复合材料机翼颤振特性的数值仿真

研究机翼振颤性能优化问题,由于复合材料机翼具有材料耦合和几何耦合的特点,传统的方法研究复合材料机翼的颤振特性比较复杂,耗时长.为解决上述问题,提出利用哈密顿原理建立了系统的运动方程,然后采用微分求积法进行离散,并编制了程序对复合材料机翼的弯扭耦合颤振速度在Matlab软件上进行了数值仿真.结果表明,微分求积法的计算结果精度高、速度快,并证明利用微分求积法分析复合材料机翼的颤振特性是可行且有效的.同时,分析了材料耦合刚度对颤振速度的影响,结果表明材料耦合刚度的绝对值稍大些才能提高机翼的颤振速度.     

用微分求积法分析轴向移动粘弹性梁的非平面非线性振动

用微分求积法分析了轴向移动粘弹性梁非平面非线性振动的动力学行为.轴向移动粘弹性梁非平面非线性振动的数学模型是一非常复杂的非线性偏微分方程组.首先用微分求积法对其控制方程组进行空间离散,得到非线性常微分方程组,然后求解常微分方程组得到数值结果.在数值结果的基础上结合非线性动力学理论,利用分叉图、时间历程图、相图对其非线性动力学特性进行了分析.     

用微分求积法分析输液管道的非线性动力学行为

将微分求积法(Differential Quadrature Method,简称DQM)应用于输液管道的非线性动力学分析,采用此法研究了受非线性约束输液管道的分岔现象和混沌运动问题.从悬臂输液管道模型出发,利用微分求积法形成管道的动力学方程.以分岔图、相平面图、时间历程图和Poincare映射等分析手段考察了系统参数(管内流速)变化对管道振动形态的影响.结果表明,在所研究的系统中存在出现倍周期分岔现象和混沌运动的参数区域,这与前人的研究成果具有一致性.这为一类结构的非线性动力响应问题提供了一种新的研究思路.     

大展弦比板弯扭耦合受迫振动分析

对于工程广泛存在的大展弦比结构,首次研究了大展弦比板弯扭耦合受迫振动响应.考虑弦向相对弯曲刚度远大于展向弯曲刚度,将弦向截面等效为刚体,考虑其绕展向轴线的扭转,应用Hamilton原理分别计算大展弦比板的势能与动能,建立两端简支的大展弦比板弯扭耦合受迫振动的动力学控制方程.将动力学控制方程进行Galerkin截断后,通过谐波平衡法和微分求积法/微分求积单元法,计算得到了大展弦比模型弯扭耦合受迫振动稳态响应的解析解及数值解,同时验证了解的截断收敛性及谐波收敛性.最后研究了外激励幅值对结构受迫振动响应的影响.结果将为工程中广泛存在的大展弦比结构设计提供指导.     

轴向运动功能梯度梁横向振动问题的保结构分析

轴向运动速度和材料的非均匀性对轴向运动功能梯度梁振动问题分析提出了严峻挑战.本文在简要回顾轴向运动功能梯度梁横向振动动力学模型基础上,基于无限维动力学系统的对称破缺理论和广义多辛分析方法,构造了横向振动模型的保结构数值格式,并在给定材料参数时给出了数值格式具有良好保结构性能的条件.分别采用微分求积法、复模态法和保结构方法分析横向振动模型的前六阶频率,发现保结构方法得到的频率结果与复模态法得到的结果吻合较好,在此基础上分析了微分求积法的主要误差来源,以指导微分求积法的改进,并为复杂动力学系统的数值求解提供了新途径.     

基于微分求积法的互连线灵敏度分析

提出一种基于微分求积法、对互连线的响应波形进行灵敏度分析的新方法．以传输线时域模型对互连 线进行建模,在此基础上导出灵敏度分析模型．由于利用了所有离散点的信息,微分求积法通常只需要较少的采样 点就能达到较高的精度．数值算例证明了该方法的有效性．     

近断层危害场的三维并行数值模拟

在采用Metis软件包进行区域分解的基础上,结合大型稀疏矩阵的行压缩存储方式,求解基于预处理共轭梯度法的有限元方程组,开发并行有限元计算程序。对三维地质模型进行计算模拟,得到的张店-仁河断裂近断层地震危害场的位移场数值计算结果表明,该并行程序取得了较好的计算加速比。     

敏度分析的数值方法比较研究

为提高优化方法中敏度计算的精度和效率,比较研究了拟梯度、复数步长微分和自动微分三种数值方法原理及实现.采用操作符重载和模板技术实现复数步长微分和自动微分,并将自动微分前向模式和反向模式结合起来计算Hesse矩阵.研究表明:拟梯度能有效地减少函数求值次数,但对高度非线性函数其计算精度较差;复数步长微分方法简单,能得到机器精度的梯度值,但需要处理复数,计算量较大;自动微分在函数求值的同时并行计算高阶精确导数值,计算量适中.     

用余弦微分求积法数值求解KdV—Burgers方程

采用余弦微分求积法（CDQM）对（1＋1）维非线性KdV—Burgers方程进行了数值求解．结果表明,所得数值解与方程的精确解相比具有明显的高精度且稳定性高,相对于其他常用方法,且公式简单,使用方便;计算量小,时间复杂性好．     

微分域网格变形的GPU加速算法

微分域网格变形方法能够较好的保持网格模型的局部细节特征,但其计算需要耗费较长的时间.结合GPU的高速并行运算性能,设计并实现了一种基于GPU的微分域网格变形算法.通过GPU进行网格的微分坐标求解、线性系统系数矩阵的Cholesky分解、线性系统求解等运算,从而将网格局部细节特征编码和解码过程以及变形结果的绘制完全通过GPU完成.实验结果表明该算法能够有效加速微分域网格变形方法的计算和绘制.     

Differential quadrature domain decomposition method for a class of parabolic equations

In this paper the differential quadrature method (DQM) and the domain decomposition method (DDM) are combined to form the differential quadrature domain decomposition method (DQDDM), in which the boundary reduction technique (BRM) is adopted. The DQDDM is applied to a class of parabolic equations, which have discontinuity in the coefficients of the equation, or weak discontinuity in the initial value condition. Two numerical examples belonging to this class are computed. It is found that the application of this method to the above mentioned problems is seen to lead to accurate results with relatively small computational effort.     

Analysis of 3D frame problems by DQEM using EDQ

The differential quadrature element method (DQEM) and extended differential quadrature (EDQ) have been proposed by the author. The development of a differential quadrature element analysis model of three-dimensional shear-undeformable frame problems adopting the EDQ is carried out. The element can be a nonprismatic beam. The EDQ technique is used to discretize the element-based governing differential equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall algebraic system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the overall algebraic system. Mathematical formulations for the EDQ-based DQEM frame analysis are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained. Numerical results demonstrate this DQEM model.     

PCA-based branch and bound search algorithms for computing K nearest neighbors

In this paper, the efficiency of branch and bound search algorithms for the computation of K nearest neighbors is studied. The most important aspects that influence the efficiency of the search algorithm are: (1) the decomposition method, (2) the elimination rule, (3) the traversal order and (4) the level of decomposition. First, a theoretical derivation of an efficient decomposition method based on principal component analysis is given. Then, different elimination rules and traversal orders are combined resulting in ten different search algorithms. Since the efficiency is strongly dependent on the level of decomposition, this user specified parameter is optimized first. This optimization is realized by a probabilistic model that expresses the total computation time in function of the node traversal cost and the distance computation cost. All comparisons are based on the total computation time for the optimal level of decomposition.     

Domain decomposition method for unstructured meshes in an OpenMP computing environment

In this paper, an efficient unstructured mesh calculation method in an OpenMP parallel computation using multi-core processor is proposed. This is a new domain decomposition method with two characteristics. The first characteristic is to define the size of the sub-block in the computation domain by the size of the cache memory in each core. The second one is to reduce idle time by distributing a defined sub-block for each core appropriately. Using the proposed method, a computation on compressible flow around a plane was able to achieve speed-up more than about 20% in comparison with a conventional method.     

Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method

The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviours of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.     

大规模系统两层递阶控制的直接分解算法

提出一个新的递阶控制的分解协调方法，它是由最优化问题的直接梯度解及性能函数的一个柔性分解组成。通过性能函数分解的自由度得到所需要的混合结构控制律，其下层控制器是闭环控制部分，上层是保证全局系统最优化的开环控制部分，局部性能函数的柔性选取，使两层优化任务的重新划分既能离线计算，也能在线修正。     

多搜索方向共轭梯度法--一种无需整体内积的共轭梯度类方法

§1.引 言 许多大型科学与工程计算问题都归结为大型稀疏线性方程组的求解,因此,在高性能并行计算机高速发展的今天,面向并行计算环境研究大型稀疏线性方程组的高效并行算法显得尤为重要. 对于大型稀疏线性方程组 Ax=b, (1)     

Achieving Scalable Parallel Molecular Dynamics Using Dynamic Spatial Domain Decomposition Techniques

To achieve scalable parallel performance in molecular dynamics simulations, we have modeled and implemented several dynamic spatial domain decomposition algorithms. The modeling is based upon the bulk synchronous parallel architecture model (BSP), which describes supersteps of computation, communication, and synchronization. Using this model, we have developed prototypes that explore the differing costs of several spatial decomposition algorithms and then use this data to drive implementation of our molecular dynamics simulator,Sigma. The parallel implementation is not bound to the limitations of the BSP model, allowing us to extend the spatial decomposition algorithm. For an initial decomposition, we use one of the successful decomposition strategies from the BSP study and then subsequently use performance data to adjust the decomposition, dynamically improving the load balance. The motivating reason to use historical performance data is that the computation to predict a better decomposition increases in cost with the quality of prediction, while the measurement of past work often has hardware support, requiring only a slight amount of work to modify the decomposition for future simulation steps. In this paper, we present our adaptive spatial decomposition algorithms, the results of modeling them with the BSP, the enhanced spatial decomposition algorithm, and its performance results on computers available locally and at the national supercomputer centers.     

Solving 2D-wave problems by the iterative differential quadrature method

In this paper, the numerical stability of an iterative method based on differential quadrature (DQ) rules when applied to solve a two-dimensional (2D) wave problem is discussed. The physical model of a vibrating membrane, with different initial conditions, is considered. The stability analysis is performed by the matrix method generalized for a 2D space-time domain. This method was presented few years ago by the same author as an analytical support to check the stability of the iterative differential quadrature method in 1D space-time domains. The stability analysis confirms here the conditionally stable nature of the method. The accuracy of the solution is discussed too.