并行算法在激光化学反应模拟中的应用研究
|
摘要
随着超短激光脉冲技术的不断发展，激光化学反应的研究已经深入到核运动的微观世界。许多化学反应实验采用常规方法无法实现，但在超快激光脉冲的照射下能够实现。激光化学反应模拟是利用计算机手段模拟分子在不同激光照射下发生的化学反应现象，计算机模拟能够得到激光化学反应全过程，研究瞬间反应的具体细节，为实际化学反应提供理论指导。目前应用最为广泛的激光化学反应模拟方法是半经典分子动力学方法，由于当模拟规模增加时，其计算量迅速增大，因此，研究高效率并行算法并应用于半经典动力学模拟具有重要意义。
本文全面系统地研究激光化学反应模拟并行算法，在此基础上设计了一系列并行算法。
本文的主要内容及创新点如下：
1．本文基于半经典分子动力学模型实现激光化学反应模拟。该模型由Fortran语言实现，并在大型计算机上构建模拟平台。该平台基于半经典的计算机模拟激光化学反应模型，能够真实反映化学反应的实际过程。通过实际的激光化学反应的模拟测试，实验结果证明该平台能够有效研究激光脉冲性质对化学反应的影响，为研究激光化学反应提供了科学可靠方法。
2．本文提出了半经典分子动力学特殊矩阵计算的优化方法和并行计算方法。通过对半经典分子动力学模拟计算的串行算法进行了测试分析，寻求耗时最大的程序模块，即大型特殊矩阵乘法计算。基于计算矩阵特征对特殊矩阵乘法进行优化，大幅降低该模块计算时间。采用Wingrad算法降低矩阵计算时间复杂度，并基于OpenMP实现矩阵乘的Winograd并行算法，有效提高计算效率。
3．本文提出了一种半经典分子动力学混合并行算法。在半经典分子动力学模拟中引入混合并行技术和双层并行算法设计。基于MPI+OpenMP混合模型和激光化学反应计算特征，设计并实现激光化学反应模拟双层并行算法，上层并行采用动态原子分割算法，下层并行采用力矩阵并行分解算法。该算法在多核集群中能够有效提高半经典分子动力学并行计算效率。
4．基于反馈机制设计动态负载均衡算法，该算法通过负载信息反馈动态调整任务分配，并将该算法应用与半经典分子动力学模拟中，在变化负载系统中，该算法具有较好的适应性。为了进一步适应复杂的频繁变化的负载系统，设计了可变周期反馈的负载均衡算法，根据实时负载调整反馈周期，从而增强算法的可适应性，负载变化较多时能缩短反馈周期，负载稳定时能延长周期，从而提高系统并行效率。针对半经典分子动力学模拟计算特征，设计了周期时间预测算法和优化原子分配方案，在多核集群中测试，采用随机运行的干扰程序动态改变系统负载，在负载动态变化环境中，该负载均衡算法具有优越的自适应性和可扩展性，能够有效提高系统整体性能。
The development of ultrashort laser pulse allows us to study photochemicalreactions at atomic level. Many chemical reactions that can not be realized bytraditional techniques become possible due to ultrashort laser technology. The mostpopular technique for studying laser induced chemical reactions is Pump-Probespectroscopy. Computer simulation of photochemical reactions is a complementaryapproch to the investigations of the photochemical reactions. Following aphotochemical reaction using computer simulation, researchers can view the chemicalreaction from reactants to products and gain the information about reactionmechanisms.
1.A model for realistic parallel simulations of photochemical reactions induced byan ultrashort laser pulses is developed and realized by Fortran90language. Theinterreaction between laser pulses and molecules is unambiguously included in themodel. The technique allows researchers to investigate the influence of the properties oflaser pulses on the outcome of chemical reactions and therefore is a realistic approach tothe study of laser control of chemical reactions. The efficiency of the program isimproved by parallel design, It provides a practical technique for performingphotochemical reactions starting from laser excitation high efficiently. In addition, itprovides many details that could not be observed experimentally.
2.An optical algorithm of special matrix multiplication is suggested in semiclassicalmolecular dynamics simulations. Based on the analysis of the serial program, the matrixmultiplication cost most time of the force calculation in semiclassical moleculardynamics simulations. The computation of these gradient matrices and theirmultiplication plays a key role in the Ehrenfest force calculation. Simplifying and thenparallelizing the computation of these nuclear gradients and the matrix multiplicationsnumerically eventually enhance the capacity of Ehrenfest MD simulation.
3.A high performance hybrid parallel algorithm for simulating photochemicalreaction is developed by introducing the concept of two layers of parallel capacity. MPIis used in conjunction with OpenMP multithreading to achieve two level parallism of the data and tasks. It is realized based on SMP cluster. It is proved that this method is afeasible parallel algorithm for simulating the photochemical reactions high-efficiently.
4.To improve the parallel efficiency on unbalancing system, A dynamic loadbalancing algorithm is designed based on the feedback model. All Tasks areredistributed by load feedback and processing ability forecast. This algorithm adoptedthe dynamic variation of the load. In this study, the algorithm is applied andimplemented in the force calculation of semiclassical molecular dynamic simulations,an optical atomic decomposition is also implemented. Compare with the static loadbalance algorithm, this dynamic load balance algorithm shows better adaptability andscalability.
本文全面系统地研究激光化学反应模拟并行算法，在此基础上设计了一系列并行算法。
本文的主要内容及创新点如下：
1．本文基于半经典分子动力学模型实现激光化学反应模拟。该模型由Fortran语言实现，并在大型计算机上构建模拟平台。该平台基于半经典的计算机模拟激光化学反应模型，能够真实反映化学反应的实际过程。通过实际的激光化学反应的模拟测试，实验结果证明该平台能够有效研究激光脉冲性质对化学反应的影响，为研究激光化学反应提供了科学可靠方法。
2．本文提出了半经典分子动力学特殊矩阵计算的优化方法和并行计算方法。通过对半经典分子动力学模拟计算的串行算法进行了测试分析，寻求耗时最大的程序模块，即大型特殊矩阵乘法计算。基于计算矩阵特征对特殊矩阵乘法进行优化，大幅降低该模块计算时间。采用Wingrad算法降低矩阵计算时间复杂度，并基于OpenMP实现矩阵乘的Winograd并行算法，有效提高计算效率。
3．本文提出了一种半经典分子动力学混合并行算法。在半经典分子动力学模拟中引入混合并行技术和双层并行算法设计。基于MPI+OpenMP混合模型和激光化学反应计算特征，设计并实现激光化学反应模拟双层并行算法，上层并行采用动态原子分割算法，下层并行采用力矩阵并行分解算法。该算法在多核集群中能够有效提高半经典分子动力学并行计算效率。
4．基于反馈机制设计动态负载均衡算法，该算法通过负载信息反馈动态调整任务分配，并将该算法应用与半经典分子动力学模拟中，在变化负载系统中，该算法具有较好的适应性。为了进一步适应复杂的频繁变化的负载系统，设计了可变周期反馈的负载均衡算法，根据实时负载调整反馈周期，从而增强算法的可适应性，负载变化较多时能缩短反馈周期，负载稳定时能延长周期，从而提高系统并行效率。针对半经典分子动力学模拟计算特征，设计了周期时间预测算法和优化原子分配方案，在多核集群中测试，采用随机运行的干扰程序动态改变系统负载，在负载动态变化环境中，该负载均衡算法具有优越的自适应性和可扩展性，能够有效提高系统整体性能。
The development of ultrashort laser pulse allows us to study photochemicalreactions at atomic level. Many chemical reactions that can not be realized bytraditional techniques become possible due to ultrashort laser technology. The mostpopular technique for studying laser induced chemical reactions is Pump-Probespectroscopy. Computer simulation of photochemical reactions is a complementaryapproch to the investigations of the photochemical reactions. Following aphotochemical reaction using computer simulation, researchers can view the chemicalreaction from reactants to products and gain the information about reactionmechanisms.
1.A model for realistic parallel simulations of photochemical reactions induced byan ultrashort laser pulses is developed and realized by Fortran90language. Theinterreaction between laser pulses and molecules is unambiguously included in themodel. The technique allows researchers to investigate the influence of the properties oflaser pulses on the outcome of chemical reactions and therefore is a realistic approach tothe study of laser control of chemical reactions. The efficiency of the program isimproved by parallel design, It provides a practical technique for performingphotochemical reactions starting from laser excitation high efficiently. In addition, itprovides many details that could not be observed experimentally.
2.An optical algorithm of special matrix multiplication is suggested in semiclassicalmolecular dynamics simulations. Based on the analysis of the serial program, the matrixmultiplication cost most time of the force calculation in semiclassical moleculardynamics simulations. The computation of these gradient matrices and theirmultiplication plays a key role in the Ehrenfest force calculation. Simplifying and thenparallelizing the computation of these nuclear gradients and the matrix multiplicationsnumerically eventually enhance the capacity of Ehrenfest MD simulation.
3.A high performance hybrid parallel algorithm for simulating photochemicalreaction is developed by introducing the concept of two layers of parallel capacity. MPIis used in conjunction with OpenMP multithreading to achieve two level parallism of the data and tasks. It is realized based on SMP cluster. It is proved that this method is afeasible parallel algorithm for simulating the photochemical reactions high-efficiently.
4.To improve the parallel efficiency on unbalancing system, A dynamic loadbalancing algorithm is designed based on the feedback model. All Tasks areredistributed by load feedback and processing ability forecast. This algorithm adoptedthe dynamic variation of the load. In this study, the algorithm is applied andimplemented in the force calculation of semiclassical molecular dynamic simulations,an optical atomic decomposition is also implemented. Compare with the static loadbalance algorithm, this dynamic load balance algorithm shows better adaptability andscalability.
引文
[1] A. H. Zewail. Femtochemistry: Ultrafast Dynamics of the Chemical Bond. Singapore:WorldScientific,1998,21-25
[2] D. J. Tannor, R. Kosloff, S. A. Rice. Coherent pulse sequence induced control of selectivity ofreactions: exact quantum mechanical calculations. J Chem Phys,1986,85(10):5805-5820
[3] A. Assion, T. Baumert, M. Bergt, et al. Control of Chemical Reactions by Feedback-OptimizedPhase-Shaped Femtosecond Laser Pulses. Science,1998,282:919-922
[4] A. H. Zewail. Femtochemistry: Chemical Reaction Dynamics and Their Control. Adv ChemPhys,1997,101:3-5
[5] W. Zhu, J. Botina, H. Rabitz. Rapidly convergent iteration methods for quantum optimalcontrol of population. J Chem Phys,1998,108:1953-1963
[6] W. Zhu, H. Rabitz. Potential surfaces from the inversion of time dependent probability densitydata. J Chem Phys,1999,111:472-480
[7] H. Rabitz, R. Vivie-Riedle, M. Motzkus, et al. Whither the Future of Controlling QuantumPhenomena. Science,2000,288:824-828
[8] W. Yin, X Gao, X Zhu, et al. An Efficient Shared Memory Based Virtual CommunicationSystem for Embedded SMP Cluster. Proceedings of the2011IEEE Sixth InternationalConference on Networking, Architecture, and Storage(NAS '11),288-294
[9] B. Sahoo, R Sourav, R. Ranjan, et al. Parallel Implementation of Exact Algorithm for PlantedMotif Search Problem using SMP Cluster. European Journal of Scientific Research,2011,64:484-496
[10] M. Ben-Nun, T. J. Martínez. Ab initio quantum molecular dynamics. Adv Chem Phys,2002,124:439-512
[11] F. Bernardi, M. Olivucci, M. A. Robb. Simulation of MC-SCF results on covalent organicmulti-bond reactions: molecular mechanics with valence bond (MM-VB). J Am Chem Soc,1992,114:1606-1616
[12] M. J. Bearpark, F. Bernardi, M. Olivucci, et al. Molecular mechanics valence bond methods forlarge active spaces-Application to conjugated polycyclic hydrocarbons. Chem Phys Lett,1994,217:513-519
[13]李鸿健,豆育升,唐红,等.激光诱导化学反应的并行计算机模拟.中国激光,2009,36(2):356-361
[14] H. Li, H. Tang, Y. Dou. Laser-induced nonthermal fragmentation of C60studied bysemiclassical dynamics simulation. Moleculer Physics,2009,107(19):2039-2044
[15] S. Yuan, W. Zhang, L. Liu, et al. Detailed Mechanism for Photoinduced Cytosine Dimerization:A Semiclassical Dynamics Simulation. J. Phys. Chem. A,2011,115:13291
[16] H. Tang, H. Li，Y Dou. Laser Induced C60Cage Opening Studied by Semiclassical DynamicsSimulation. Int. J. Mol. Sci.,2011,12,353-361
[17] D. Porezag, T. Frauenheim, H. Kohler, et al. Construction of tight-binding-like potentials on thebasis of density functional theory: Apllication to carbon. Phys Rev B,1995,51:12947
[18] M. Bisson, M. Bernaschi, S. Melchionna. Parallel Molecular Dynamics with Irregular DomainDecomposition. Commun. Comput. Phys.,2011,10:1071-1088
[19]刘正华,杨决宽,陈云飞.分子动力学并行算法的优化与应用.计算机应用研究,2008,25(3):718-720
[20] J. Kevin, O. Bowers, C. Efmond, et al. Scalable Algorithms for Molecular DynamicsSimulations on Commodity Clusters. Proceedings of the2006International Conference onParallel Processing(ICPP'06),84-96
[21] P. Thompson, S. J. Plimpton, W. Mattson, et al. General formulation of pressure and stresstensor for arbitrary many-body interaction potentials under periodic boundary conditions. JChem Phys,2009,131(1),154107
[22] J. V. Sumanth, R. S. David, J. Hong. Adaptive Load Balancing for Long-Range MDSimulations in A Distributed Environment. Proceedings of the2006International Conferenceon Parallel Processing(ICPP'06),135-146
[23] J. V. Sumanth, R. S. David, J. Hong. Adaptive Load-Balancing for Force-Decomposition Based3-Body Molecular Dynamics Simulations in a Heterogeneous Distributed Environment withVariable Number of Processors. The2007International Conference on Parallel Processing(ICPP '07),552-565
[24] X. Yang, Y. Dou, Q. Hu. Progress and challenges in high performance computer technology. JComput Sci Technol,2006,21(5):674-681
[25] M. Tripathy, C.R. Tripathy. A Distributed Shared Memory Cluster Architecture With DynamicLoad Balancing. Journal of Emerging Trends in Computing and Information Sciences,2012,3:231-240
[26]杨际祥,谭国真,王荣生.并行与分布式计算动态负载均衡策略综述.电子学报,2010,38(5):1122-1130
[27]王广芳,钟志伟,赵先武.分布式计算机系统(DCS)负载均衡算法.计算机工程与设计,1995,16(5):57-63
[28]陈国良.并行计算─结构算法编程.北京:高等教育出版社，2003,45-47
[29]杜晓梅,王广益,李利.最新TOP500超级计算机分析.中国教育网络,2010,8:11-14
[30]都志辉.高性能计算并行编程技术.北京:清华大学出版社,2001,56-67
[31]张林波,迟学斌,莫则尧.并行计算导论.北京:清华大学出版社,2006,158-162
[32] N. Lu, Z. T. Taylor, D. P. Chassin, et al. Parallel Computing Environments and Methods forPower Distribution System Simulation. Power Engineering Society General Meeting(PESGM2005),215-220
[33] G. D. Li, D. F. Zhang. A Distributed Object Based Framework for Paralle Computations.Journal of Software,2002,13(3):342-353
[34] C. C. Fung, S. Y. Chow, K. P. Wong. A Low-Cost Parallel Computing Platform for PowerEngineering Applications.5th International Conference on Advances in Power System Control,Operation and Management(APSCOM'2000),354-358
[35] G. Fadlallah, M. Lavoie, L. A. Dessaint. Parallel Computing Environments and Methods.Parallel Computing in Electrical Engineering(MPCEE'2000),2-7
[36]豆育升,唐红,李鸿健.光化学反应的计算机模拟方法研究.系统仿真学报,2009,21(3):894-899
[37] W. Zhou. Multi-core Computing and Programming.武汉:华中科技大学出版社,2009,88-96
[38] P. S. Pacheco. Parallel Programming with MPI. California:Morgan Kaufmann Publishers,1997,155-158
[39] M. D. Jones, R. Yao. Parallel programming for OSEM reconstruction with MPI, OpenMP, andhybrid MPI-OpenMP. Nuclear Science Symposium Conference Record,2004,5:3036-3042
[40] C. J. Duran, A. Labarta. Dynamic load balancing of MPI+OpenMP applications. ParallelProcessing (ICPP'04),195-202
[41] J. Bahi, R. Couturier, F. Vernier. Synchronous distributed load balancing on dynamic networks.Journal of Parallel and Distributed Computing,2005,65(11):1397-1405
[42] S. Jang, J. Yoo. An Efficient Load Balancing Mechanism in Distributed Virtual Environments.ETRI Journal,2008,30(4):618-620
[43] L. Ricolindo, C. Banicescu. Dynamic load balancing with adaptive factoring methods inscientific applicatons. The Journal of Supercomputing,2008,44(1):41-63
[44] P Berenbrink, T Friedetzky, R Martin. On the Stability of Dynamic Diffusion Load Balancing.Algorithmica,2008,50(3):329-350
[45] Y. B. Wang, R. Hyatt. An improved algorithm of two choices in randomized dynamicloadbalancing. Proceedings of the fifth International Conference on Algorithms andArchitectures for Parallel Processing(ICAAPP'2002),432-445
[46] F. Smit.分子模拟-从算法到应用(汪文川译).北京:化学工业出版社,2002,132-145
[47] A. R. Leach. Molecular Modeling Principles and Applications.北京:世界图书出版公司,2003,166-184
[48]陈正隆，徐为人，汤立达.分子模拟的理论与实践.北京:化学工业出版社,2007,56-59
[49]林梦海.量子化学简明教程.北京:化学工业出版社,2005,86-89
[50] R. E. Allen, T. Dumitrica, B. R. Torralva. Ultrafast Physical Processes in Semiconductors.Academic: New York,2001,188-198
[51] D. Porezag, T. Trauenheim, T. Kohler, et al. Construction of tight-binding-like potentials on thebasis of density-functional theory: Application to carbon. Phys Rev B,1995,51,12947-12957
[52] A. Sieck, D. Porezag, T. Frauenheim, et al. Structure and vibrational spectra of low-energysilicon clusters. Phys Rev A,1997,56:4890-4898
[53] T. Frauenheim, F. Weich, T. Kohler. Density-functional-based construction of transferablenonorthogonal tight-binding potentials for Si and SiH. Phys Rev B,1995,52:11492-11501
[54] G. Serifert, H. Eschrig, W. Z. Bieger. An Approximation Variant of LCAO-X-Alpha Methods.Phys Chem,1986,267:529-540
[55] H. Eschrig. Optimized LCAO method and the electronic structure of etended systems. Berlin:Akademie Verlag,1988,45-49
[56] J. P. Perdew, A. Zunger. Self-interaction correction to density-functional approximations formany-electron systems. Phys Rev B,1981,23:5048-5079
[57] D. Marx，J. Hutter. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods.Cambridge:Cambridge University Press,2009,255-268
[58] H. Eschrig, I. Bergert. Optimized LCAO Version for Band-Structure Calculations-Applicationto Copper. Phys Status Solid,1978,90:621-635
[59] J. E. Inglesfield. The effective quasiparticle potential in molecules and solids. Mol Phys,1979,37:873-878.
[60] J. Sakuri. Modern quantum mechanics. New York:Addison-Wesley,1985,27-35
[61] W. Press, B. Flannery, S. Teukolsky, et al. Numerical Recipes in Fortran. Cambridge:Cambridge U P,1988,179-186
[62] H. Gould, J. Tobochnik. An Introduction to Computer Simulation Methods. New York:Addison Wesley,1988,289-295
[63] J. Tully. Mixed quantum–classical dynamics. Farad Discuss,1998,110:407-419.
[64] J. Tully. Nonadiabatic dynamics in Modern methods for multu-dimensional dynamicscomputations in chemistry. Singapore:World Scientific,1998,48-56
[65] M. D. Hack, D. G. Truhlar. Nonadiabatic Trajectories at an Exhibition. J Phys Chem,2000,A104:7917-7926
[66] S. Pedersen, J. L. Herek, A. H. Zewail. The Validity of The “Diradical” Hypothesis: DirectFemtosecond Studies of the Transition-State Structures. Science,1994,266:1359-1369
[67] R. B. Woodward, R. Hoffmann. The conservation of orbital symmetry. New York: AcademicPress,1970,87-90
[68]李鸿健,白明泽,唐红,等.混合并行技术在激光化学反应模拟中的应用.计算机应用,2010,30(6):1687-1689
[69]谭福平,刘洪刚. Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法.应用数学与计算数学学报,2004,1:94-98
[70]周德俊,邢永丽.S-W型二阶矩阵快速乘法的最少乘法运算次数.工程数学学报,1999,1:90-94
[71]周德俊,林彦芬,田增保.二阶矩阵快速乘法的一个新的算法集合.高等学校计算数学学报,1996,04:90-93
[72]吕竹青,周德俊,林彦芬,等. Strassen与Winograd快速矩阵乘法研究.高等学校计算数学学报,1993,3:207-217
[73] R. Asanovic, R. Bodik. The Landscape of Parallel Computing Research: A View from Berkeley,Electrical Engineering and Computer Sciences University of California at Berkeley. TechnicalReport, December18,2006
[74]陈勇，陈国良，李春生，何家华. SMP机群混合编程模型研究.小型微型计算机系统,2004,25(10):1763-1767
[75] E. L. Lusk，W. W.Gropp. A taxonomy of programming models for symmetric muItiprocessorsand SMP clusters. Proceedings of Programming Models for Massively Parallel Computers,1995,12-17
[76] Y. Tanaka, M. Matsuda, M. Ando, et al. Compas: a pentium pro PC-based SMP cluster and itsexperience. IPPS Workshop on Personal Computer Based Networks of Workstations (IPPS'98),486-497
[77] Y. Chen, G. Chen, Y. Xu, et al. Implementation and evaluation of MPI+OpenMP programmingmodel on Dawning3000. Proceedings of the21stIASTED International Conference(IASTED'03),2003,732-737
[78] D. S. Henty. Performance of Hybrid Message passing and Shared Memory Parallels forDiscrete Element Modeling. In Proceedings of the ACM/IEEE conference on Supercomputing,2000,655-672
[79] R. Rabenseifner, G. Wellein. Communication and Optimization Aspects of Parallelprogramming Models on Hybrid Architecture. International Journal of High performanceComputing Applications,2003,17(1):49-62
[80] F. Cappello, D. Etiemble. MPI Versus MPI+OpenMP on IBM SP for the NAS Benchmarks. InProceedings of the2000ACM/IEEE Conference on Supercomputing(CDROM2000),465-475
[81] G. Timothy, B. Mattson, A. Sanders, er al.并行编程模式(敖富江译).北京:清华大学出版社,2005,44-55
[82] H. J. Li, H. Tang, Y. S. Dou, et al. A Parallel Algorithm for Simulating Photochemical Reaction.2008IFIP International Conference on Network and Parallel Computing (NPC2008),258-262
[83] P. Eric, B. Thierry, D. Trystram. Large scale simulation of parallel molecular dynamics Paralleland Distributed Processing,13th International and10th Symposium on Parallel and DistributedProcessing,1999,166-178
[84] B. R. Brooks, R. E. Bruccoleri, B. D.Olafson, et al. CHARMM: A Program for MacromolecularEnergy, Minimization, and Dynamics Calculations. J Comput Chem.1983,4:187-217
[85] D. Spoel, E. Lindahl, B. Hess, et al. GROMACS: Fast, Flexible, and Free, Journal ofComputational Chemistry,2005,26(16):1701-1718
[86] J. B. Kevin, C. Edmond, H. F. Xu, et.al. Scalable Algorithms for Molecular DynamicsSimulations on Commodity Clusters. Proceedings of the2006International Conference onParallel Processing,2006,84-96
[87] J. Kevin, B. R. Dror. The midpoint method for parallelization of particle simulations. TheJournal of Chemical Physics,2006,124:184109
[88] K. Nomura, R. Kalia, A. Nakano, et al. A scalable parallel algorithm for large-scale reactiveforce-field molecular dynamics simulations. Computer Physics Communications,2008,178:73-87
[89] J. Li, Z. Zhou, R. Sadus.Modified force decomposition algorithms for calculating three-bodyinteractions via molecular dynamics. Computer Physics Communications,2006,175:683-691
[90]李鸿健,唐红,豆育升,等.基于SMP集群的激光化学反应模拟效率分析.计算机应用研究,2011,28(4):1232-1241
[91] L. Kale, R. Skeel, M. Bhandarkar, et al. NAMD2: Greater Scalability for Parallel MolecularDynamics. Journal of Computational Physics,1999,151:283-312
[92] M. Dahlin. Interpreting Stale Load Information. IEEE Transactionson Parallel and DistributedSystem,2000,11(10):1033-1047
[93]蒋江,张民选,廖湘科.基于多种资源的负载均衡算法的研究.电子学报,2002,30(8):1148-1152
[94] G. B. Zheng. Archieving High Performance on Extremely Large Parallel Machines:Performance Prediction and Load Balancing[D]. Urbana:UIUC,2005
[95] A. Gissti, M. R. Naiouf. Dynamic Load Balancing in Parallel Processing on Non-HomogeneousClusters. Journal of Computer Science Technology,2005,5(4):272-278
[96] D. Ferrari, S. Zhou. A Load Index for Dynamic Load Balancing. Proceedings of1986ACMFall joint computer conference,1986,684-690
[97] Y. Wang, R. Hyatt. An improved algorithm of two choices in randomized dynamic loadbalancing. Proceedings of the fifth international conference on Algorithms and Architecturesfor parallel processing,2002,440-445
[98]王洁,傅勇,王永炎,等.基于反馈的实时集群系统中的负载均衡方法.计算机工程与设计,2009,30(13):3046-3059
[99] T. Kunz. The Influence of Different Workload Descriptions on a Heuristic Load BalancingScheme. IEEE Transactions on Software Engineering,1991,17(7):725-730
[100] S. Zhou, J. Wang, X. Zheng, et al. Utopia: load sharing facility for large, heterogeneousdistributed computer system. Software Practice and Experience,1993,23(12):1305-1306
[101]李鸿健,孙世新,豆育升,等.一种可变周期反馈的动态负载均衡算法.电子测量与仪器学报,2011,25(11):952-958.
[102]胡凯,马雪洁,邓可.网络机群计算的负载指标研究与实现.计算机工程与设计,2007,28(4):829-831
[103] A. Meliones, T. Varvarigon. A metacomputingenvironment for demanding applications:design, implementation, experiments and business benefit. Future Generation ComputingSystems,1999,15:787-806
[104] P. C. Roth, D. C. Arnold. Software-based multicast/reduction network for scalable tools.Phoenix Arizona:SC,2003
[105]鞠九滨,杨鲲,徐高潮.使用资源利用率作为负载均衡系统的负载指标.软件学报,1996,7(4):238-243
[106] P. B. Dervan, T. Uyehara, D. S. Santilli. Synthesis and Thermal Decomposition of cis-3,4,5,6-Tetrahydropyridazine-3,4-d2Relative Rates of Rotation, Cleavage, and Closure forTetramethylene. J Am Chem Soc,1980,102:3863-3873
[107] F Yong，W Hongan，L Chenyang，et a1. Distributedutilization control for real-tim e clusterswith load balancing. Proc of the27th Real-Time System Symp,2006:137-146
[2] D. J. Tannor, R. Kosloff, S. A. Rice. Coherent pulse sequence induced control of selectivity ofreactions: exact quantum mechanical calculations. J Chem Phys,1986,85(10):5805-5820
[3] A. Assion, T. Baumert, M. Bergt, et al. Control of Chemical Reactions by Feedback-OptimizedPhase-Shaped Femtosecond Laser Pulses. Science,1998,282:919-922
[4] A. H. Zewail. Femtochemistry: Chemical Reaction Dynamics and Their Control. Adv ChemPhys,1997,101:3-5
[5] W. Zhu, J. Botina, H. Rabitz. Rapidly convergent iteration methods for quantum optimalcontrol of population. J Chem Phys,1998,108:1953-1963
[6] W. Zhu, H. Rabitz. Potential surfaces from the inversion of time dependent probability densitydata. J Chem Phys,1999,111:472-480
[7] H. Rabitz, R. Vivie-Riedle, M. Motzkus, et al. Whither the Future of Controlling QuantumPhenomena. Science,2000,288:824-828
[8] W. Yin, X Gao, X Zhu, et al. An Efficient Shared Memory Based Virtual CommunicationSystem for Embedded SMP Cluster. Proceedings of the2011IEEE Sixth InternationalConference on Networking, Architecture, and Storage(NAS '11),288-294
[9] B. Sahoo, R Sourav, R. Ranjan, et al. Parallel Implementation of Exact Algorithm for PlantedMotif Search Problem using SMP Cluster. European Journal of Scientific Research,2011,64:484-496
[10] M. Ben-Nun, T. J. Martínez. Ab initio quantum molecular dynamics. Adv Chem Phys,2002,124:439-512
[11] F. Bernardi, M. Olivucci, M. A. Robb. Simulation of MC-SCF results on covalent organicmulti-bond reactions: molecular mechanics with valence bond (MM-VB). J Am Chem Soc,1992,114:1606-1616
[12] M. J. Bearpark, F. Bernardi, M. Olivucci, et al. Molecular mechanics valence bond methods forlarge active spaces-Application to conjugated polycyclic hydrocarbons. Chem Phys Lett,1994,217:513-519
[13]李鸿健,豆育升,唐红,等.激光诱导化学反应的并行计算机模拟.中国激光,2009,36(2):356-361
[14] H. Li, H. Tang, Y. Dou. Laser-induced nonthermal fragmentation of C60studied bysemiclassical dynamics simulation. Moleculer Physics,2009,107(19):2039-2044
[15] S. Yuan, W. Zhang, L. Liu, et al. Detailed Mechanism for Photoinduced Cytosine Dimerization:A Semiclassical Dynamics Simulation. J. Phys. Chem. A,2011,115:13291
[16] H. Tang, H. Li，Y Dou. Laser Induced C60Cage Opening Studied by Semiclassical DynamicsSimulation. Int. J. Mol. Sci.,2011,12,353-361
[17] D. Porezag, T. Frauenheim, H. Kohler, et al. Construction of tight-binding-like potentials on thebasis of density functional theory: Apllication to carbon. Phys Rev B,1995,51:12947
[18] M. Bisson, M. Bernaschi, S. Melchionna. Parallel Molecular Dynamics with Irregular DomainDecomposition. Commun. Comput. Phys.,2011,10:1071-1088
[19]刘正华,杨决宽,陈云飞.分子动力学并行算法的优化与应用.计算机应用研究,2008,25(3):718-720
[20] J. Kevin, O. Bowers, C. Efmond, et al. Scalable Algorithms for Molecular DynamicsSimulations on Commodity Clusters. Proceedings of the2006International Conference onParallel Processing(ICPP'06),84-96
[21] P. Thompson, S. J. Plimpton, W. Mattson, et al. General formulation of pressure and stresstensor for arbitrary many-body interaction potentials under periodic boundary conditions. JChem Phys,2009,131(1),154107
[22] J. V. Sumanth, R. S. David, J. Hong. Adaptive Load Balancing for Long-Range MDSimulations in A Distributed Environment. Proceedings of the2006International Conferenceon Parallel Processing(ICPP'06),135-146
[23] J. V. Sumanth, R. S. David, J. Hong. Adaptive Load-Balancing for Force-Decomposition Based3-Body Molecular Dynamics Simulations in a Heterogeneous Distributed Environment withVariable Number of Processors. The2007International Conference on Parallel Processing(ICPP '07),552-565
[24] X. Yang, Y. Dou, Q. Hu. Progress and challenges in high performance computer technology. JComput Sci Technol,2006,21(5):674-681
[25] M. Tripathy, C.R. Tripathy. A Distributed Shared Memory Cluster Architecture With DynamicLoad Balancing. Journal of Emerging Trends in Computing and Information Sciences,2012,3:231-240
[26]杨际祥,谭国真,王荣生.并行与分布式计算动态负载均衡策略综述.电子学报,2010,38(5):1122-1130
[27]王广芳,钟志伟,赵先武.分布式计算机系统(DCS)负载均衡算法.计算机工程与设计,1995,16(5):57-63
[28]陈国良.并行计算─结构算法编程.北京:高等教育出版社，2003,45-47
[29]杜晓梅,王广益,李利.最新TOP500超级计算机分析.中国教育网络,2010,8:11-14
[30]都志辉.高性能计算并行编程技术.北京:清华大学出版社,2001,56-67
[31]张林波,迟学斌,莫则尧.并行计算导论.北京:清华大学出版社,2006,158-162
[32] N. Lu, Z. T. Taylor, D. P. Chassin, et al. Parallel Computing Environments and Methods forPower Distribution System Simulation. Power Engineering Society General Meeting(PESGM2005),215-220
[33] G. D. Li, D. F. Zhang. A Distributed Object Based Framework for Paralle Computations.Journal of Software,2002,13(3):342-353
[34] C. C. Fung, S. Y. Chow, K. P. Wong. A Low-Cost Parallel Computing Platform for PowerEngineering Applications.5th International Conference on Advances in Power System Control,Operation and Management(APSCOM'2000),354-358
[35] G. Fadlallah, M. Lavoie, L. A. Dessaint. Parallel Computing Environments and Methods.Parallel Computing in Electrical Engineering(MPCEE'2000),2-7
[36]豆育升,唐红,李鸿健.光化学反应的计算机模拟方法研究.系统仿真学报,2009,21(3):894-899
[37] W. Zhou. Multi-core Computing and Programming.武汉:华中科技大学出版社,2009,88-96
[38] P. S. Pacheco. Parallel Programming with MPI. California:Morgan Kaufmann Publishers,1997,155-158
[39] M. D. Jones, R. Yao. Parallel programming for OSEM reconstruction with MPI, OpenMP, andhybrid MPI-OpenMP. Nuclear Science Symposium Conference Record,2004,5:3036-3042
[40] C. J. Duran, A. Labarta. Dynamic load balancing of MPI+OpenMP applications. ParallelProcessing (ICPP'04),195-202
[41] J. Bahi, R. Couturier, F. Vernier. Synchronous distributed load balancing on dynamic networks.Journal of Parallel and Distributed Computing,2005,65(11):1397-1405
[42] S. Jang, J. Yoo. An Efficient Load Balancing Mechanism in Distributed Virtual Environments.ETRI Journal,2008,30(4):618-620
[43] L. Ricolindo, C. Banicescu. Dynamic load balancing with adaptive factoring methods inscientific applicatons. The Journal of Supercomputing,2008,44(1):41-63
[44] P Berenbrink, T Friedetzky, R Martin. On the Stability of Dynamic Diffusion Load Balancing.Algorithmica,2008,50(3):329-350
[45] Y. B. Wang, R. Hyatt. An improved algorithm of two choices in randomized dynamicloadbalancing. Proceedings of the fifth International Conference on Algorithms andArchitectures for Parallel Processing(ICAAPP'2002),432-445
[46] F. Smit.分子模拟-从算法到应用(汪文川译).北京:化学工业出版社,2002,132-145
[47] A. R. Leach. Molecular Modeling Principles and Applications.北京:世界图书出版公司,2003,166-184
[48]陈正隆，徐为人，汤立达.分子模拟的理论与实践.北京:化学工业出版社,2007,56-59
[49]林梦海.量子化学简明教程.北京:化学工业出版社,2005,86-89
[50] R. E. Allen, T. Dumitrica, B. R. Torralva. Ultrafast Physical Processes in Semiconductors.Academic: New York,2001,188-198
[51] D. Porezag, T. Trauenheim, T. Kohler, et al. Construction of tight-binding-like potentials on thebasis of density-functional theory: Application to carbon. Phys Rev B,1995,51,12947-12957
[52] A. Sieck, D. Porezag, T. Frauenheim, et al. Structure and vibrational spectra of low-energysilicon clusters. Phys Rev A,1997,56:4890-4898
[53] T. Frauenheim, F. Weich, T. Kohler. Density-functional-based construction of transferablenonorthogonal tight-binding potentials for Si and SiH. Phys Rev B,1995,52:11492-11501
[54] G. Serifert, H. Eschrig, W. Z. Bieger. An Approximation Variant of LCAO-X-Alpha Methods.Phys Chem,1986,267:529-540
[55] H. Eschrig. Optimized LCAO method and the electronic structure of etended systems. Berlin:Akademie Verlag,1988,45-49
[56] J. P. Perdew, A. Zunger. Self-interaction correction to density-functional approximations formany-electron systems. Phys Rev B,1981,23:5048-5079
[57] D. Marx，J. Hutter. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods.Cambridge:Cambridge University Press,2009,255-268
[58] H. Eschrig, I. Bergert. Optimized LCAO Version for Band-Structure Calculations-Applicationto Copper. Phys Status Solid,1978,90:621-635
[59] J. E. Inglesfield. The effective quasiparticle potential in molecules and solids. Mol Phys,1979,37:873-878.
[60] J. Sakuri. Modern quantum mechanics. New York:Addison-Wesley,1985,27-35
[61] W. Press, B. Flannery, S. Teukolsky, et al. Numerical Recipes in Fortran. Cambridge:Cambridge U P,1988,179-186
[62] H. Gould, J. Tobochnik. An Introduction to Computer Simulation Methods. New York:Addison Wesley,1988,289-295
[63] J. Tully. Mixed quantum–classical dynamics. Farad Discuss,1998,110:407-419.
[64] J. Tully. Nonadiabatic dynamics in Modern methods for multu-dimensional dynamicscomputations in chemistry. Singapore:World Scientific,1998,48-56
[65] M. D. Hack, D. G. Truhlar. Nonadiabatic Trajectories at an Exhibition. J Phys Chem,2000,A104:7917-7926
[66] S. Pedersen, J. L. Herek, A. H. Zewail. The Validity of The “Diradical” Hypothesis: DirectFemtosecond Studies of the Transition-State Structures. Science,1994,266:1359-1369
[67] R. B. Woodward, R. Hoffmann. The conservation of orbital symmetry. New York: AcademicPress,1970,87-90
[68]李鸿健,白明泽,唐红,等.混合并行技术在激光化学反应模拟中的应用.计算机应用,2010,30(6):1687-1689
[69]谭福平,刘洪刚. Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法.应用数学与计算数学学报,2004,1:94-98
[70]周德俊,邢永丽.S-W型二阶矩阵快速乘法的最少乘法运算次数.工程数学学报,1999,1:90-94
[71]周德俊,林彦芬,田增保.二阶矩阵快速乘法的一个新的算法集合.高等学校计算数学学报,1996,04:90-93
[72]吕竹青,周德俊,林彦芬,等. Strassen与Winograd快速矩阵乘法研究.高等学校计算数学学报,1993,3:207-217
[73] R. Asanovic, R. Bodik. The Landscape of Parallel Computing Research: A View from Berkeley,Electrical Engineering and Computer Sciences University of California at Berkeley. TechnicalReport, December18,2006
[74]陈勇，陈国良，李春生，何家华. SMP机群混合编程模型研究.小型微型计算机系统,2004,25(10):1763-1767
[75] E. L. Lusk，W. W.Gropp. A taxonomy of programming models for symmetric muItiprocessorsand SMP clusters. Proceedings of Programming Models for Massively Parallel Computers,1995,12-17
[76] Y. Tanaka, M. Matsuda, M. Ando, et al. Compas: a pentium pro PC-based SMP cluster and itsexperience. IPPS Workshop on Personal Computer Based Networks of Workstations (IPPS'98),486-497
[77] Y. Chen, G. Chen, Y. Xu, et al. Implementation and evaluation of MPI+OpenMP programmingmodel on Dawning3000. Proceedings of the21stIASTED International Conference(IASTED'03),2003,732-737
[78] D. S. Henty. Performance of Hybrid Message passing and Shared Memory Parallels forDiscrete Element Modeling. In Proceedings of the ACM/IEEE conference on Supercomputing,2000,655-672
[79] R. Rabenseifner, G. Wellein. Communication and Optimization Aspects of Parallelprogramming Models on Hybrid Architecture. International Journal of High performanceComputing Applications,2003,17(1):49-62
[80] F. Cappello, D. Etiemble. MPI Versus MPI+OpenMP on IBM SP for the NAS Benchmarks. InProceedings of the2000ACM/IEEE Conference on Supercomputing(CDROM2000),465-475
[81] G. Timothy, B. Mattson, A. Sanders, er al.并行编程模式(敖富江译).北京:清华大学出版社,2005,44-55
[82] H. J. Li, H. Tang, Y. S. Dou, et al. A Parallel Algorithm for Simulating Photochemical Reaction.2008IFIP International Conference on Network and Parallel Computing (NPC2008),258-262
[83] P. Eric, B. Thierry, D. Trystram. Large scale simulation of parallel molecular dynamics Paralleland Distributed Processing,13th International and10th Symposium on Parallel and DistributedProcessing,1999,166-178
[84] B. R. Brooks, R. E. Bruccoleri, B. D.Olafson, et al. CHARMM: A Program for MacromolecularEnergy, Minimization, and Dynamics Calculations. J Comput Chem.1983,4:187-217
[85] D. Spoel, E. Lindahl, B. Hess, et al. GROMACS: Fast, Flexible, and Free, Journal ofComputational Chemistry,2005,26(16):1701-1718
[86] J. B. Kevin, C. Edmond, H. F. Xu, et.al. Scalable Algorithms for Molecular DynamicsSimulations on Commodity Clusters. Proceedings of the2006International Conference onParallel Processing,2006,84-96
[87] J. Kevin, B. R. Dror. The midpoint method for parallelization of particle simulations. TheJournal of Chemical Physics,2006,124:184109
[88] K. Nomura, R. Kalia, A. Nakano, et al. A scalable parallel algorithm for large-scale reactiveforce-field molecular dynamics simulations. Computer Physics Communications,2008,178:73-87
[89] J. Li, Z. Zhou, R. Sadus.Modified force decomposition algorithms for calculating three-bodyinteractions via molecular dynamics. Computer Physics Communications,2006,175:683-691
[90]李鸿健,唐红,豆育升,等.基于SMP集群的激光化学反应模拟效率分析.计算机应用研究,2011,28(4):1232-1241
[91] L. Kale, R. Skeel, M. Bhandarkar, et al. NAMD2: Greater Scalability for Parallel MolecularDynamics. Journal of Computational Physics,1999,151:283-312
[92] M. Dahlin. Interpreting Stale Load Information. IEEE Transactionson Parallel and DistributedSystem,2000,11(10):1033-1047
[93]蒋江,张民选,廖湘科.基于多种资源的负载均衡算法的研究.电子学报,2002,30(8):1148-1152
[94] G. B. Zheng. Archieving High Performance on Extremely Large Parallel Machines:Performance Prediction and Load Balancing[D]. Urbana:UIUC,2005
[95] A. Gissti, M. R. Naiouf. Dynamic Load Balancing in Parallel Processing on Non-HomogeneousClusters. Journal of Computer Science Technology,2005,5(4):272-278
[96] D. Ferrari, S. Zhou. A Load Index for Dynamic Load Balancing. Proceedings of1986ACMFall joint computer conference,1986,684-690
[97] Y. Wang, R. Hyatt. An improved algorithm of two choices in randomized dynamic loadbalancing. Proceedings of the fifth international conference on Algorithms and Architecturesfor parallel processing,2002,440-445
[98]王洁,傅勇,王永炎,等.基于反馈的实时集群系统中的负载均衡方法.计算机工程与设计,2009,30(13):3046-3059
[99] T. Kunz. The Influence of Different Workload Descriptions on a Heuristic Load BalancingScheme. IEEE Transactions on Software Engineering,1991,17(7):725-730
[100] S. Zhou, J. Wang, X. Zheng, et al. Utopia: load sharing facility for large, heterogeneousdistributed computer system. Software Practice and Experience,1993,23(12):1305-1306
[101]李鸿健,孙世新,豆育升,等.一种可变周期反馈的动态负载均衡算法.电子测量与仪器学报,2011,25(11):952-958.
[102]胡凯,马雪洁,邓可.网络机群计算的负载指标研究与实现.计算机工程与设计,2007,28(4):829-831
[103] A. Meliones, T. Varvarigon. A metacomputingenvironment for demanding applications:design, implementation, experiments and business benefit. Future Generation ComputingSystems,1999,15:787-806
[104] P. C. Roth, D. C. Arnold. Software-based multicast/reduction network for scalable tools.Phoenix Arizona:SC,2003
[105]鞠九滨,杨鲲,徐高潮.使用资源利用率作为负载均衡系统的负载指标.软件学报,1996,7(4):238-243
[106] P. B. Dervan, T. Uyehara, D. S. Santilli. Synthesis and Thermal Decomposition of cis-3,4,5,6-Tetrahydropyridazine-3,4-d2Relative Rates of Rotation, Cleavage, and Closure forTetramethylene. J Am Chem Soc,1980,102:3863-3873
[107] F Yong，W Hongan，L Chenyang，et a1. Distributedutilization control for real-tim e clusterswith load balancing. Proc of the27th Real-Time System Symp,2006:137-146