Efficient methods for evaluating periodic electrostatic interactions on high performance computers

Ewald summation is traditionally employed to treat the long ranged Coulomb interactions of particle systems with periodic boundary conditions (PBC). PBC are often the most appropriate conditions for suppressing surface effects in molecular dynamics (MD) simulations. The dissertation first presents a comprehensive survey of variants of Ewald summation methods including conventional, Fourier, and multipole-based algorithms. The most efficient method for truly evaluating Ewald summation is the Particle-Mesh Ewald (PME) method. PME reduces the cost of computing the Ewald summation, an [/cal O](N²) algorithm in its traditional formulation, to [/cal O](N/ /log/ N) where N is the number of particles in the system. In addition to algorithmic improvements, using parallel processing allows larger particle systems to be simulated in practical time frames. This dissertation addresses the problem of efficiently and accurately evaluating long- range interactions for periodic assemblies of particles on both sequential and parallel computers. Two efficient new methods, referred to as DPME and MPME, are devised and implemented in this dissertation to efficiently evaluate Ewald summation. These methods allow for longer, larger, and more realistic simulations. The Distributed Particle-Mesh Ewald (DPME) method is a new PME-based method for computing Ewald summation in parallel. The efficiency of DPME is demonstrated on a network of workstations and the Cray T3D using message-passing and shared-memory constructs. DPME uses spatial decomposition to distribute the workload. Several spatial decomposition schemes are demonstrated and compared. New expressions for the energy, force, and electric field are developed to extend the PME method to include fixed and induced point-dipoles in addition to point-charges. This formulation is implemented in another original code, the Multipole Particle-Mesh Ewald (MPME). MPME uses spline-interpolation to approximate the charges and dipoles onto a 3-D grid. The reciprocal-space component of Ewald summation is efficiently computed in MPME with arbitrarily high accuracy. MPME uses an iterative scheme to evaluate the self consistent dipoles. A predictive technique is incorporated and shown to reduce the number of iterations needed for convergence. The overhead of evaluating polarizability in MPME is only 25% over PME. MPME is tested with polarizable water although the method is applicable to heterogeneous systems.