Adaptive Strategy for the Damping Parameters in an Iteratively Regularized Gauss–Newton Method

In this paper, a convergence analysis of an adaptive choice of the sequence of damping parameters in the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed operator equations is presented. The selection criterion is motivated from the damping parameter choice criteria, which are used for the efficient solution of nonlinear least-square problems. The performance of this selection criterion is tested for the solution of nonlinear ill-posed model problems.     

Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems

The Davidson method is a preconditioned eigenvalue technique aimed at computing a few of the extreme (i.e., leftmost or rightmost) eigenpairs of large sparse symmetric matrices. This paper describes a software package which implements a deflated and variable-block version of the Davidson method. Information on how to use the software is provided. Guidelines for its upgrading or for its incorporation into existing packages are also included. Various experiments are performed on an SGI Power Challenge and comparisons with ARPACK are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

半无限带状各向异性材料的应力效应衰减估计

对带端面负载的半无限带状各向异性弹性材料建立了Saint-Venant原理.应用能量方法确立了应力效应衰减率的下界,得出了用各向异性材料的弹性常量表示的估计显式.最后,为了说明所得结果,对带端面负载、纤维偏离主轴的石墨-环氧树脂的衰减率给出数值实例.     

求解微分方程初值问题的一种弧长法

对于连续介质力学问题中导出的微分方程初值问题,常常具有解奇异性,如不连续、Ｓｔｉｆ性质或激波间断·本文通过在相应空间,引入一个或数个弧长参数变量,克服解的奇异性·对于常微分方程组引入弧长参数变量后,奇异性得以消除和削弱,应用一般的解常微分方程组的方法（如Ｒｕｎｇｅ＿Ｋｕｔａ法）求解·对于偏微分方程引入弧长参数变量后,在相应的空间离散成常微分方程组,用解奇异性常微分方程组相同的方法即可求解·本文给出了两个算例     

高温、高压、高应变速率动态过程晶体塑性有限元理论模型及其应用

对于高温、高压、高应变速率加载条件下的材料冲击变形行为,动态晶体塑性模型能够直接反映晶体中塑性滑移的各向异性及其对温度、压力和微观组织结构的依赖性,因而广泛应用于材料的动态冲击力学响应、微观结构演化以及动态损伤破坏的模拟。本文综述了高压冲击下动态晶体塑性有限元的理论模型,主要包括变形运动学、包含状态方程的超弹性本构模型和晶体塑性本构模型,涉及位错滑移、相变、孪生等塑性变形机制,以及层裂、绝热剪切带等动态破坏方式。     

Spectral approximation for drainage of an Elastico‐viscous liquid and error analysis

A Fourier‐Galerkin spectral method is proposed and used to analyze a system of quasilinear partial differential equations governing the drainage of liquids of the Oldroyd four‐constant type. It is shown that, Fourier‐Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier‐Galerkin approximations to the system of quasilinear partial differential equations are developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 492–505, 2012     

Identifying the viscoelastic properties of soft matter from the indentation response of a hard film-soft substrate system

The indentation technique is widely used in measuring the mechanical properties of soft matter at the microscale or nanoscale,but still faces challenges by these unique properties as well as the consequent strong surface adhesion, including the strong nonlinear effect, unclear judgment of the contact point, difficulties in estimating the contact area, and the risk of the indenter piercing the sample. Here we propose a two-step method to solve these problems: lay a hard film on a soft matter, and obtain the viscoelastic properties of this soft matter through the indentation response of this composite structure. We first establish a theoretical indentation model of the hard film-soft substrate system based on the theory of plates, elastic-viscoelastic correspondence principle and Boltzmann superposition principle. To verify the correctness of this method, we measure the mechanical properties of the methyl vinyl silicone rubber(MVSR) covered by a Cu nanofilm. Finally, we test the effectiveness and error sensitivity of this method with the finite element method(FEM). The results show that our method can accurately measure the mechanical properties of soft matter, while effectively circumventing the problems of the traditional indentation technique.     

The first excited single-proton resonance in ~(15)F by complex-scaled Green's function method

The complex-scaled Green's function(CGF)method is employed to explore the single-proton resonance in 15F.Special attention is paid to the first excited resonant state 5/2+,which has been widely studied in both theory and experiments.However,past studies generally overestimated the width of the 5/2+state.The predicted energy and width of the first excited resonant state 5/2+by the CGF method are both in good agreement with the experimental value and close to Fortune's new estimation.Furthermore,the influence of the potential parameters and quadruple deformation effects on the resonant states are investigated in detail,which is helpful to the study of the shell structure evolution.     

湍流大气传输中跟踪抖动对远场影响的仿真研究

分析了跟踪抖动对湍流大气传输远场光斑的影响。基于麦克斯韦电磁场理论,采用大气相干长度对大气湍流进行描述,推导了发射光束因跟踪抖动导致光轴偏离的远场表达式。在此基础上,利用相位屏法模拟抖动引起的倾斜相位和大气折射率起伏引起的相位调制,并采用低频补偿的功率谱反演法对传输过程进行了数值仿真。分析了不同跟踪抖动、湍流强度条件下远场光斑质心脱靶量的变化,以及不同尺寸模拟目标的回波概率。分析结果表明,在传输距离为10 km时,强湍流造成的远场光斑脱靶量可达几十μrad;当跟踪抖动较大时,湍流强弱对脱靶量影响差别很小。最后,对一定尺寸的模拟目标,从探测回波概率的角度给出了发射系统跟踪抖动量的控制范围。     

概率盒框架下混合认知不确定声场的响应预测

针对含概率盒-证据混合认知不确定参数声场的响应预测问题,提出了一种概率盒框架下的改进区间蒙特卡洛方法。该方法首先将混合认知不确定参数转换为纯概率盒形式,然后结合有限元方法推导出混合认知不确定声场的盖根鲍尔多项式代理模型,再采用蒙特卡洛方法求解代理模型得到声压响应。以含概率盒-证据混合认知不确定参数的二维管道声场模型和卡车乘客舱声腔模型为例,计算结果表明混合认知不确定参数影响下的声压响应为概率盒形式,其包括声压响应极值和相应的概率信息,并且所提方法较常规混合离散方法效率更优,较基于一阶摄动法的区间蒙特卡洛方法准确性更高。研究结果表明:所提方法可以有效预测混合认知不确定声场的声压响应,并可进行声学性能的风险和保守估计。