解大型非对称特征问题的精化块不完全正交化算法

0引言 块Arnoldi方法~[5]是解大型非对称特征值问题的正交投影方法，然而Jia~[3]的分析表     

模糊随机桁架结构的动力特性双因子分析法

针对模糊随机桁架结构的动力特性分析,提出了一种新的模糊随机有限元方法．当结构的物理参数和几何尺寸同时具有模糊随机性时,利用模糊因子法和随机因子法建立了结构刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构动力特性模糊随机变量的计算表达式;之后利用随机变量的矩法和代数综合法,推导出结构特征值的数字特征的计算式．通过算例分析了模糊随机桁架结构参数的模糊随机性对其动力特性的影响．该方法的优点是能准确反映结构某一参数的模糊随机性对结构特征值及其数字特征的影响．     

流固耦合方程组间断Galerkin方法的探索

主要通过对复杂接触表面问题以及流固耦合方程组中边界间断问题的分析,探讨其间断Galerkin方法的有限元计算.保留有限元线性离散的计算优势,有效地弱化了边界间断对流场中速度的影响,得到流固耦合方程组的空间半离散有限元格式,为数值计算提供了有力的理论支撑.     

非线性特征值问题的二次近似方法

本文研究求解非线性特征值问题的数值方法.基于矩阵值函数的二次近似,将非线性特征值问题转化为二次特征值问题,提出了求解非线性特征值问题的逐次二次近似方法,分析了该方法的收敛性.结合求解二次特征值问题的Arnoldi方法和Jacobi-Davidson方法,给出求解非线性特征值问题的一些二次近似方法.数值结果表明本文所给算法是有效的.     

海上浮式风力机及其动力学问题

深水风资源更为丰富,随着科技进步风电场正逐步向水深百米及以上的海域发展．海上浮式风力机、浮式基础以及系泊系统作业时,受到风浪流等的联合作用．就不同海上浮式风力机形式及其典型结构对应的气动载荷、水动力载荷,浮式风力机系统与环境动力的耦合问题、处理方法和可能的发展方向作了简要的评述．充分考虑作业背景的环境流场和风力机尺度,针对不同的流动特征综合各种理论方法和计算手段,更为准确地进行空气动力学-水动力学-控制系统-结构耦合分析是研究的难点和发展方向.     

非线性特征值的Brauer-型定位集

非线性特征值问题在阻尼结构动力分析,时滞系统稳定性分析,量子点的数值模拟和流固结构振动分析等领域有广泛应用,其特征值对于实际问题的解决至关重要.本文研究非线性特征值的定位问题,通过两行元素和加权技术得到了Brauer-型定位集及其简化形式,证明了其优于已有的结果,并应用其分析一类时滞系统的稳定性.     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

基于GMRES算法的弹性结构强耦合小变形流激振动分析

使用混合广义变分原理,将基于Lagrange表述的小位移变形结构振动问题与基于Euler描述的不可压缩粘性流动问题,统一在功率平衡的框架下建立流固系统的耦合控制方程．用有限元格式做空间离散后,再用广义梯形法将有限元控制方程转化为增量型的线性方程组,该方程组的系数矩阵具有非对称性,其中元素含对流效应和时间因子．将GMRES算法与振动分析的Newmark法和流动分析的Hughes预测多修正法结合,发展成一种基于GMRES-Hughes-Newmark的稳定算法,用于计算具有复杂几何边界的强耦合流激振动问题．以混流式水轮机叶道为数值算例的计算表明,模拟结果与试验实测结果吻合较好．     

一种迭代格式的有限元并行算法*

本文提出了一种求解有限元方程的迭代格式的并行算法.该方法在线性代数方程迭代解法的基础上,引进并行运算步骤;并且运用加权残数方法,通过选择适当的权函数,推导了该并行算法的有限元基本格式.该方法在西安交通大学BLXSI-6400并行计算机上程序实现.计算结果表明它能有效地提高运算速度,减少计算时间,是一种有效的求解大型结构有限元方程的并行算法.     

新的耦合mKdV方程族及其Liouville可积的无限维Hamilton结构

根据第Ⅱ屠格式,从一个特征值问题出发,本文推得了一族新的耦合ｍＫｄＶ方程,然后用迹恒等式人出了其无限维Ｈａｍｉｌｔｏｎ结构。最后证明了该Ｈａｍｉｌｔｏｎ方程族是Ｌｉｏｕｖｉｌｌｅ可积的,并且有无穷多个彼此对合的公共守恒密度。     

The numerical simulation of a typical fluid-structure interaction problem

To determine the dynamic response of a structure under the influence of the fluid flow one must solve a coupled computational fluid dynamics (CFD) and computational structural dynamics (CSD) mathematical problem. This paper presents the comparison of two methods for the calculation of the fluid-structure interaction. The first one is of explicit-implicit type and uses a staggered time advancement of the fluid and structure problems. The second uses a fully implicit discretization in the physical time of the fluid-structure equations and an explicit advancement in the dual-time. The physical fluid-structure problem is accompanied by the equations of the mesh motion, which are written as for a pseudo-structural system with its own dynamics. Representative numerical results are presented for the two degrees of freedom tipical section in unsteady transonic flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new algorithm for total variation based image denoising

We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.     

Convergence of a Lagrangian scheme for a compressible Naviers–Stokes model defined on a domain depending on time

This paper deals with the numerical resolution of the Navier–Stokes equations defined on a time dependent domain. We give an existence result for a fluid-structure interaction problem in which the boundary is governed by a thin plate operator. We propose to solve the fluid equations with the characteristics method. We approach the total derivative with a “regularized” finite difference scheme and we study the convergence of the discrete problem towards the continuous one.     

A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices

Summary In this paper we describe a block version of Arnoldi's method for computing a few eigenvalues with largest or smallest real parts. The method is accelerated via Chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum. A parallel implementation of this method is investigated on the eight processor Alliant FX/80. Numerical results and comparisons with simultaneous iteration on some Harwell-Boeing matrices are reported.     

双层规划问题的一种模式搜索Filter方法

双层规划在工程设计和经济管理中应用广泛,结合模式搜索方法和Filter方法提出了一种解决双层规划问题的算法—模式搜索Filter方法.算法以Filter法思想构造接受准则,以模式搜索提供迭代方向和步长,能够有效的解决一类双层规划问题.     

Eigenvalues of the discretized Navier-Stokes equation with application to the detection of Hopf bifurcations

This paper is concerned with a numerical approach to the problem of finding the leftmost eigenvalues of large sparse nonsymmetric generalised eigenvalue problems which arise in stability studies of incompressible fluid flow problems. The matrices have a special block structure that is typical of mixed finite element discretizations for such problems. The numerical approach is an extension of the hybrid technique introduced by Saad [22] and utilizes the idea of preconditioning the eigenvalue problem before applying Arnoldi's method. Two preconditioners, one a modified Cayley transform, the other a Chebyshev polynomial transform, are compared in numerical experiments on a double diffusive convection problem and the Cayley transform proves superior. The Cayley transform is then used to provide numerical results for the finite Taylor problem.     

ARNOLDI TYPE ALGORITHMS FOR LARGE UNSYMMETRIC MULTIPLE EIGENVALUE PROBLEMS

1.IntroductionTheLanczosalgorithm[Zo]isaverypowerfultoolforextractingafewextremeeigenvaluesandassociatedeigenvectorsoflargesymmetricmatrices[4'5'22].Sincethe1980's,considerableattentionhasbeenpaidtogeneralizingittolargeunsymmetricproblems.Oneofitsgen...     

Pressure Boundary Conditions for Blood Flows

Simulations of blood flows in arteries require numerical solutions of fluid-structure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessels. Among the various simplifications which have been proposed, the surface pressure model leads to a hierarchy of simpler models including one that involves only the pressure. The model exhibits fundamental frequencies which can be computed and compared with the pulse. Yet unconditionally stable time discretizations can be constructed by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls will be shown to be efficient and accurate as an approximation of the full fluid structure interaction problem.     

A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics

A new method for the calculation of fluid-structure interaction (FSI) of highly flexible bodies is presented. This innovative algorithm demonstrates the strong coupling of a commercial computational fluid dynamics code with an in-house coded structural solver. The strong response of the pressure distribution to the displacement can be approximated by a reduced order model for the fluid solver. The Jacobian of this reduced order model is then used in the structural solver to obtain a stable and full implicit iteration scheme. The method is demonstrated on a 2D model of a flexible aortic valve during the cardiac cycle. Furthermore, the model is able to calculate shear stresses on the leaflet.     

直管束流固耦合振动的数值模拟

为了研究反应堆结构中的诸如燃料棒、蒸汽发生器和其它换热器传热管束等的流体-结构交互作用问题,利用有限体积法离散大涡模拟(large eddy simulation, LES)的流体控制方程,用有限元方法求解结构动力学方程,并结合动网格技术,建立三维流体诱发振动的数值模型,模拟直管束中流体的流动及结构振动,实现计算结构动力学(computational structure dynamics, CSD)与计算流体力学(computational fluid dynamics, CFD)之间的联合仿真．首先,基于流固耦合方法对单管的流致振动特性进行了详细分析,得到了其动力学响应与流场特性;其次基于建立的传热管束流致振动计算模型,研究了两并列管、两串列管以及3×3正方形排列管束的流致振动行为．