On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0,10000]

Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data,we have done a reliable simulation of chaotic solution of Lorenz equation in a rather long interval 0 t 10000 LTU(Lorenz time unit).Such a kind of mathematically reliable chaotic simulation has never been reported.It provides us a numerical benchmark for mathematically reliable long-term prediction of chaos.Besides,it also proposes a safe method for mathematically reliable simulations of chaos in a finite but long enough interval.In addition,our very fine simulations suggest that such a kind of mathematically reliable long-term prediction of chaotic solution might have no physical meanings,because the inherent physical micro-level uncertainty due to thermal fluctuation might quickly transfer into macroscopic uncertainty so that trajectories for a long enough time would be essentially uncertain in physics.     

Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations

A parallel implementation of the electromagnetic dual-primal finite element tearing and interconnecting algorithm (FETI-DPEM) is designed for general three-dimensional (3D) electromagnetic large-scale simulations. As a domain decomposition implementation of the finite element method, the FETI-DPEM algorithm provides fully decoupled subdomain problems and an excellent numerical scalability, and thus is well suited for parallel computation. The parallel implementation of the FETI-DPEM algorithm on a distributed-memory system using the message passing interface (MPI) is discussed in detail along with a few practical guidelines obtained from numerical experiments. Numerical examples are provided to demonstrate the efficiency of the parallel implementation.     

激波诱导火焰界面失稳的并行化学加速计算

在带有详细化学反应机理的可压缩反应流数值模拟中,化学反应源项的计算会极大增加计算时间,基于建表技术的化学加速算法可以通过查找数据表中的数据来替代化学反应计算,从而有效提高计算效率,但数据表尺寸的过度增长会导致计算的中断.文章提出了基于两种数据表容量控制策略的并行动态存储/删除算法,并在激波诱导火焰界面失稳的数值模拟中进行了应用,以考察算法的性能.两种数据表容量控制策略分别为单表容量（M_sin）控制和总表容量（M_tot）控制,当单个数据表尺寸达到M_sin或总数据表尺寸达到M_tot时,对数据表进行节点删除,以保证计算的正常进行.计算结果表明,文章提出的基于表容量控制的并行加速算法,其计算准确度和计算效率之间存在关联,具有较好计算准确度算例显示了较高的计算效率.在不同的M_sin和M_tot条件下,计算的化学加速比在2.73~3.93之间.两种表控策略的组合影响了数据表删除的频率和删除之间的同步性,当数据表删除频率小、删除同步性强时,化学加速比要更高.      

三维激光烧蚀瑞利-泰勒不稳定性并行计算

给出了用三维激光烧蚀不稳定性程序求解的物理方程组,简要介绍了所用的数值方法.根据所模拟问题的物理性质和数值模拟方法探索了在多处理机上实行并行计算的技术和方法,并行效率达75%,在此基础上进行了三维多模激光烧蚀不稳定性的数值模拟,深化了对有关物理规律的认识.     

基于"块-单元"数据结构的分子动力学并行计算

开发了一种基于"块-单元"数据结构的可扩展并行算法,以实现大规模、非均匀分子动力学模拟.它采用空间填充曲线将三维区域分解转换为-维负载平衡问题,然后用基于实测的多层均权法求解,以保持处理机间负载均衡.在一个MPP并行机的500个CPU上,模拟包含2.1×108个粒子的三维金属微喷射模型,该算法获得了420倍的加速比.     

一种可扩展的三维半导体器件并行数值模拟算法

在基于漂移-扩散模型的三维半导体器件数值模拟中,通过有限体积法进行数值离散,采用完全耦合的牛顿迭代求解非线性代数方程组,并使用基于代数多重网格预条件子的GMRES方法求解牛顿迭代中的线性方程组,构造一种稳健且高度可扩展的非结构四面体网格上求解半导体方程的并行算法.基于PHG平台实现该算法的并行计算程序,并对PN结和MOS场效应晶体管等问题进行了最大网格规模达到5亿单元、最大并行规模达到1 024进程的大规模数值模拟实验,结果表明,该算法计算效率高,可扩展性好.     

二维三温流体力学数值模拟程序的并行化

基于消息传递,通过设计并行算法和组织网格划分,实现了二维三温流体力学Lagrange数值模拟串行程序(Lared-Ⅰ)的并行化。结合物理问题特性和程序的执行特征,设计了动态负载平衡方法,进一步提高并行计算性能。并给出两个并行计算环境上的数值实验结果。     

Mathematical analysis of coupled parallel simulations

A set of parallel replicas of a single simulation can be statistically coupled to closely approximate long trajectories. In many cases, this produces nearly linear speedup over a single simulation ( M times faster with M simulations), rendering previously intractable problems within reach of large computer clusters. Interestingly, by varying the coupling of the parallel simulations, it is possible in some systems to obtain greater than linear speedup. The methods are generalizable to any search algorithm with long residence times in intermediate states.     

基于修正并行光滑粒子动力学方法三维变系数瞬态热传导问题的模拟

为了解决传统光滑粒子动力学(SPH)方法求解三维变系数瞬态热传导方程时出现的精度低、稳定性差和计算效率低的问题,本文首先基于Taylor展开思想拓展一阶对称SPH方法到三维热传导问题的模拟,其次引入稳定化处理的迎风思想,最后基于相邻粒子标记和MPI并行技术,结合边界处理方法得到一种能够准确、高效地求解三维变系数瞬态热传导问题的修正并行SPH方法.通过对带有Direclet和Newmann边界条件的常/变系数三维热传导方程进行模拟,并与解析解进行对比,对提出的方法的精度、收敛性及计算效率进行了分析;随后,运用提出的修正并行SPH方法对三维功能梯度材料中温度变化进行了模拟预测,并与其他数值结果做对比,准确地展现了功能梯度材料中温度变化过程.     

A parallel Vlasov solver based on local cubic spline interpolation on patches

A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semi-Lagrangian algorithm that approaches the Vlasov equation on a grid of phase space. As this kind of method requires a huge computational effort, the simulations are carried out on parallel machines. To that purpose, we present a local cubic splines interpolation method based on a domain decomposition, e.g. devoted to a processor. Hermite boundary conditions between the domains, using ad hoc reconstruction of the derivatives, provide a good approximation of the global solution. The method is applied on various physical configurations which show the ability of the numerical scheme.     

二电子系列关联能的并行计算

用组态相互作用方法计算了二电子体系电子关联能,为了获得高精度的结果往往需要巨大的计算量,以往单个处理器上的串行计算通常存在着机时长,内存不够的严重困难,为此采用并行分块消去迭地,同时在多个处理器上并行计算,得到了了基态关联能。     

Parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm

It is shown that numerical simulations of fully-developed plasma turbulence can be successfully parallelized in time using the parareal algorithm. The result is far from trivial, and even unexpected, since the exponential divergence of Lagrangian trajectories as well as the extreme sensitivity to initial conditions characteristic of turbulence set these type of simulations apart from the much simpler systems to which the parareal algorithm has been applied to this day. It is also shown that the parallel gain obtainable with this method is very promising (close to an order of magnitude for the cases and implementations described), even when it scales with the number of processors quite differently to what is typical for spatial parallelization.     

Chiral-glass transition in a diluted dipolar-interaction Heisenberg system

Recently, numerical simulations reveal that a spin-glass transition can occur in the three-dimensional diluted dipolar system. By defining the chirality of triple spins in a diluted dipolar Heisenberg spin glass, we study the chiral ordering in the system using parallel tempering algorithm and heat bath method. The finite-size scaling analysis reveals that the system undergoes a chiral-glass transition at finite temperature.     

3维全电磁粒子模拟大规模并行程序NEPTUNE

 介绍了自主编制的3维全电磁粒子模拟大规模并行程序NEPTUNE的基本情况。该程序具备对多种典型高功率微波源器件的3维模拟能力,可以在数百乃至上千个CPU上稳定运行。该程序使用时域有限差分(FDTD)方法更新计算电磁场,采用Buneman-Boris算法更新粒子运动状态,运用质点网格法（PIC）处理粒子与电磁场的耦合关系,最后利用Boris方法求解泊松方程对电场散度进行修正,以确保计算精度。该程序初步具备复杂几何结构建模能力,可以对典型高功率微波器件中常见的一些复杂结构,如任意边界形状的轴对称几何体、正交投影面几何体,慢波结构、耦合孔洞、金属线和曲面薄膜等进行几何建模。该程序将理想导体边界、外加波边界、粒子发射与吸收边界及完全匹配层边界等物理边界应用于几何边界上,实现了数值计算的封闭求解。最后以算例的形式,介绍了使用NEPTUNE程序对磁绝缘线振荡器、相对论返波管、虚阴极振荡器及相对论速调管等典型高功率微波源器件进行的模拟计算情况,验证了模拟计算结果的可靠性,同时给出了并行效率的分布情况。     

并行建表化学加速算法研究及其在气相斜爆轰模拟中的应用

采用详细化学反应机理对气相斜爆轰问题开展数值计算时,由于组分之间的特征时间尺度相差很大,反应源项的直接积分(direct integration,DI)求解通常存在强烈的刚性及非线性现象,导致计算量很大.为了在不损失计算精度的基础上有效减少化学反应过程的计算时间,针对包含2H2+O2详细机理的二维斜爆轰并行计算,提出两...     

One-way hash function construction based on the spatiotemporal chaotic system

Based on the spatiotemporal chaotic system,a novel algorithm for constructing a one-way hash function is proposed and analysed.The message is divided into fixed length blocks.Each message block is processed by the hash compression function in parallel.The hash compression is constructed based on the spatiotemporal chaos.In each message block,the ASCII code and its position in the whole message block chain constitute the initial conditions and the key of the hash compression function.The final hash value is generated by further compressing the mixed result of all the hash compression values.Theoretic analyses and numerical simulations show that the proposed algorithm presents high sensitivity to the message and key,good statistical properties,and strong collision resistance.     

Lattice Boltzmann simulations on GPUs with ESPResSo

For the dynamics of macromolecules in solution, hydrodynamic interactions mediated by the solvent molecules often play an important role, although one is not interested in the dynamics of the solvent itself. In computer simulations one can therefore save a large amount of computer time by replacing the solvent with a lattice fluid. The macromolecules are propagated by Molecular Dynamics (MD), while the fluid is governed by the fluctuating Lattice-Boltzmann (LB) equation. We present a fluctuating LB implementation for a single graphics card (GPU) coupled to a MD simulation running on conventional processors (CPUs). Particular emphasis lies on the optimization of the combined code. In our implementation, the LB update is performed in parallel with the force calculation on the CPU, which often completely hides the additional computational cost of the LB. Compared to our parallel LB implementation on a conventional quad-core CPU, the GPU LB is 50 times faster, and we show that a whole commodity cluster with Infiniband interconnnect cannot outperform a single GPU in strong scaling. The presented code is part of the open source simulation package ESPResSo ().     

煤油超燃冲压发动机三维大规模并行数值模拟

在我国巨型计算机上,采用1024个CPU对煤油燃料超燃冲压发动机燃烧流场进行三维大规模并行数值模拟.计算软件采用自主研发的并行软件AHL3D,控制方程采用雷诺平均的N-S方程,无粘项计算采用Steger-Warning矢通量分裂格式,湍流模型采用k-ω双方程模型,煤油分子式采用正癸烷代替.计算给出的发动机壁面压强分布与试验测量结果有较好的一致性.结果表明,凹槽是发动机主要的着火区和火焰稳定区,同时,由于燃料的喷注形成的回流区也起到一定的稳焰作用.计算结果验证了AHL3D程序和采用的理论模型可以用于模拟煤油燃料超燃冲压发动机内部的复杂流动.     

Particle-Mesh Ewald(PME)算法的GPU加速

讨论在NVIDIACUDA开发环境下,用GPU加速分子动力学模拟中静电作用的长程受力计算部分.采用Particle-Mesh Ewald(PME)方法,将其分解为参数确定、点电荷网格离散、离散网格的傅立叶变换、静电热能求解与静电力求解5个部分,并分别分析各部分的GPU实现.此方法已成功用于7个不同大小的生物分子体系的模拟计算,达到了7倍左右的加速.该程序可耦合到现有分子动力学模拟软件中,或作为进一步开发的GPU分子动力学程序的一部分,显著加速传统分子动力学程序.