Implement Hiptmair-Xu auxiliary space preconditioners for Hdiv

[tensorFan]

The following ingredients are needed.

• [x] A: The stiffness matrix on (a vector of) nodal VEM space
• [x] Pi: Projection of a vector nodal element to the RT space
• [ ] Pi: Projection of a vector nodal element to the RT space, optimize the function
• [x] C: The curl operator mapping from the nodal space to the RT space
• [x] S: The smoother on (a vector of) nodal VEM space
• [x] The preconditioner P = Pi A_inv Pi^T + C A_inv C^T + S + C S C^T, by creating a function that does the application to avoid computing A_inv.
• [x] Test the largest and smallest eigenvalues of the system M v = lambda P v

[tensorFan]

Having some trouble with the Revise package, can't get it to accept my newest module. The smoother should be done now anyways, waiting on implementing the curl until I know exactly what we need there. I think basically it will be multiplying cell_faces with face_nodes.

Not sure how to implement this projection though, from vector nodal to RT. Not sure at all

[tensorFan]

Projection ingredients:

• face_nodes
• normal

Idea: We want the projection to preserve the divergence of the basis functions, so it should preserve the integral of the normal component. This latter requirement gives enough equations to define the projection

[tensorFan]

I think the last task Test the largest and smallest eigenvalues of the system M v = lambda P v should read Test the largest and smallest eigenvalues of the system M v = lambda inv(P) v according to the text in page 4 of the Hiptmair paper (P = B and we say that BA is the preconditioned system)