An Integrated Parallelizable Algorithm for Computer Motion Simulation of Large-Sized Bio-Molecular Structures

2017 ◽  
Author(s):  
Shanzhong (Shawn) Duan
Keyword(s):  
Fast Multipole Method ◽  
Equations Of Motion ◽  
Molecular Structures ◽  
Motion Simulation ◽  
Fast Multipole ◽  
Molecular Method ◽  
Simulation Procedure ◽  
Solution Of Equations ◽  
Multipole Method ◽  
Solving Equations

In this paper, an integrated parallelizable algorithm is presented for computer simulation of dynamics of multibody molecular structures in polymers and biopolymers. The algorithm is developed according to an integrated O(N) simulation procedure developed by the author for calculating interatomic forces and forming/solving equations of motion for large-sized bio-molecular structures. Specifically, the simulation procedure is created via a proper integration between a parallelizable multibody molecular simulation method (PMMM) produced by the author and a parallelizable fast multipole method (PFMM). PFMM is utilized for calculation of atomic forces such as Van der Waals and Coulomb attractions between the atomics in the molecular structures. The parallelizable multibody molecular method is used for forming/solving equations of motion of large-sized molecular structures in polymers and biopolymers. Currently, the calculation of interatomic forces and formation/solution of equations of motion are treated separately by various procedures. For instance, Fast Multipole Method (FMM) and Cell Multipole Method (CMM) are applied for calculating interatomic forces only. Cartesian Coordinate Method (CCM) and Internal Coordinate Molecular Dynamics Method (ICMM) have been introduced independently for forming/solving equations of motion. Though formation and solution of equations of motions, and atomic force calculations are needed for same molecular structure, there is no direct conversation between two group methods. The proposed algorithm integrates multibody molecular method with fast multipole method in a parallel fashion so that both calculating atomic forces and forming/solving equations of motion can be carried out concurrently in a combined procedure. Computational loads associated with these two simulation tasks then can be divided among sub-chains, and each sub-chain is allocated to a processor on a parallel computing system via a proper integration between PFMM and PMMM. The algorithm can be used on both shared-memory and distributed-memory parallel computational systems. Compared with its counterpart of the integrated O(N) procedure developed by the author before, this algorithm has a computational complexity of O(logN) theoretically (N is number of subsets). The algorithm may find its applications for force calculation and motion simulation associated with large-sized molecular structures of polymers and biopolymers.

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.

Implementation of an Integrated Sequential Procedure for Computer Simulation of Dynamics of Multibody Molecular Structures in Polymers and Biopolymers

2019 ◽  
Author(s):  
Akara Hay ◽  
Shanzhong (Shawn) Duan
Keyword(s):  
Molecular Structure ◽  
Computer Simulation ◽  
Computational Efficiency ◽  
Fast Multipole Method ◽  
Equations Of Motion ◽  
Chain Structure ◽  
Molecular Structures ◽  
Molecular Chain ◽  
Fast Multipole ◽  
Multipole Method

Abstract This paper presents the implementation results of an integrated sequential algorithm, which the second author developed mathematically in a pseudo code format previously to improve computational efficiency of computer simulation of the dynamical behaviors of multibody molecular structures in polymers and biopolymers. This new algorithm is a seamless integration between multibody molecular algorithm (MMA: a multibody-dynamics-based procedure for motion simulation of molecular structure) and fast multipole method (FMM). The fast multipole method is used to calculate interatomic forces from potentials, and the multibody molecular algorithm is used to generate equations of motion associated with molecular structures. The algorithm improves computational efficiency when comparing with its counterpart procedures. A study case of an opened-chain molecular structure was used to demonstrate the algorithm works and to study improvement of computing efficiency of the algorithm. The algorithm is coded in MATLAB and run on both laptop and workstations computers with various numbers of molecules along the chain. FMM started with scaling all atoms into a box with coordinate ranges to ensure numerical stability of subsequent operations. The flow of calculations in FMM was carried out along the chain structure with five computational passes. MMA began with numbering subsets, forming bond graph, and developing three computing passes along the chain structure. Flows of both calculations and data in FMM and MMA were lined up recursively along the chain structure to obtain an O(N)1 computational efficiency. Simulation results were compared with results produced by MMA and traditional methods of FMM for interatomic force calculation procedure. Implementation presented in this paper first proves that the integration between FMM and MMA works and the integrated algorithm improves computing efficiency associated with both calculation of interatomic forces from potentials and formation/solution of equations of motion. Implementation results also indicates that the integrated algorithm works more efficiently for a large-sized molecular chain than a small-sized molecular chain. Further work is needed to optimize the related FMM codes.

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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