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This talk compares the performance of a Poisson solver based on the Fast Multipole Method (FMM-PS) to a Multigrid solver. While Multigrid has been widely used in the fluid dynamics setting, this research suggests that the FMM-PS should be considered an important alternative. Both algorithms are O(N), and fast implementations of both have been developed, adapted to work in the context of a projection method for fluid simulation. I'll describe the FMM-PS and give an overview of projection methods for computational fluid dynamics, and I'll present test problems that demonstrate how the FMM-PS is competitive with Multigrid in terms of accuracy and robustness.