Extension of the fast multipole method for the rectangular cells with an anisotropic partition tree structure

2020 ◽  
Vol 41 (14) ◽  
pp. 1353-1367 ◽  
Author(s):  
Yoshimichi Andoh ◽  
Noriyuki Yoshii ◽  
Susumu Okazaki
Keyword(s):  
Fast Multipole Method ◽  
Tree Structure ◽  
Partition Tree ◽  
Fast Multipole ◽  
Multipole Method

An Integrated Procedure for Computer Simulation of Dynamics of Multibody Molecular Structures in Polymers and Biopolymers

2015 ◽  
Author(s):  
Shanzhong (Shawn) Duan
Keyword(s):  
Computer Simulation ◽  
Molecular System ◽  
Fast Multipole Method ◽  
Equations Of Motion ◽  
Molecular Structures ◽  
Tree Structure ◽  
Fast Multipole ◽  
Computational Costs ◽  
Multipole Method ◽  
Multipole Methods

Though computational molecular dynamics is an effective tool for nano-scale phenomenon analysis, computational costs associated with its computer simulation are extremely high. There are two major computational steps associated with computer simulation of dynamics of molecular structures. They are calculation of interatomic forces and formation and solution of the equations of motion. Currently, these two computational steps are treated separately in most commonly-used methods. For example, Fast Multipole Method (FMM) and Cell Multipole Method (CMM) have been used for calculation of interatomic forces, and Cartesian Coordinate Method (CCM) and Internal Coordinate Molecular Dynamics Method (ICMD) have been created for the formation and solution of equations of motion of an atomistic molecular system. In this paper, a new procedure is presented through a proper integration between multibody molecular algorithms (MMA) and fast multipole methods to improve computational efficiency for computer simulation of the dynamical behaviors of multibody molecular structures in polymers and biopolymers. For the computational costs associated with interatomic forces, a fast multipole method is used to calculate the interatomic forces due to the potentials. For the computational costs associated with formation and solution of equations of motion, a multibody molecular algorithm developed by the author in his previous work will be utilized to integrate with fast multipole methods. The algorithm significantly improves computational efficiency when comparing with its counterpart procedures. The fast multipole method begins by scaling all atoms into a box with coordinate ranges to ensure numerical stability of subsequent operations. The parent box is then divided into half in the direction of each Cartesian axis and each child box is then subdivided to form a computational family tree. The flow of calculations is carried out along the tree structure with five passes. The fast multipole method has been improved and modified to achieve better effectiveness and higher efficiency since it was created. The multibody molecular algorithm starts with numbering subsets, forming bond graph, and developing three computing passes along the tree structure of an atomistic molecular system. Computing data flows in the fast multipole method and the multibody molecular algorithm will properly line up with the parent-child recursive relationship along the configuration of the tree structure due to linear recursive natures of both fast multipole method and multibody molecular algorithm. Then the time spent on the recursive simulation passes in the fast multipole method for computing forces may overlap with the time spent on the three recursive computational passes in the multibody molecular algorithm for forming and solving equations of motion.

A Fourier-series-based kernel-independent fast multipole method

2011 ◽  
Vol 230 (15) ◽  
pp. 5807-5821 ◽  
Author(s):  
Bo Zhang ◽  
Jingfang Huang ◽  
Nikos P. Pitsianis ◽  
Xiaobai Sun
Keyword(s):  
Fourier Series ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Multipole Method

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

1992 ◽  
Vol 278 ◽  
Author(s):  
Steven R. Lustig ◽  
J.J. Cristy ◽  
D.A. Pensak
Keyword(s):  
Canonical Ensemble ◽  
Yukawa Potential ◽  
Direct Method ◽  
Fast Multipole Method ◽  
Parallel Computers ◽  
Massively Parallel ◽  
Fast Multipole ◽  
Massively Parallel Computers ◽  
Multipole Method ◽  
Execution Times

AbstractThe fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale asO(N2). The FMM execution times scale asO(N) on sequential workstations and vector processors and asymptotically0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

A new version of the Fast Multipole Method for the Laplace equation in three dimensions

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 229-269 ◽  
Author(s):  
Leslie Greengard ◽  
Vladimir Rokhlin
Keyword(s):  
Laplace Equation ◽  
Fast Multipole Method ◽  
High Accuracy ◽  
Three Dimensions ◽  
Potential Fields ◽  
Diagonal Form ◽  
Fast Multipole ◽  
Reasonable Cost ◽  
Multipole Method ◽  
Translation Operators

We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.

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