Dear Thomas and All,

Merry Christmas (2 years later).

The fastest method to solve the 2-D and 3-D Poisson problem is multigrid. It has linear runtime and storage in the number of grid points in your problem. If the equation coefficients are constant (i.e. true isotropic Laplacian), no storage is required except for the solution. You do NOT need to store a sparse matrix of equation coefficients.

It is of course also much faster and requires less storage than PCG and mldivide. Its parallel efficiency is also superior to these methods if you run matlab with multiple executors.

You will probably need to code it yourself, but it is not hard. It took me a couple of days once.

See http://www.amazon.com/Multigrid-Ulrich-Trottenberg/dp/012701070X

Oren