Efficient mpc creation with same dofs, different coefficient

[conpierce8]

Motivation

Another feature request motivated by wave propagation: to compute a band structure for periodic media, we prescribe the wavevector $k$ through the Bloch boundary conditions, which are applied with a multipoint constraint, then solve the eigenvalue problem to obtain the eigenfrequencies. To produce the entire band structure, we iterate through a range of $k$ and repeatedly construct and solve the eigenvalue problem. Since the multipoint constraint is repeatedly applied to the same set of slave and master dofs, it is desirable to re-use the information about the slave and master dofs, and thus only need to update the coefficients of the mpc at each step of the iteration.

Requested improvement

Make MultiPointConstraint.create_periodic_constraint_topological (and create_periodic_constraint_geometrical, etc.) return the mpc_data object that is generated by the C++ layer. Then it can be saved and the mpc_data.coeffs array updated at each iteration, e.g.

mpc = MultiPointConstraint(V)
mpc_data = mpc.create_periodic_constraint_topological( ... )
for k in np.linspace(0, 1, N):
    mpc_data.coeffs[:] = k
    mpc = MultiPointConstraint(V)
    mpc.add_constraint_from_mpc_data(mpc_data)
    mpc.finalize()
    # Solve eigenvalue problem

Note: this is already possible by directly accessing the C++ wrapper layer, i.e. with

mpc_data = dolfinx_mpc.cpp.mpc.create_periodic_constraint_topological( ... )

but the suggested improvement would result in cleaner code and eliminate the need for users to directly call the C++ layer.