Are there some approximate or randomised algorithms to numerically solve Poisson's Equation in Partial Differential Equations.(http://en.wikipedia.org/wiki/Poisson%27s_equation). The best algorithms I know of are Multigrid methods(http://en.wikipedia.org/wiki/Multigrid_methods), but they are deterministic and are O(n). Are there Randomised or approximate algos to solve this problem.

You can modify the method described here for the Laplace equation to work for Poisson. 


How about the fast multipole method? (Or does that count as multigrid?) 

