Yet another fast multipole method without multipoles --- Pseudo-particle multipole method
Journal of Computational Physics, 1998 In this paper we describe a new approach to implement the O(N) fast multipole method and $O(N\log N)$ tree method, which uses pseudoparticles to express the potential field.
Makino, Junichiro
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X‐ray magnetic circular dichroism
Major Reference Works, Page 508-515., 2022 International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.
Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the ...
Gerrit van der Laan C. Chantler +2 more
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Periodic Fast Multipole Method
, 2021 A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach extends to the oscillatory equations of mathematical physics, including the Helmholtz and Maxwell equations, but we ...
Pei, Ruqi +3 more
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Fast multipole methods for particle dynamics [PDF]
Molecular Simulation, 2006 The growth of simulations of particle systems has been aided by advances in computer speed and algorithms. The adoption of O(N) algorithms to solve N-body simulation problems has been less rapid due to the fact that such scaling was only competitive for relatively large N.
J, Kurzak, B M, Pettitt
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A Parallel Directional Fast Multipole Method [PDF]
SIAM Journal on Scientific Computing, 2014 This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must ...
Benson, Austin R. +4 more
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A fast multipole method for stellar dynamics [PDF]
, 2014 The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations.
Dehnen, Walter
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Molecular Dynamics of Yukawa System using the Fast Multipole Method [PDF]
, 2001 In order to perform the large-scale molecular dynamics simulation of the Yukawa system, a mathematical expression for molecular dynamics using the fast multipole method is described. The model simulations are also performed to test the performance of our
Kishimoto, Tokunari +3 more
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Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem [PDF]
, 1999 The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate -but fast - methods such as the fast multipole method; however ...
Chew, WC, Koc, S, Song, J
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Generalized fast multipole method
IOP Conference Series: Materials Science and Engineering, 2010 The fast multipole method (FMM) is a technique allowing the fast calculation of long-range interactions between N points in O(N) or O(N ln N) steps with some prescribed error tolerance. The FMM has found many applications in the field of integral equations and boundary element methods, in particular by accelerating the solution of dense linear systems ...
Pierre-David Létourneau +2 more
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Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions [PDF]
, 2007 An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles.
Alexey Neelov +9 more
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