分布式巨正则Monte Carlo模拟算法的研究与实现
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摘要
本项科研工作的目的是实现一个可用于模拟纳米尺度孔或缝中受限Lennard-Jones 流体密度分布的巨正则Monte Carlo 系统,并使这个系统有较高的收敛速度。
Monte Carlo 模拟在数学、物理和工程技术领域有着广泛的应用,具有算法简单,灵活性强等特点。但该方法受到了收敛速度的限制,同时若想增加一位精度,需要增加近100 倍的计算量。为了提高巨正则Monte Carlo 模拟的效率和速度,本文在现有的单机版的巨正则Monte Carlo 模拟系统的基础上提出了一种分布式的巨正则Monte Carlo 算法,并进行了实现。整个分布式系统呈献给使用者的是一个与单机版的巨正则Monte Carlo 系统完全一致的界面,参与计算的局域网内的其它客户机对分布式巨正则Monte Carlo 模拟系统的使用者透明。该算法使用RMI、Applet、Servlet、JSP 等技术协同局域网内多台自治的计算同时进行模拟计算,并且通过系统动态调整不同客户机上的任务量,实现客户机的负载平衡。通过动态检测非发起计算的客户机在模拟过程中的状态,可以将失效节点上的任务自动迁移到其它的节点,从而保证了个别节点失效时,模拟的正常进行。
本文使用加权和算法处理各个客户端返回的模拟结果,保证迭代次数多的客户机的结果保持高的优先级。提高了结果处理的合理性。
本文也比较了使用不同数目客户端时的模拟的收敛速度,并且通过优化各客户端和服务器的通信频率,取得了较高的加速比。
使用本文实现的巨正则Monte Carlo 系统,模拟了纳米尺度孔和缝中受限Lennard-Jones 流体的密度分布,并与使用密度泛函理论(DFT)和使用单机版的Monte Carlo 模拟得出的结果进行了相互比较,其中DFT 结果与分布式Monte Carlo 结果基本吻合,单机版Monte Carlo 方法的结果与分布式巨正则Monte Carlo 结果完全一致,比较结果很好的印证了本文提出的算法的正确性。
由于本文实现的分布式巨正则Monte Carlo 系统需要模拟具有不同墙势的纳米尺度孔和缝中的密度分布,通过利用Spring 的动态依赖注射技术把系统对墙势的依赖关系的确定推迟到运行期,使系统可以动态的更换所需的墙势,从而提高了系统的可重用性。
In this paper, our works is of development to the Monte Carlo program, which can simulate the density distribution of Lennard-Jones fluids, confined in square nanoscale channels with Lennard-Jones walls, and decrease the time of convergence.
The Monte Carlo simulation is ubiquitous in the fields of mathematics, physics and engineering and technologies. Monte Carlo algorithm has the merits of simple, flexible and etc, but this algorithm is restricted by speed of convergence. In order to improve bit accuracy, the one hundred-time simulation iteration will be increased. We studied and implement a distributed algorithm to quicken Grand Canonical Monte Carlo (GCMC) simulation convergence and improve the efficiency of simulation. The whole distributed simulation system represents a single user interface as same as the serial Monte Carlo simulation program, and the other nodes in the LAN are of transparence for system user. The implementation of algorithm employed the technologies of RMI, Applet, Servlet and JSP technologies. This algorithm harmonizes the autonomic computers in the LAN to run simulation program in parallel and readjust the loading balance dynamically to wipe off the bottle-neck of speed. By the detecting the status of nodes during the simulation, the program can find the halted nodes and move it’s task to the running nodes.
In this paper, we sum up the results from the different clients with the weight to increase the influence of client running more iteration.
In the chap 4, we measured the acceleration with different number of client, and
the result is satisfied. Density distribution of Lennard-Jones fluids confined in square nanoscale channels with Lennard-Jones walls was simulated with our program, and the results were compared with results of DFT and no parallel Monte Carlo simulation, that prove the correctness of algorithm. In order to simulate the density distribution of Lennard-Jones fluids confined different Lennard-Jones walls, we employed dependence injection (DI) of Spring to postpone the dependence relation of system on wall to runtime, so the simulation system can exchange the wall dynamically, and support variable wall potential to improve the reuse of this program. On the basise of researching on the distributed system architecture, we combine the technologies of J2EE specifications to design and code the distributed GCMC system which holds on the high accuracy. The algorithm overcomes the shortcoming of old GCMC simulation algorithm, and shows a new way to improve the convergence speed of simulation.
Monte Carlo 模拟在数学、物理和工程技术领域有着广泛的应用,具有算法简单,灵活性强等特点。但该方法受到了收敛速度的限制,同时若想增加一位精度,需要增加近100 倍的计算量。为了提高巨正则Monte Carlo 模拟的效率和速度,本文在现有的单机版的巨正则Monte Carlo 模拟系统的基础上提出了一种分布式的巨正则Monte Carlo 算法,并进行了实现。整个分布式系统呈献给使用者的是一个与单机版的巨正则Monte Carlo 系统完全一致的界面,参与计算的局域网内的其它客户机对分布式巨正则Monte Carlo 模拟系统的使用者透明。该算法使用RMI、Applet、Servlet、JSP 等技术协同局域网内多台自治的计算同时进行模拟计算,并且通过系统动态调整不同客户机上的任务量,实现客户机的负载平衡。通过动态检测非发起计算的客户机在模拟过程中的状态,可以将失效节点上的任务自动迁移到其它的节点,从而保证了个别节点失效时,模拟的正常进行。
本文使用加权和算法处理各个客户端返回的模拟结果,保证迭代次数多的客户机的结果保持高的优先级。提高了结果处理的合理性。
本文也比较了使用不同数目客户端时的模拟的收敛速度,并且通过优化各客户端和服务器的通信频率,取得了较高的加速比。
使用本文实现的巨正则Monte Carlo 系统,模拟了纳米尺度孔和缝中受限Lennard-Jones 流体的密度分布,并与使用密度泛函理论(DFT)和使用单机版的Monte Carlo 模拟得出的结果进行了相互比较,其中DFT 结果与分布式Monte Carlo 结果基本吻合,单机版Monte Carlo 方法的结果与分布式巨正则Monte Carlo 结果完全一致,比较结果很好的印证了本文提出的算法的正确性。
由于本文实现的分布式巨正则Monte Carlo 系统需要模拟具有不同墙势的纳米尺度孔和缝中的密度分布,通过利用Spring 的动态依赖注射技术把系统对墙势的依赖关系的确定推迟到运行期,使系统可以动态的更换所需的墙势,从而提高了系统的可重用性。
In this paper, our works is of development to the Monte Carlo program, which can simulate the density distribution of Lennard-Jones fluids, confined in square nanoscale channels with Lennard-Jones walls, and decrease the time of convergence.
The Monte Carlo simulation is ubiquitous in the fields of mathematics, physics and engineering and technologies. Monte Carlo algorithm has the merits of simple, flexible and etc, but this algorithm is restricted by speed of convergence. In order to improve bit accuracy, the one hundred-time simulation iteration will be increased. We studied and implement a distributed algorithm to quicken Grand Canonical Monte Carlo (GCMC) simulation convergence and improve the efficiency of simulation. The whole distributed simulation system represents a single user interface as same as the serial Monte Carlo simulation program, and the other nodes in the LAN are of transparence for system user. The implementation of algorithm employed the technologies of RMI, Applet, Servlet and JSP technologies. This algorithm harmonizes the autonomic computers in the LAN to run simulation program in parallel and readjust the loading balance dynamically to wipe off the bottle-neck of speed. By the detecting the status of nodes during the simulation, the program can find the halted nodes and move it’s task to the running nodes.
In this paper, we sum up the results from the different clients with the weight to increase the influence of client running more iteration.
In the chap 4, we measured the acceleration with different number of client, and
the result is satisfied. Density distribution of Lennard-Jones fluids confined in square nanoscale channels with Lennard-Jones walls was simulated with our program, and the results were compared with results of DFT and no parallel Monte Carlo simulation, that prove the correctness of algorithm. In order to simulate the density distribution of Lennard-Jones fluids confined different Lennard-Jones walls, we employed dependence injection (DI) of Spring to postpone the dependence relation of system on wall to runtime, so the simulation system can exchange the wall dynamically, and support variable wall potential to improve the reuse of this program. On the basise of researching on the distributed system architecture, we combine the technologies of J2EE specifications to design and code the distributed GCMC system which holds on the high accuracy. The algorithm overcomes the shortcoming of old GCMC simulation algorithm, and shows a new way to improve the convergence speed of simulation.
引文
[1] 张桂芹. 蒙特卡罗法在工程项目经济评价中的应用. 北京动力经济学院学报[J]. 1994, (1) :71～77.
[2] 徐钟济. 蒙特卡罗方法[M].上海:上海科学技术出版社,1985.
[3] 李建保. 蒙特卡罗方法[EB/OL]. http://www.database.cpst.net.cn, 2002,08,06.
[4] Frenkel,Smit. Understanding Molecular Simulation ——Form Algorithms to Application[M].汪文川. 北京:化学工业出版社,2002.
[5] S.Tanenaum Andrew, Van Steen Marten. Distributed Systems Principles and Paradigms[M]. New Jersey: Prentice Hall, 2002.
[6] Emmerich Wolfgang. Engineering Distributed Objects[M]. Wiley & Sons, 2000.
[7] 宁葵,严毅. 分布式计算技术发展研究.微机发展[J]. 2004, 14(8) :14～16.
[2] 徐钟济. 蒙特卡罗方法[M].上海:上海科学技术出版社,1985.
[3] 李建保. 蒙特卡罗方法[EB/OL]. http://www.database.cpst.net.cn, 2002,08,06.
[4] Frenkel,Smit. Understanding Molecular Simulation ——Form Algorithms to Application[M].汪文川. 北京:化学工业出版社,2002.
[5] S.Tanenaum Andrew, Van Steen Marten. Distributed Systems Principles and Paradigms[M]. New Jersey: Prentice Hall, 2002.
[6] Emmerich Wolfgang. Engineering Distributed Objects[M]. Wiley & Sons, 2000.
[7] 宁葵,严毅. 分布式计算技术发展研究.微机发展[J]. 2004, 14(8) :14～16.