Advances in Astronomy

Volume 2016, Article ID 9049828, 5 pages

http://dx.doi.org/10.1155/2016/9049828

## Adjacent Zero Communication Parallel Cloud Computing Method and Its System for -Body Problem with Short-Range Interaction Domain Decomposition

School of Computer Science, South China Normal University, Guangzhou 510631, China

Received 30 January 2016; Accepted 3 March 2016

Academic Editor: Juan L. G. Guirao

Copyright © 2016 Dingju Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Although parallel computing is used in the existing numerical solutions of -body problem, tons of communications between particles render the parallel efficiency extremely low. Despite the fact that domain decomposition based on short-range interaction is used, when is exceedingly large and lots of communications exist between particles in adjacent areas, the parallel efficiency remains terribly low. This paper puts forward adjacent zero communication parallel cloud computing method for -body problem with short-range interaction domain decomposition. According to this method, the adjacent subblock data are exchanged and redundantly stored without acquiring data from other subblocks in the parallel processing, so the waiting time for data transmission can be saved and hence the parallel processing efficiency can be enhanced substantially.

#### 1. Introduction

-body problem [1] means particles between which there is universal gravitation are given in three-dimensional space and solving the space time state of motion of these particles under the conditions of given initial position and velocity. If the planets in the universe are regarded as particles, then we can consider the motion of the planets under the universal gravitation to be an -body problem. When , it is greatly difficult or even unable to adopt analytical method (its basic principle is to present the coordinate and velocity of the celestial bodies as approximate analytical expressions in the form of series in time or other small parameters in order to discuss the changes in the celestial bodies’ coordinate or orbit along with time) or qualitative method (using the qualitative theories of differential equation to study the macrolaws and global nature of -body in the long term) to obtain solutions. The most feasible method is to adopt numerical method [2] (directly obtaining the specific position and time of the celestial bodies at a certain time via the computing methods of differential equation [3]). In the -body problem [4], the velocity and position of particles under the universal gravitation need to be recalculated at a certain time step. Therefore, the calculation of the updated velocity and displacement of each particle at each time step needs to add other particles’ interaction results on this particle, but this causes the calculation amount complexity of each time step to be . The larger the time step is, the greater the error is; the smaller the time step is, the closer it is to the reality. When is very large and the time step (TS) is very small, serial computing cannot work, since the serial computing always cannot complete the calculation whose complexity is within TS. As a result, when is very large and TS is very small, parallel computing must be used to accelerate the numerical solutions of -body problem [5, 6].

In the traditional parallel computing [7–9] and cloud computing [10, 11], large numbers of adjacent data blocks in complex network [12] of -body need to be exchanged, so inaccessibility of the needed data in the communications of adjacent data blocks will result in the waiting of parallel process and lower the efficiency of parallel processing. In case of using parallel computing to solve the -body problem, the calculation of the updated velocity and displacement of each particle at each time step needs to add other particles’ interaction results on this particle, so each particle needs to communicate with the remaining particles in each TS. Therefore, times of communications need to be carried out in each TS. Such frequent and large numbers of communications will greatly lower the efficiency of parallel computing, thereby depriving the advantages of parallel computing. That is why we need to find a method to reduce the amount of communication. Hence, we need to simplify the -body problem as the -body problem under the short-range interaction. Such simplification is effective, since the applied force between distant particles is weak, the long-distant effect can be neglected, and only the short-range effect is considered. Therefore, each particle only needs to communicate with the short-range particles without communicating with other particles, which significantly cuts the communication traffic. Domain decomposition is to divide the physical domain into subdomains of the same number as the processors. In each TS, each processor calculates the force, velocity, and displacement of all particles within its domain, and when the particle moves to a new subdomain, it will be distributed to a new processor. In order to calculate the force of particles within its domain, the processor only needs to know the information about the particles of the adjacent subdomains. Domain decomposition parallel algorithm is highly suitable to solve this -body problem of short-range interaction, because it leads only the adjacent domains to need mutual communication to acquire the interaction between the particles in adjacent domains.

If the quantity of the particles in each domain is still very considerable, then even if only the communications in adjacent domains are needed, the communication traffic remains heavy and still greatly affects the parallel efficiency. Therefore, this paper proposes adjacent zero communication parallel cloud computing method for adjacent data which can almost completely eliminate all communications in solving the -body problem with short-range interaction domain decomposition.

#### 2. Adjacent Zero Communication Parallel Cloud Computing Method

The flowchart of the adjacent zero communication parallel cloud computing method is presented in Figure 1. This adjacent zero communication parallel cloud computing method includes the following steps.