:

getfem::mesh_fem mf_interpole(mfu.linked_mesh());
pfem ifem = getfem::new_interpolated_fem(mf, mim);
dal::bit_vector nn = mfu.convex_index();
mf_interpole.set_finite_element(nn, ifem);
getfem::asm_mass_matrix(SM1, mim, mfu, mf_interpole);

The object pointed by ifem contains all the information concerning the interpolation. It could use a lot of memory. As pfem is a smart pointer (a boost intrusive_ptr), the interpolated fem will be automatically destroyed when the last pointer on it is destroyed. To obtain a better accuracy, it is better to refine the integration method (with IM_STRUCTURED_COMPOSITE for instance) rather than increase its order.

mixed methods with different meshes

to be described ...

mortar methods

to be described ...