A new approach for rapid evaluation of the potential field in three dimensions

Efficient evaluation of the potential field is an essential requirement for simulation of large ensembles of particles in many applications, including astrophysics, plasma physics, molecular dynamics, very large-scale integra tion systems and micro-electromechanical systems. Current methods use multi pole expansion of spherical harmonics for the potential field, which is com putationally expensive in terms of running time and memory requirements whe n a high degree of accuracy is desired. In this paper, a new approach is pr esented for efficient and rapid evaluation of the potential field in three dimensions. The mathematical background for the proposed approach stems fro m an exponential integral representation of Green's function, 1/r, and an a pproximation to the integral by using Gauss quadratures, which distinctivel y differs from the theory of spherical harmonics. The translations are simp le in structure, error-free and independent of the approximation, which ena bles the overall accuracy and computational performance to be controlled ex ternally via the approximation. In addition, the gradient of the potential can be readily retrieved as a by-product of the:computational process, More importantly, the memory requirement is independent of the desired degree o f accuracy. The technique presented here opens new possibilities for effici ent distributed computing and parallel processing of large-scale simulation of particle systems.