Comments on P(3)M, FMM, and the Ewald method for large periodic coulombic systems

Prompted by the need to simulate large molecular or gravitational systems and the availability of multiprocessor computers, alternatives to the standard Ewald calculation of Coulombic interactions have been developed. The two most popular alternatives, the fast multipole method (FMM) and the particle-particle particle-mesh (P(3)M) method are compared here to the Ewald method for a single processor machine. Parallel processor implementations of the P(3)M and Ewald methods are compared. The P(3)M method is found to be both faster than the FMM and easier to implement efficiently as it relies on commonly available software (FFT subroutines). Both the Ewald and P(3)M method are easily implemented on parallel architectures with the P(3)M method the clear choice for large systems.