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Characterization of the accuracy of the fast multipole method in particle simulations

Felipe A. Cruz, L. A. Barba
2009 International Journal for Numerical Methods in Engineering  
This has brought dramatic increase in the capability of particle simulations in many application areas, such as electrostatics, particle formulations of fluid mechanics, and others.  ...  Although the literature on the subject provides theoretical error bounds for the FMM approximation, there are not many reports of the measured errors in a suite of computational experiments.  ...  Introduction In particle simulations, often the dynamics results from the summation of all pair-wise forces in the ensemble of particles.  ... 
doi:10.1002/nme.2611 fatcat:wgqegq2es5cmtij4eoe4l6qvhm

PGAS-FMM: Implementing a distributed fast multipole method using the X10 programming language

Josh Milthorpe, Alistair P. Rendell, Thomas Huber
2013 Concurrency and Computation  
In contrast to previous simulations of ion trajectories in cyclotron resonance mass spectrometers, our code enables both simulation of realistic particle numbers and guaranteed error bounds.  ...  This paper demonstrates the use of X10 to implement FMM for simulation of electrostatic interactions between ions in a cyclotron resonance mass spectrometer.  ...  Andrew Haigh implemented rotation-based operators for the FMM code.  ... 
doi:10.1002/cpe.3039 fatcat:vglyij3nvjdwxbek4vu7t5fk2u

Simulating cosmic structure formation with the GADGET-4 code [article]

Volker Springel, Rüdiger Pakmor, Oliver Zier, Martin Reinecke
2021 arXiv   pre-print
adapted to high dynamic range zoom-calculations with extreme variability of the particle number density in the simulated volume.  ...  Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes.  ...  that were instrumental for the test simulations of this paper.  ... 
arXiv:2010.03567v2 fatcat:5a4skp2vfzemnh4wkdp3cwhfae

Simulating cosmic structure formation with the GADGET-4 code

Volker Springel, Rüdiger Pakmor, Oliver Zier, Martin Reinecke
2021 Monthly notices of the Royal Astronomical Society  
adapted to high dynamic range zoom-calculations with extreme variability of the particle number density in the simulated volume.  ...  Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes.  ...  that were instrumental for the test simulations of this paper.  ... 
doi:10.1093/mnras/stab1855 fatcat:xlfwvefqxjfmvki5v4uzgmekdq

A fast algorithm for simulation of periodic flows using discrete vortex particles

Túlio R. Ricciardi, William R. Wolf, Alex M. Bimbato
2017 Journal of the Brazilian Society of Mechanical Sciences and Engineering  
The fast multipole method, FMM, is applied for the solution of singular terms appearing in the power series expansion and also for the exponential series expansion.  ...  The novel algorithm provides computational savings of nearly 240 times for double-precision simulations with one million particles when compared to the direct calculation of the Biot-Savart law.  ...  Finally, for a large number of particles, the nearfield cost in the FMM is dominant.  ... 
doi:10.1007/s40430-017-0902-x fatcat:evtsnzdrgrff5o2e7y2pnusquy

Fast Multipole Method for particle interactions: an open source parallel library component [chapter]

F. A. Cruz, M. G. Knepley, L. A. Barba
2010 Lecture Notes in Computational Science and Engineering  
In this process, we also contribute to the understanding of how the accuracy of the multipole approximation depends on the parameter choices available to the user.  ...  We are developing an open source, parallel implementation of the fast multipole method, to be made available as a component of the PETSc library.  ...  CHARACTERIZATION OF THE MULTIPOLE APPROXIMATION Overview of the algorithm The FMM is based on the idea that the influence of a cluster of particles can be approximated by an agglomerated quantity, when  ... 
doi:10.1007/978-3-642-14438-7_30 fatcat:a2glr2bdefgjpkt3l7zsroe2qu

Hierarchical N-body Simulations with Autotuning for Heterogeneous Systems

Rio Yokota, Lorena Barba
2012 Computing in science & engineering (Print)  
With the current hybridization of treecodes and FMMs, combined with auto-tuning capabilities on heterogeneous architectures, the flexibility of fast N-body methods has been greatly enhanced.  ...  Acknowledgements We're grateful for the support from the US National Science Foundation and the Office of Naval Research. Recent grant numbers are NSF OCI-0946441, and ONR award #N00014-11-1-0356.  ...  These first simulations were able to compute only in the order of a 100 particles.  ... 
doi:10.1109/mcse.2012.1 fatcat:qhfjkfnvtfde5iguma5b4gb2fm

Fast Force Algorithms and Solar System Integrations

Paul Wiegert, Douglas McNeil, Martin Duncan, Hal Levison
2004 Astronomical Journal  
, and often with only modest increases in the short-term error.  ...  As implemented, they involve the direct computation of the distances between each pair of N particles, a process whose effort grows as O(N 2 ).  ...  The distribution of errors is essentially bimodal (local field done to machine accuracy, far field done approximately by FMM), and an average may not characterize it particularly well.  ... 
doi:10.1086/380927 fatcat:e7vlxodfxbfhthbemmul3jbuza

Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

C Chen, S Aubry, T Oppelstrup, A Arsenlis, E Darve
2018 Modelling and Simulation in Materials Science and Engineering  
The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares.  ...  In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles.  ...  Unlike the Taylor FMM, the original FMM introduced by Greengard and Rokhlin [20] for particle simulations is based on spherical harmonics expansion.  ... 
doi:10.1088/1361-651x/aab7bb fatcat:qngqohyve5be3aoa2lazsw26pi

A fast algorithm for Brownian dynamics simulation with hydrodynamic interactions

Shidong Jiang, Zhi Liang, Jingfang Huang
2013 Mathematics of Computation  
The results presented in [9] demonstrates the importance of including hydrodynamic interactions in a dynamic simulation of many-particle Brownian systems.  ...  The first row indicates the ratio L/a with L the side length of the simulation box and a the radius of each particle.  ... 
doi:10.1090/s0025-5718-2013-02672-5 fatcat:hibxyibq65hu7afp5mjzqq2j2m

HSMA: An O(N) electrostatics package implemented in LAMMPS [article]

Jiuyang Liang, Jiaxing Yuan, Zhenli Xu
2021 arXiv   pre-print
To establish the validity of our implementation, we have presented extensive comparisons to the widely used particle-particle particle-mesh (PPPM) algorithm in LAMMPS and other dielectric solvers.  ...  With the proper choice of algorithm parameters and parallelization setup, the package enables calculations of electrostatic interactions that outperform the standard PPPM in speed for a wide range of particle  ...  The authors acknowledge the Center for High Performance Computing at Shanghai Jiao Tong University for the computing resources. The work of J. Liang and Z.  ... 
arXiv:2104.05260v1 fatcat:chanqvi4xnaiblc4anm3wpljse

Fast multipole methods for particle dynamics

J. Kurzak, B. M. Pettitt
2006 Molecular Simulation  
The growth of simulations of particle systems has been aided by advances in computer speed and algorithms.  ...  The computational efficiency of the new methods facilitates both simulations of large systems as well as longer and therefore more realistic simulations of smaller systems.  ...  The work done at Pacific Northwest National Laboratory is a part of a Computational Grand Challenge Project in the Environmental Molecular Sciences Laboratory sponsored by the Department of Energy's Office  ... 
doi:10.1080/08927020600991161 pmid:19194526 pmcid:PMC2634295 fatcat:yiokoxqhsfgdff5e5ph5vo4364

Viscous Vortex Particle Method Coupling with Computational Structural Dynamics for Rotor Comprehensive Analysis

Wenguo Zhu, Marco Morandini, Shu Li
2021 Applied Sciences  
Numerical validations are carried, out and the results are compared with the experiments and simulation results in the literature.  ...  A fast summation method is introduced to accelerate the evolution of particleparticle-induced velocity and its derivative as well as panel–particle interactions.  ...  Data Availability Statement: The data can be obtained upon request from the corresponding author. Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/app11073149 fatcat:qdinuexvsjcapnadosy53lhm64

A parallel implementation of a new fast algorithm for N-body simulations [article]

P. Londrillo, C. Nipoti, L. Ciotti
2002 arXiv   pre-print
In addition, both the Faber-Jackson and Kormendy relations are not reproduced by our simulations.  ...  The code has been applied to intensive numerical investigations of galaxy mergers, in particular focusing on the possible origin of some of the observed scaling relations of elliptical galaxies.  ...  Computations have been performed at the CINECA center (Bologna) under the INAF financial support. L.C. was supported by MURST CoFin2000.  ... 
arXiv:astro-ph/0212130v1 fatcat:kurj22b24far3ct2yue3er6jca

MOLECULAR DYNAMICS SIMULATIONS OF BIOMOLECULES: Long-Range Electrostatic Effects

Celeste Sagui, Thomas A. Darden
1999 Annual Review of Biophysics and Biomolecular Structure  
In particular, we discuss the Ewald summation methods, the fast particle mesh methods, and the fast multipole methods.  ...  In this article, we introduce the basic issues for an accurate representation of the relevant electrostatic interactions.  ...  The FMM allows a larger number of particles in the leaf cells, to optimize efficiency.  ... 
doi:10.1146/annurev.biophys.28.1.155 pmid:10410799 fatcat:awktlf4xczdozirdufmw5jw3om
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