Ewald and Multipole Methods for Periodic N -Body Problems

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Many realistic biomolecular simulations require use of periodic boundary conditions to create a surface-free environment for the molecule of interest and associated solvent molecules to interact. Electrostatic interactions are the principal computational cost of such simulations. We have implemented two codes: a parallel variant of an Ewald summation method which computes the effect of infinite periodic boundary conditions, and a parallel variant of a multipole algorithm which explicitly computes the interactions within a large but finite periodic system. Each has a regime of applicability, with Ewald favoring smaller systems and fewer processors, and the multipole methods favoring larger systems and more processors. Simulations can now include a full treatment of periodic electrostatics to three or four significant figures of accuracy for a computational cost equivalent to that of a 12Å cutoff simulation.