Leslie Greengard

A fast algorithm for particle simulations

An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature. For a system ofNparticles, an amount of work of the orderO(N2) has traditionally been required to evaluate all pairwise interactions, unless some approximation or truncation method is used. The algorithm of the present paper requires an amount of work proportional toNto evaluate all interactions to within roundoff error, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.

A New Version of the Fast Multipole Method for the Laplace Equation in Three Dimensions.

Abstract : We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.

A Fast Adaptive Multipole Algorithm for Particle Simulations

This paper describes an algorithm for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are described by Coulombs law. Unlike previously published schemes, the algorithm of this paper has an asymptotic CPU time estimate of

The fast Gauss transform

O(N)

A wideband fast multipole method for the Helmholtz equation in three dimensions

, where N is the number of particles in the simulation, and does not depend on the statistics of the distribution for its efficient performance. The numerical examples we present indicate that it should be an algorithm of choice in many situations of practical interest.

Fast Algorithms for Classical Physics

Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like

Accelerating fast multipole methods for the Helmholtz equation at low frequencies

NM

Spectral Deferred Correction Methods for Ordinary Differential Equations

as N and M increase; this makes it very expensive to carry out such calculations on a large scale. In this paper, an algorithm is presented which evaluates the sum of N Gaussians at M arbitrarily distributed points in

Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation

C \cdot (N + M)

A parallel version of the fast multipole method

work, where C depends only on the precision required. When