For a very large mixed-poisson problem with lowest order Raviart-Thomas elements (RT0), I plan on using an iterative solver. However, this kind of problem is not positive-definite (saddle point problem IIRC), thus standard preconditioners (like jacobi) will not converge well for large-problems.
I was told that the algebraic multigrid preconditioner is the one of the most common methods to achieving fast convergence for Krylov solvers. My question is, what would it look like for a mixed-poisson problem? Or if there are better preconditioning methods, do point them out to me.