二维自适应非结构网格DSMC并行算法研究

研究了二维自适应非结构网格DSMC并行算法实现的过程.首先提出了一类非结构网格自适应策略,有效降低了网格尺度对计算结果的影响,提高了流场的分辨率;然后基于PC-CLUSTER群机并行体系结构与消息传递库MPI并行环境,利用分区并行思想,设计了非结构网格DSMC并行算法,节约了计算时间.利用For-tran90的动态分配内存技术编制了通用计算程序;最后对过渡流域高超声绕流进行了数值模拟,计算结果初步验证了算法的可行性与有效性.     

混凝土细观力学分析程序中的快速算法与并行算法设计

针对一套混凝土细观力学分析程序,在分析其计算方法与计算效率的不足之后,提出了采用稀疏矩阵与稀疏向量技术来高效实现有限元刚度矩阵装配过程的算法,并采用双门槛不完全Cholesky分解预条件技术与CG法相结合来高效地求解稀疏线性方程组。之后,从整体上提出了一个将有限单元分布与未知量分布有机结合的并行算法设计方案,并分别针对刚度矩阵装配、双门槛不完全Cholesky分解、稀疏矩阵与稠密向量相乘、稀疏向量相加等核心算法,进行了相应的并行算法设计。最后,在由每节点2 CPU的8个Intel Xeon节点采用千兆以太网连成的机群上,针对两个混凝土数值试样进行了数值实验,第一个试样含44117个网格点与53200个有限单元,第二个试样含71013个网格点与78800个有限单元;对第一个试样,原串行程序进行全程567次加载计算需要984.83小时约41天,采用文中串行算法后,模拟时间减少到22531秒约6.26小时,采用并行算法在16个CPU上的模拟时间进一步降为3860秒约1.07小时。对第二个试样,原串行程序进行全程94次加载计算需要467.19小时约19.5天,采用文中串行算法后,模拟时间减少到11453秒约3.18小时,采用并行算法在16个CPU上的模拟时间进一步降为1704秒约28.4分钟。串行算法的改进与并行算法的设计大大缩短了计算时间,对加快混凝土力学性能的分析研究具有重要意义。     

非线性动力有限元重叠区域分裂的隐式并行算法

针对大规模结构非线性瞬态动力分析非常耗时,提出了相应的并行算法。该算法采用无条件稳定的Ne-wmark-β方法(平均加速技术)进行时间积分,并结合区域分裂技术进行分析。它不同于已有的采用非重叠区域的并行算法,而是采用重叠区域的并行算法。对给定结构有限元分析的质量、阻尼、刚度矩阵进行分裂可推出重叠区域分裂算法的计算公式。为改善每一步的求解,采用预估和校正子方案。编写了该算法的程序,在工作站机群上实现了数值算例,验证了算法的性能。计算结果表明该算法优于非重叠区域分裂算法。     

有限元子结构并行算法的性能分析

 对有限元子结构并行算法的主要步骤进行了归纳，比较准确地 计算了算法的计算量和通信量. 并在此基础上分析了算法的性能和可 扩展性，最后指出了影响算法并行效率的关键因素，并给出了算法优 化方向和改进建议.     

拉氏反变换的数值并行算法及其在弹性动力学边界元法中的应用

本文讨论了快速拉氏反变换的数值并行算法,并将其应用于瞬态弹性动力学的边界元法。为了本文提出的并行算法的优越性,还给出了串行算法,最后将串行和并行计算结果与解析解进行了比较,说明本文方法的正确性和有效性。对拉氏反变换的数值并行算法及其应用于瞬态弹性动力学边界元法的优越性进行了研究。从计算时间可以看出,并行计算的时间比串行计算时间可大幅度减少,说明了本文方法的优越性。     

两类润滑剂物性参数和摩擦系数的高通量分子动力学计算

提出了离子液体和酯类化合物两类润滑剂物性参数和摩擦系数的高通量分子动力学计算框架,建立了通过分子几何拓扑结构-力场参数分配-分子模型构建-参数计算的全流程高通量方法,利用充足的计算资源,可以实现万级规模的高通量并发计算. 创新性地提出了两层高通量并发-并行算法:第一层将润滑剂库分块,每一块并发计算;第二层单个润滑剂采用多CPU并行计算,大大提高了计算效率. 以离子液体为例测试了高通量算法和代码,最大进行了100级高通量计算,结果表明,该高通量算法具有很好的稳定性和计算效率,得到的物性参数和摩擦系数与实验值相吻合.      

大规模边界元分析的子域并行算法及其工程应用

为了扩大边界元多域分析的计算规模,对边界元子域并行算法进行了研究,针对不同的使用情况研制了不同的算法。算法引入分块技术以解决内存不足的矛盾,引入选主元或局部选主元技术以提高数值稳定性。特别是发展了多机一域算法,可以灵活解决不均匀子域划分的负载平衡问题。数值试验结果和实际工程应用都表明算法是有效的。     

隐式重启动Arnoldi/Lanczos法的子区域并行算法

针对求解有限元分析的特征值问题,提出了一种隐式重启动Arnoldi/Lanczos方法的子区域并行算法。隐式重启动Arnoldi/Lanczos利用重启动技术以提高所需谱的收敛性,并能有效处理Krylov基形成问题、存储所需的内存问题、计算成本问题。并行算法中采取子区域接子区域方法、重叠和非重叠网格划分技术。采用压缩数据结构来储存系数矩阵。对Krylov的数值线性代数运算和隐式重启动法中的数值线性代数运算的并行化进行了研究。数值算例表明:该算法具有良好的适用性和效率,适合分布式储存体系的机群。     

无网格Galerkin法GPU加速并行计算及其应用

针对无网格Galerkin法计算耗时的问题,采用逐节点对法来组装刚度矩阵、共轭梯度法求解基于CSR格式存储的稀疏线性方程组,提出了一种利用罚函数法施加本质边界条件的EFG法GPU加速并行算法,给出了刚度矩阵和惩罚刚度矩阵的统一格式,以及GPU加速并行算法的流程图。编写了基于CUDA构架平台的GPU程序,且在NVIDIA GeForce GTX 660显卡上通过数值算例对所提算法进行了性能测试与分析比较,探讨了影响加速比的因素。算例结果验证了所提算法的可行性,并在满足计算精度的前提下,其加速比最大可达17倍;同时线性方程组的求解对加速比起决定性影响。     

基于CUDA的有限元矩阵并行装配算法研究

构建航天飞行器的结构有限元模型是准确模拟飞行仿真、完成飞行器在轨飞行阶段结构故障监测和诊断的基础。采用细长体飞行器简化梁模型，提出新的基于CUDA（Compute Unified Device Architecture）的有限元单元刚度矩阵生成和总刚度矩阵组装算法。依据梁单元矩阵的对称性，结合GPU硬件架构提出并行生成算法并进行改进。为有效减少装配时间，在装配过程中采用着色算法，提出了基于GPU（Graphics Processing Unit）共享内存的非零项组装策略，通过在不同计算平台下算例对比，验证了新算法的快速性。数值算例表明，本文算法的求解效率较高，针对一定计算规模内的模型可满足快速计算与诊断的实时性要求。     

有限元分析快速解法

基于结构分析有限元方程组的特征，提出了在刚度矩阵及其因子的超方程概念下的细胞稀疏索引存贮方案。与传统的稀疏索引存贮方案相比，它可以减少磁盘空间和内存的占用量约30％。同时，这一存贮方案也可以减少关于索引的操作.结合双向循环展开技术，发展了一种适合于多维有限元分析的快速稀疏直接静力求解方法。工程算例表明，所建议的方案在存贮量和速度方面显著地改进了直接求解法的效率。     

Fractional step algorithm for estuarine mass transport

A successful and economical fractional step algorithm for the convection-dispersion-reaction equation is described. Exact solutions are adopted for the reaction and convection steps, the latter by the introduction of a moving co-ordinate system. The dispersion step uses an optimized finite difference algorithm which specifically accommodates the grid non-uniformity. The excellent performance of the algorithm is confirmed by numerical experiments together with computations of the Fourier response and integrated square error characteristics.     

A high‐order mass‐lumping procedure for B‐spline collocation method with application to incompressible flow simulations

This paper presents new developments of the staggered spline collocation method for cost‐effective solution to the incompressible Navier–Stokes equations. Maximal decoupling of the velocity and the pressure is obtained by using the fractional step method of Gresho and Chan, allowing the solution to sparse elliptic problems only. In order to preserve the high‐accuracy of the B‐spline method, this fractional step scheme is used in association with a sparse approximation to the inverse of the consistent mass matrix. Such an approximation is constructed from local spline interpolation method, and represents a high‐order generalization of the mass‐lumping technique of the finite‐element method. A numerical investigation of the accuracy and the computational efficiency of the resulting semi‐consistent spline collocation schemes is presented. These schemes generate a stable and accurate unsteady Navier–Stokes solver, as assessed by benchmark computations. Copyright © 2003 John Wiley & Sons, Ltd.     

On preconditioning a nonsingular matrix

For a nonsingular n by n matrix A, a diagonal matrix D^* is derived which minimizes an upper bound on the spectral condition number of DA. Replacement of the linear system Ax=c with the prescaled system D^*Ax=D^*c requires about 3n² operations for dense matrices and fewer for sparse, banded matrices and is recommended for the conjugate gradient and other methods of solution. Examples are given showing the advantageous effect of prescaling on condition number, and a simple computational algorithm is presented. The extension to nondiagonal scaling matrices is discussed.     

A NEW HIGH PERFORMANCE SPARSE STATIC SOLVER IN FINITE ELEMENT ANALYSIS WITH LOOP-UNROLLING

In the previous papers, a high performance sparse static solver with two-level unrolling based on a cell-sparse storage scheme was reported. Although the solver reaches quite a high efficiency for a big percentage of finite element analysis benchmark tests, the MFLOPS （million floating operations per second） of LDL^T factorization of benchmark tests vary on a Dell Pentium IV 850 MHz machine from 100 to 456 depending on the average size of the super-equations, i.e., on the average depth of unrolling. In this paper, a new sparse static solver with two-level unrolling that employs the concept of master-equations and searches for an appropriate depths of unrolling is proposed. The new solver provides higher MFLOPS for LDL^T factorization of benchmark tests, and therefore speeds up the solution process.     

Symmetric Gauss-Seidel multigrid solution of the Euler equations on structured and unstructured grids

The efficient symmetric Gauss-Seidel (SGS) algorithm for solving the Euler equations of inviscid, compressible flow on structured grids, developed in collaboration with Jameson of Stanford University, is extended to unstructured grids. The algorithm uses a nonlinear formulation of an SGS solver, implemented within the framework of multigrid. The earlier form of the algorithm used the natural (lexicographic) ordering of the mesh cells available on structured grids for the SGS sweeps, but a number of features of the method that are believed to contribute to its success can also be implemented for computations on unstructured grids. The present paper reviews, the features of the SGS multigrid solver for structured gr0ids, including its nonlinear implementation, its use of “absolute” Jacobian matrix preconditioning, and its incorporation of multigrid, and then describes the incorporation of these features into an algorithm suitable for computations on unstructured grids. The implementation on unstructured grids is based on the agglomerated multigrid method developed by Sørensen, which uses an explicit Runge-Kutta smoothing algorithm. Results of computations for steady, transonic flows past two-dimensional airfoils are presented, and the efficiency of the method is evaluated for computations on both structured and unstructured meshes.     

基于ESGA遗传算法的水射流自驱旋转喷头优化设计

超高压水射流自驱旋转型喷头是目前广泛应用于船壁除锈的一种装置,其布局方式直接影响船壁除锈的效率和质量,目前喷头布局多依赖工程经验,缺少准确的理论分析和优化技术支持。针对水射流自驱旋转型喷头的布局优化问题,在传统遗传算法（genetic algorithm,GA）的基础上,提出一种基于“锦标赛选择”的精英策略遗传算法（elitist strategy genetic algorithm,ESGA）,该算法通过采用种群进化过程中精英个体直接保留到下一代的进化策略,从而有效提高算法的全局收敛能力和算法的鲁棒性。结合旋转喷头扫掠冲击性能和轨迹特征,以喷头移动路径垂直打击面上的能量分布均匀度为衡量标准,建立超高压水射流自驱旋转型喷头的螺旋扫掠冲击离散化时间优化模型,并分别利用两种遗传算法对其进行优化改进。对一字形水射流自驱旋转型喷头的布局优化研究发现,经ESGA算法优化的旋转喷头,其扫掠冲击能量分布均匀度较原喷头布局提升了47.2%,其收敛精度也高于GA算法。经对ESGA算法优化后的喷头实验验证发现,ESGA优化方案较原设计方案除锈效率提高了42.0%。改进的ESGA优化算法可行性强,能够在收敛...     

Optimal image watermarking scheme based on chaotic map and quaternion wavelet transform

In this paper, an intelligent watermarking scheme optimized by adaptive differential evolution (ADE) is proposed based on chaotic map and quaternion wavelet transform (QWT). Watermark is first scrambled by a piecewise linear chaotic map to increase security and then inserted into the real QWT amplitude coefficients intelligently. ADE algorithm is explored to optimize the watermarking parameter (i.e., scaling factors) automatically. The experimental results demonstrate the high robustness against common signal processing operations, especially geometrical distortions of the proposed algorithm. Comparison results also indicate the superiority of the proposed algorithm over the existing watermarking algorithm.     

大规模动力系统改进的快速精细积分方法

提出一种针对大规模动力系统的改进的快速精细积分方法（FPIM）。以精细积分方法为基础,利用大规模动力系统矩阵的稀疏性和动力问题的物理特性,分析了矩阵指数的特殊结构,并基于此给出一种计算大规模动力系统矩阵指数及其动力响应的高效率方法。