量子动力学中并行算法的发展与应用

发布时间：2018-05-22 07:52

本文选题：GPU加速 + 化学反应动力学　；参考：《中国科学院研究生院（武汉物理与数学研究所）》2013年博士论文

【摘要】：本文针对量子动力学理论研究中并行算法问题,发展了Shepard插值方法的计算势能的GPU算法；研究了范德华体系振转光谱的束缚态理论计算的MPI/OpenMP并行算法；研究了X+NH3反应的七维量子动力学理论方法和MPI/OpenMP并行算法,并应用于研究Cl (2P)+NH3/ND3反应。本论文的研究工作如下： 1.采用改进的Shepard插值方法构造的势能面被广泛用于化学反应动力学研究,这种构造方法通过对从头算数据点进行插值来获得任意构型的能量,采用该方法构造的势能面精度高,能够更精准地研究化学反应动力学。但是在实际运用中,插值势能面计算量大,从而限制了该方法的应用。本工作基于GPU的强大计算能力和高度并行性特点,发展采用Shepard插值方法计算势能的GPU新算法。并以H+H2O? H2+OH, H+NH3?H2NH2,H+CH4?H2+CH3这3个反应的势能面为例对算法进行验证,发现GPU算法相对CPU算法具有明显的优越性,并且GPU加速比随着体系增大而增大,随着数据点增加而增加。 2.范德华体系振转光谱的束缚态理论计算需求精确求解Schrodinger方程,由于体系的波函数展开为各个坐标基函数的乘积,所以体系基函数的大小随原子数增加呈指数增加,计算时间和内存需求也随之增加。需要应用并行化计算方案使计算得以实现。我们针对线性分子-线性分子组成的范德华体系振转光谱的理论研究,开发了束缚态计算的并行算法,采用节点间采用MPI和节点内采用OpenMP的并行方案,并针对N2O-N2O体系验证了该并行算法,结果显示计算效率明显提高,加速比是1.67倍到8.6倍。 3. Cl+NH3在过渡态前后都有较深的势阱,对量子动力学理论计算提出了挑战。在动力学计算中,我们采用X+YCZ2类型的七维量子动力学模型,其中不参与反应的NH2基团在反应过程中保持不变,采用该模型我们对Cl+NH3和Cl+ND3两个反应进行了研究,计算结果显示Cl+NH3和Cl+ND3有相似的动力学行为,而且反应几率都是非常小,与实验观测一致。由于该反应Cl+ND3比较复杂,Cl原子有较重的质量,因此,基函数大小为3.175*109,势能格点的数目为3.78*1010,传播时间为是25000a.u,是当前量子动力学研究中计算量最大的工作之一。
[Abstract]:In order to solve the problem of parallel algorithm in quantum dynamics theory, the GPU algorithm for calculating potential energy of Shepard interpolation method and the MPI/OpenMP parallel algorithm for the calculation of bound state theory of vibrational spectra of van der Waals system are developed in this paper. The seven dimensional quantum dynamics theory and MPI/OpenMP parallel algorithm for X NH3 reaction are studied, and applied to the study of Cl 2 P) NH3/ND3 reaction. The research work of this thesis is as follows: 1. The potential energy surface constructed by the improved Shepard interpolation method is widely used in the study of chemical reaction kinetics. The energy of arbitrary configuration is obtained by interpolating the ab initio data points. The potential energy surface constructed by this method has high accuracy. It is possible to study the kinetics of chemical reaction more accurately. However, the application of interpolation potential energy surface is limited because of the large amount of calculation in practice. Based on the strong computing power and high parallelism of GPU, a new GPU algorithm using Shepard interpolation method to calculate potential energy is developed. And H H 2O? The potential energy surface of the three reactions H 2O H, H NH 3H 2NH 2H CH4?H2 CH3 is used as an example to verify the algorithm. It is found that the GPU algorithm has obvious advantages over the CPU algorithm, and the GPU acceleration ratio increases with the increase of the system and increases with the increase of the data points. 2. The calculation of the bound state theory of van der Waals system requires the exact solution of the Schrodinger equation. Because the wave function of the system is the product of each coordinate basis function, the size of the basis function of the system increases exponentially with the increase of the number of atoms. Computing time and memory requirements also increase. Parallel computing scheme is needed to realize the computation. In this paper, we develop a parallel algorithm for the calculation of bound states in Van der Waals system with linear molecular and linear molecular composition. We adopt the parallel scheme of MPI between nodes and OpenMP within nodes. The parallel algorithm is verified for the N2O-N2O system. The results show that the computational efficiency is improved obviously, and the speedup ratio is 1.67 to 8.6 times. 3. Cl NH3 has a deep potential well before and after the transition state, which challenges the theoretical calculation of quantum dynamics. In the kinetic calculation, we adopt the seven dimensional quantum dynamics model of X YCZ2 type, in which the NH2 group that does not participate in the reaction remains constant during the reaction process. Using this model, we study the Cl NH3 and Cl ND3 reactions. The calculated results show that Cl NH3 and Cl ND3 have similar kinetic behaviors, and the probability of reaction is very small, which is consistent with the experimental observation. Because of the heavy mass of the complex Cl ND3 atom, the basis function is 3.175 ~ 109, the number of potential energy lattice is 3.78 ~ 1010, and the propagation time is 25000a.u. it is one of the most computational tasks in quantum dynamics research.
【学位授予单位】：中国科学院研究生院（武汉物理与数学研究所）
【学位级别】：博士
【学位授予年份】：2013
【分类号】：O413.1;TP338.6

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