Modified Fast Multipole Method for Coarse-Grained Molecular Simulations

Abstract

More than 90% of computational cost in molecular simulations is associated with pairwise potential evaluations. Fast Multipole Method (FMM) is the most advanced algorithm with O(n) computational complexity where n is the number of atoms in the system. This method has also been used in coarse-grained molecular simulations with the same computational complexity. This paper as a continuation of [1] presents a novel derivation and implementation of the FMM for coarse-grained simulations through which the cost reduces to O(NlogN) where N denotes the number of rigid clusters in the system, while N<<n. These formulations developed in the Cartesian coordinates take advantage of the rigidity of the rigid clusters to express the fast multipole formulations. In other words, the far field potential is expressed in terms of the physical and geometrical properties of the clusters such as the entire charge, the location of the center of charge, and the pseudo-inertia tensor of the cluster about its charge center. This tensor is constant for rigid clusters if expressed in terms of the body-fixed unit vectors. As such, it is calculated for each cluster before the simulation, and is just updated with the appropriate orientation matrix. A novel binary divide and conquer scheme as opposed to the available octree method is developed for the efficient implementation of the algorithm. As such, the potential of each cluster is recursively calculated in an assembly-disassembly pass using this developed binary tree. The presented method is highly compatible with coarse-grained models of chain biopolymers, and significantly improves the computations associated with pairwise interactions compared to the current FMM.[1] Long-range force and moment calculations in multiresolution simulations of molecular systems, Mohammad Poursina, Kurt S. Anderson, Journal of Computational Physics, Volume 231, Issue 21, p. 7237-7254, 2012.