• Corpus ID: 16031976

A FAST ADAPTIVE MULTIPOLE ALGORITHM FOR PARTICLE SIMULATIONS *

@inproceedings{CARRIERtAFA,
  title={A FAST ADAPTIVE MULTIPOLE ALGORITHM FOR PARTICLE SIMULATIONS *},
  author={J. CARRIERt and Leslie Greengardt and V. ROKHLINt}
}
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 Coulomb's law. Unlike previously published schemes, the algorithm of this paper has an asymptotic CPU time estimate of O(N), 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… 

Figures and Tables from this paper

Fast multipole methods for particle dynamics
TLDR
The basic mathematics behind fast summations applied to long ranged forces is presented along with advanced techniques for accelerating the solution, including the most recent developments.
Fast Updating Multipole Coulombic Potential Calculation
We present a numerical method to efficiently and accurately re-compute the Coulomb potential of a large ensemble of charged particles after a subset of the particles undergoes a change of position.
Parallel Fast Multipole Algorithm using MPI
TLDR
The fast multipole algorithm is implemented, using MPI, based on optimal communication scheme which minimizes the communication and synchronization overhead and is scalable and portable.
Fast Multipole Solvers for Three-Dimensional Radiation and Fluid Flow Problems
TLDR
A fast multipole solver with application to both 3-D radiation problems (calculation of the heat flux from the evolving temperature field in an absorbing medium) and3-D fluid flow is developed by using a more general kernel for the associated volume integrals.
Integral Equation Methods for Particle Simulations in Creeping Flows
Abst rac t In tegra l equation methods for computing the hydrodynamic interactions among solid particles suspended in a creeping flow are presented. The particles may have arbitrary shape and they
AN IMPLEMENTATION OF THE FAST MULTIPOLE METHOD FOR HIGH ACCURACY PARTICLE TRACKING OF INTENSE BEAMS
TLDR
A single level version of the fast multipole method is implemented in the software package COSY Infinity for charged particle beams, resulting in a highly accurate algorithm for simulation of intense beams without averaging such as encountered in PIC methods.
Fast evaluation of vector splines in two dimensions
TLDR
This paper establishes the series approximation theory and presents the implementation details of the algorithm, which is based on the fast multipole method and has an asymptotic CPU time estimate of O(N), where N is the number of data points.
A two-dimensional fast solver for arbitrary vortex distributions
A method which is capable of an efficient calculation of the two-dimensional stream function and velocity field produced by a large system of vortices is presented in this report. This work is based
Improvement of the Stokesian Dynamics method for systems with a finite number of particles
  • K. Ichiki
  • Mathematics
    Journal of Fluid Mechanics
  • 2002
An improvement of the Stokesian Dynamics method for many-particle systems is presented. A direct calculation of the hydrodynamic interaction is used rather than imposing periodic boundary conditions.
...
...

References

SHOWING 1-10 OF 10 REFERENCES
A fast algorithm for particle simulations
An Efficient Program for Many-Body Simulation
TLDR
This paper describes both the particular program and the methodology underlying such speedups that reduced the running time of a large problem $(N = 10,000)$ by a factor of four hundred.
Computer simulation using particles
Computer experiments using particle models A one-dimensional plasma model The simulation program Time integration schemes The particle-mesh force calculation The solution of field equations
Numerical study of slightly viscous flow
  • A. Chorin
  • Physics
    Journal of Fluid Mechanics
  • 1973
A numerical method for solving the time-dependent Navier–Stokes equations in two space dimensions at high Reynolds number is presented. The crux of the method lies in the numerical simulation of the
A Matrix Problem with Application to Rapid Solution of Integral Equations
TLDR
It is shown that arbitrarily accurate approximate solutions can be computed in $O(n\log n)$ arithmetic operations for large n, provided that $z(t)$ is sufficiently smooth.
A fast algorithm for the multiplication of generalized Hilbert matrices with vectors
On presente un algorithme rapide de complexite logarithmique pour la multiplication des matrices de Hilbert generalisees par des vecteurs
A fast algorithm for Trummer'sproblem, LCSR-TR- 77
  • A fast algorithm for Trummer'sproblem, LCSR-TR- 77
  • 1985
SIGACT News ACM Special Interest Group on Automata and Computability Theory
  • SIGACT News ACM Special Interest Group on Automata and Computability Theory
  • 1985