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We present an implementation of the fast multipole method for computing coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected $O(N)$ scaling of that…

Chemical Physics · Physics 2015-06-22 Jonathan P. Coles , Michel Masella

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…

Numerical Analysis · Mathematics 2018-01-08 Austin R. Benson , Jack Poulson , Kenneth Tran , Björn Engquist , Lexing Ying

The Fast Multipole Method (FMM) computes pairwise interactions between particles with an efficiency that scales linearly with the number of particles. The method works by grouping particles based on their spatial distribution and…

Computational Physics · Physics 2025-08-05 He Zhang

The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…

Numerical Analysis · Mathematics 2014-03-20 Cris Cecka , Eric Darve

A novel code for the approximate computation of long-range forces between N mutually interacting bodies is presented. The code is based on a hierarchical tree of cubic cells and features mutual cell-cell interactions which are calculated…

Astrophysics · Physics 2009-11-07 Walter Dehnen

We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…

Numerical Analysis · Mathematics 2023-05-30 Isuru Fernando , Andreas Klöckner

We summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-called Multi-particle collision…

We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…

Mathematical Software · Computer Science 2013-01-10 Qi Hu , Nail A. Gumerov , Ramani Duraiswami

Smoothed particle hydrodynamics (SPH) is positioned as having ideal conservation properties. When properly implemented, conservation of total mass, energy, and both linear and angular momentum is guaranteed exactly, up to machine precision.…

Instrumentation and Methods for Astrophysics · Physics 2021-07-16 Oleg Korobkin , Hyun Lim , Irina Sagert , Julien Loiseau , Christopher Mauney , M. Alexander R. Kaltenborn , Bing-Jyun Tsao , Wesley P. Even

Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…

Numerical Analysis · Mathematics 2022-01-05 Guannan Hu , Sarah L. Dance

The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for…

Fluid Dynamics · Physics 2024-03-05 Hang Su , Eric E Keaveny

In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free space component and four types of reaction field…

Numerical Analysis · Mathematics 2020-05-26 Bo Wang , Wen Zhong Zhang , Wei Cai

Recently, a new framework to compute the photoionization rate in streamer discharges accurately and efficiently using the integral form and the fast multipole method (FMM) was presented. This paper further improves the efficiency of this…

Plasma Physics · Physics 2021-12-21 Bo Lin , Chijie Zhuang

This paper deals with the complex problem of how to simulate multiparticle contacts. The collision process is responsible for the transfer and dissipation of energy in granular media. A novel model of the interaction force between particles…

Computational Physics · Physics 2007-05-23 Leszczynski Jacek

We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…

Machine Learning · Computer Science 2015-02-16 William B. March , George Biros

The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function…

Machine Learning · Computer Science 2025-09-26 Emilio McAllister Fognini , Marta M. Betcke , Ben T. Cox

Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…

Computational Physics · Physics 2021-04-09 Cheng Qian , Mingyu Wang , Abdulkadir C. Yucel

In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…

Numerical Analysis · Computer Science 2019-10-23 Ali Rezaei , Fahd Siddiqui , Giorgio Bornia , Mohamed Y. Soliman

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…

Mathematical Software · Computer Science 2016-11-04 Jianyu Huang , Leslie Rice , Devin A. Matthews , Robert A. van de Geijn

Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic or electromagnetics. However, their cost strongly increases…

Numerical Analysis · Mathematics 2022-02-11 Igor Chollet , Xavier Claeys , Pierre Fortin , Laura Grigori