Follow this link to a useful (and free) matlab code that is basically a PDE solver adapted to common problems like diffusion, convection-diffusion, Stokes flow and Navier-Stokes flow problems (incompressible fluid dynamics).
I am talking about ifiss2.2 or Incompressible Flow & Iterative Solver Software Version 2.2.
There you will read that:
It has built-in multigrid and Krylov subspace solvers and includes a variety of appropriate preconditioning strategies for each problem.
Licence: LGPL
pretty sure that I am going to use it.
thank you Tito