Generalized Aggregation Multilevel solver

The paper presents a Generalized Aggregation Multilevel (GAM) solver, which automatically constructs nearly optimal auxiliary coarse models based on the information available in the source grid only. GAM solver is a hybrid solution scheme where approximation space of each aggregate (group of neighbouring elements) is adaptively and automatically selected depending on the spectral characteristics of individual aggregates. Adaptive features include automated construction of auxiliary aggregated model by tracing ‘stiff’ and ‘soft’ elements, adaptive selection of intergrid transfer operators, and adaptive smoothing. An obstacle test consisting of nine industry problems, such as ring–strut–ring structure, casting setup in airfoil, nozzle for turbines, turbine blade and diffuser casing as well as on poor conditioned shell problems, such as High Speed Civil Transport, automobile body and canoe, was designed to test the performance of GAM solver. Comparison to the state of the art direct and iterative (PCG with Incomplete Cholesky preconditioner) is carried out. Numerical experiments indicate that GAM solver possesses an optimal rate of convergence by which the CPU time grows linearly with the problem size, and at the same time, robustness is not compromised, as its performance is almost insensitive to problem conditioning. © 1997 John Wiley & Sons, Ltd.     

High-performance multilevel iterative aggregation solver for large finite-element structural analysis problems

The present study is aimed to overcome difficulties faced with industrial applications of multilevel iterative methods to arbitrary finite element (FE) structural analysis problems. The coarse grid concept, used in multigrid methods, is substituted with an aggregation coarse model based on the mechanical principle. On the base of this approach together with previously developed multilevel preconditioner, an efficient iterative equation solver FEAGS was developed for using in standard comprehensive finite element software systems. Numerical examples for analyses of three-dimensional (3-D) frame structures demonstrate the efficiency of the method. Comparison with incomplete Cholesky conjugate gradient (ICCG) method and direct methods is presented.     

RVE-based multilevel method for periodic heterogeneous media with strong scale mixing

A Representative Volume Element based multilevel (multigrid) solution method for wave propagation problems in periodic heterogeneous media is developed. The intergrid transfer operators are constructed from the solution of the Representative Volume Element (RVE) problem. It is shown that the convergence of the RVE-based multilevel method improves with increasing material heterogeneity and decreasing time integration step. Numerical results confirm theoretical estimates.     

基于多层次迭代修正的纤维增强复合薄壁截顶圆锥壳振动响应分析

提出了一种纤维增强复合薄壁截锥壳的振动响应分析模型。针对纤维增强复合薄壁截锥壳的结构特点,考虑基础激励载荷方向与母线的夹角、纤维铺层方向与x轴的夹角,利用板壳振动理论、复弹性模量等方法对所研究结构进行了理论建模。利用双向梁函数法表示振型函数,并通过能量法和模态叠加法对其固有特性和振动响应进行求解。为了验证模型的正确性,基于自行搭建的振动测试平台,以TC300/环氧树脂基纤维增强复合薄壁截锥壳为对象,进行了振动特性测试。为减小因样件加工时产生的材料参数误差影响,开发了二分粒子群迭代法对材料参数进行修正。研究发现,测试结果与理论计算获得的共振响应误差最大不超过3.0%,验证了所提出的理论模型与计算方法的正确性和有效性。     

Coarse division transform based preconditioner for boundary element problems

This paper is devoted to the development of efficient preconditioners for an iterative solution of equation sets arising in the Boundary Element Method (BEM). A standard collocation system of equations is transformed to a new basis associated with an auxiliary coarse division model for boundary unknowns and solved in this basis. New systems have rapidly decreasing coefficients and by neglecting a large number of them it is possible to construct readily invertible, sparse preconditioners for iterative procedures. The specific features of the transformed matrix can be attributed to the analytical properties of integral equations. Although the transformation is based on an auxiliary coarse division model, it does not require any additional operations with boundary elements. All manipulations necessary to construct the mapping are performed on the level of algebraic equations. Numerical experiments included in the paper confirm a high rate of convergence of the developed iterative scheme.     

线性回归模型中的递推辨识及其应用

摘要：因机械系统振动响应离散差分方程可以改写为关于结构模态参数的线性回归形式,对于此线性回归形式中的结构模态参数的辨识问题可转化为系统辨识理论中线性回归模型的未知参数矢量的辨识估计问题。当系统对象在白噪声激励下,常规的最小二乘辨识法可以给出参数估计的无偏估计。当系统对象在有色噪声作用下,在常规最小二乘辨识法的基础上提出一种新的可分离迭代最小二乘辨识法。在缺乏关于噪声的统计先验信息,仅有噪声为未知但有界的情况下,提出一种带死区的最小二乘辨识法,该辨识法不仅能给出未知参数矢量的一致性无偏估计,而且还能保证参数估计值逐渐向真值靠拢,任何相邻两估计值之间的逼近程度远远小于噪声的上界。在有界噪声出现的情况下,该算法的鲁棒性可以通过在参数修正方程中引入死区的方法来增强。最后用理论上的仿真算例和弹簧-质量-阻尼系统的振动响应来验证两方法的有效性和可行性。     

Perturbation Bounds and Condition Numbers for a Complex Indefinite Linear Algebraic System

We consider perturbation bounds and condition numbers for a complex indefinite linear algebraic system, which is of interest in science and engineering. Some existing results are improved, and illustrative numerical examples are provided.     

标准综合贡献评估指标体系及验证

本文以现代系统论为基础,从"标准系统"的观点出发,尝试建立了"标准综合贡献评估指标体系",并结合100家上海现代农业、汽车制造、食品生产加工企业的调查数据,对这3个典型行业中重点企业的标准综合贡献进行了定量分析,从而实现对该指标体系的实证。     

可对称化不定非线性问题的不精确Newton法

本文讨论了处理可对称化不定问题的不精确Newton方法,并针对问题的特殊结构提出了不精确Newton-PSMINRES算法。理论分析与数值试验表明,Newton-PSMINRES算法优于其它处理可对称化不定问题的不精确Newton-Krylov算法。     

绿色包装设计的多层次灰色综合评价模型

绿色包装是有效解决包装与环境关系的主要途径,对绿色包装设计方案的定量评价是其中重要问题.多层次灰色综合评价方法考虑了所有评价因素的影响,能保留各层次评价过程中的全部信息.为了科学地评价绿色包装设计方案的优劣,依据其评价指标体系,采用多层次灰色综合评价模型对其给出客观评价.     

Performance of a Petrov–Galerkin algebraic multilevel preconditioner for finite element modeling of the semiconductor device drift‐diffusion equations

This study compares the performance of a relatively new Petrov–Galerkin smoothed aggregation (PGSA) multilevel preconditioner with a nonsmoothed aggregation (NSA) multilevel preconditioner to accelerate the convergence of Krylov solvers on systems arising from a drift‐diffusion model for semiconductor devices. PGSA is designed for nonsymmetric linear systems, Ax=b, and has two main differences with smoothed aggregation. Damping parameters for smoothing interpolation basis functions are now calculated locally and restriction is no longer the transpose of interpolation but instead corresponds to applying the interpolation algorithm to A^T and then transposing the result. The drift‐diffusion system consists of a Poisson equation for the electrostatic potential and two convection–diffusion‐reaction‐type equations for the electron and hole concentration. This system is discretized in space with a stabilized finite element method and the discrete solution is obtained by using a fully coupled preconditioned Newton–Krylov solver. The results demonstrate that the PGSA preconditioner scales significantly better than the NSA preconditioner, and can reduce the solution time by more than a factor of two for a problem with 110 million unknowns on 4000 processors. The solution of a 1B unknown problem on 24 000 processor cores of a Cray XT3/4 machine was obtained using the PGSA preconditioner. Copyright © 2010 John Wiley & Sons, Ltd.