解最小二乘问题GSOR方法中最优参数的确定

在求解最小M乘问题的广义超松驰方法（GSOR）中,主要涉及到预条件矩阵P的选取,加速参数的选取以及矩阵向量计算．讨论了在预条件矩阵P选定之后,如何选取加速参数才能使收敛速度最快,并且给出一个数值实验,可以看出,理论分析与实际效果是统一的．     

以对称反对称分裂预条件处理GMRES(m)的不精确牛顿法潮流计算

针对大规模电力系统修正方程式高度稀疏的特点,研究了一种基于对称反对称预处理的不精确牛顿法。利用矩阵的对称反对称分裂,提出一种新的预处理子,并将其与GMRES(m)算法相结合,改进潮流计算的收敛性和收敛速度。IEEE300节点系统的计算结果验证了所提算法的有效性。     

优化牛顿-拉夫逊算法雅可比矩阵的正交预处理方法研究

预处理雅可比矩阵可以大大改善潮流计算方程的收敛性和速度,而寻找有效的预处理方法则是关键。研究了预处理的基本原理,以最低条件数为主要依据,提出正交方法预处理雅克比矩阵,相对于目前较为流行的P-Q分解法,理论上更加简单且操作方便。借助Matlab仿真工具,预处理几个典型的IEEE多节点系统,验证了正交预处理方法相对P-Q方法,计算时间更短但具备相当的有效性和适用范围。     

油藏数值模拟中BILU0-GMRES方法的应用

在油藏数值模拟中通常需要将数学模型转化为大规模线性方程组,求解这些方程组将耗费大量的时间。考虑到黑油模型的物理特性,将其在油藏节点上离散得到的子阵视为构成系数矩阵的基本元素,利用块不完全LU0(BILU0)预处理方法与块广义极小残量法(BGMRES)相结合,迭代求解方程组得到BILU0-GMRES方法。该方法具有更强的稳定性和收敛性,它能提高系数矩阵迭代的速度,减少迭代收敛的次数,并且矩阵规模越大,这种优势越明显。对严重非均质边底水油藏SPE9的测试结果表明,块预处理GMRES方法具有较高的精度,能够准确模拟油藏的开发过程并对生产动态作出预测。     

非静力模式GRAPES的预条件技术研究

GRAPES是中国气象科学研究院研制的一个非静力格点模式,该模式以大气运动的全可压运动方程为基础,采用半隐半Lagrange方案。在模式积分中,每个时间步需要求解关于气压梯度力的三维离散Helmholtz方程,该方程组的求解在整个数值模拟时间中占70%左右,为加速求解过程,采用高效预条件技术是必然选择。将提出的多行双门槛不完全分解预条件与国内外常用的多种其他预条件技术进行了比较,同时,考查了针对不完全分解预条件的加性Schwarz与基于因子组合的两种并行化预条件技术,结果发现,多行双门槛不完全分解预条件优于包括ILUT在内的其他不完全分解预条件,且加性Schwarz略优于基于因子组合的并行预条件技术。     

CPU-GPU混合计算构架在岩土工程有限元分析中的应用

计算机技术的快速发展促进了岩土工程数值模拟技术的进步和有限元仿真技术的应用。对于三维有限元建模,有限元离散所获得的线性方程系统规 模较大,这些线性方程系统的求解通常支配着整个有限元计算的时间。为了提高有限元求解的效率,需要采用先进的基础迭代算法和高性能计算构架。使用 性价比较高的GPU计算硬件对目前流行的预处理Krylov子空间迭代法进行了加速,重点研究了GPU对Krylov子空间迭代过程中矩阵矢量乘积的加速效果。由于 预处理迭代方法的计算性能依赖于计算构架,采用数值算例对几种流行的预处理迭代方法在不同计算构架下的计算性能进行了评测,对在不同计算构架下采 用何种预处理迭代方法给出了相应的建议。     

A Block Diagonal Preconditioner for Generalised Saddle Point Problems

A lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.     

A scalable multi‐level preconditioner for matrix‐free µ‐finite element analysis of human bone structures

The recent advances in microarchitectural bone imaging disclose the possibility to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. Coupling these imaging possibilities with microstructural finite element (µFE) analysis offers a powerful tool to improve bone stiffness and strength assessment for individual fracture risk prediction. Many elements are needed to accurately represent the intricate microarchitectural structure of bone; hence, the resulting µFE models possess a very large number of degrees of freedom. In order to be solved quickly and reliably on state‐of‐the‐art parallel computers, the µFE analyses require advanced solution techniques. In this paper, we investigate the solution of the resulting systems of linear equations by the conjugate gradient algorithm, preconditioned by aggregation‐based multigrid methods. We introduce a variant of the preconditioner that does not need assembling the system matrix but uses element‐by‐element techniques to build the multilevel hierarchy. The preconditioner exploits the voxel approach that is common in bone structure analysis, and it has modest memory requirements, at the same time robust and scalable. Using the proposed methods, we have solved in 12min a model of trabecular bone composed of 247 734 272 elements, yielding a matrix with 1 178 736 360 rows, using 1024 CRAY XT3 processors. The ability to solve, for the first time, large biomedical problems with over 1 billion degrees of freedom on a routine basis will help us improve our understanding of the influence of densitometric, morphological, and loading factors in the etiology of osteoporotic fractures such as commonly experienced at the hip, spine, and wrist. Copyright © 2007 John Wiley & Sons, Ltd.     

Neuroprotective Effects of Ischemic Preconditioning and Postconditioning on Global Brain Ischemia in Rats through the Same Effect on Inhibition of Apoptosis

Transient forebrain or global ischemia induces neuronal death in vulnerable CA1 pyramidal cells with many features. A brief period of ischemia, i.e., ischemic preconditioning, or a modified reperfusion such as ischemic postconditioning, can afford robust protection of CA1 neurons against ischemic challenge. Therefore, we investigated the effect of ischemic preconditioning and postconditioning on neural cell apoptosis in rats. The result showed that both ischemic preconditioning and postconditioning may attenuate the neural cell death and DNA fragment in the hippocampal CA1 region. Further western blot study suggested that ischemic preconditioning and postconditioning down-regulates the protein of cleaved caspase-3, caspase-6, caspase-9 and Bax, but up-regulates the protein Bcl-2. These findings suggest that ischemic preconditioning and postconditioning have a neuroprotective role on global brain ischemia in rats through the same effect on inhibition of apoptosis.     

低压配电用SPD动作负载试验研究

依据IEC61643-1:2005中7.6.4的规定,对Ⅰ、Ⅱ级电涌保护器进行动作负载试验中的确定续流大小的预备性试验与动作负载预处理试验时的现象,通过对冲击相角、施加不同Uc值、SPD(SPD,surge protection devices)设计结构等的分析,提出①Ⅰ、Ⅱ级电涌保护器在动作负载试验中最易出现续流或者燃烧爆炸等危险现象的相角为40°～60°和220°～240°,而并不是90°和270°;②试验时施加的Uc值对试验现象起着重要作用,Uc越小试品越不易产生续流等现象,Uc越大越易产生续流等;③内部使用铜织带作为连接结构的SPD,在试验过程中,铜织带或因过长、或因高低压连接点距离太近等结构因素产生高压端铜织带被电动力打断等现象;④通过对相角和不同Uc的分析,提出了一种利用Uc的变化率(K)及K.Usinθ来对确定续流与预处理试验中最易发生续流相角进行解释。这对工程师对理解Ⅰ、Ⅱ级电涌保护器进行动作负载试验时的试验现象提供了试验和理论支持,并为SPD设计者提供了修整思路,具有一定的工程意义。