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.
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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?) 

