Showing papers by "Leslie Greengard published in 1987"
TL;DR: 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, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.
5,003 citations
Proceedings Article•
01 Dec 1987
TL;DR: Modifications necessary for implementation of the fast multipole method on parallel architectures are described and it is shown that the expected time requirements grow as log N when using N processors.
23 citations
01 Jan 1987
TL;DR: In this paper, the use of the fast multipole method (FMM) was explored for gridless particle simulations. But the FMM algorithm requires O(n log n ) operations.
Abstract: The numerical solution to N -body problems in gravitation or electrostatics has traditionally been obtained via particle-in-cell methods (PIC) since direct evaluation of all pairwise interparticle forces, requiring O ( N 2 ) operations, is too expensive. Recently, hierarchical solvers, which use tree data structures and lumped-force approximations, have made gridless simulations feasible in O ( N log N ) operations. In this paper, we explore the use of the fast multipole method (FMM) - a highly accurate order O ( N ) algorithm - in particle simulations. We briefly describe the FMM and its relation to other methods. Technical considerations of gridless simulations such as discrete particle fluctuations, sampling errors and boundary conditions are discussed and compared with PIC methodology. Examples of electrostatic simulations in plasma physics are presented.
1 citations