解线性约束优化问题的新锥模型信赖域3法

本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法．论文采用零空间技术消除了新锥模型子问题中的线性等式约束，用折线法求解转换后的子问题，并给出了解线性等式约束优化问题的信赖域方法．论文提出并证明了该方法的全局收敛性，并给出了该方法解线性等式约束优化问题的数值实验．理论和数值实验结果表明新锥模型信赖域方法是有效的，这给出了用新锥模型进一步研究非线性优化的基础．     

强Guass-seidel法求解有限元模型修正问题

有限元模型修正是一类特殊的二次反特征值问题．我们将有限元模型修正看成二次规划问题来解决,并采用非线性Gauss－Seidel方法来求解其相应的Lagrange对偶函数．最后,给山的数值文验说明方法的有效性．     

一类二阶延迟微分方程梯形方法的延迟依赖稳定性分析

本文涉及一类二阶延迟微分方程数值方法的稳定性研究．通过运用边界轨迹法,分析了梯形方法的延迟依赖稳定区域并找到其准确边界．随后建立了解析和数值稳定区域的联系并从理论上证明了梯形方法能完全保持模型问题的延迟依赖稳定性．     

流形上微分方程的算法

流形上微分方程的数值方法,是近十多年发展起来的、当前热门的数值方法．特别是所谓的的李群方法是在动力学问题的需求下诞生的,它能在弯曲的空间中进行离散化,根本不会出现‘违约问题’．人们将它应用到动力学方程模型等,取得了不少成果,应用前景看好．它的出现可以说是20世纪数值数学领域的新成就．本文主要介绍这一新的理论,并提出了许多急待解决的新的课题．     

激波管中动态相变的数值研究

用松弛模型研究了范德瓦流体中的激波管问题．当松弛参数趋于0时模型存在一个确定的黎曼解．在数值方面推导了松弛格式（relaxing）和完全松弛格式（relaxed）．在一维问题中,对于不同的剖面,数值模拟显示结果趋向于黎曼解,在理论上和数值上研究了参数的影响．对于特定的初始激波剖面,观察到了非经典的反射波．在二维问题中,研究了曲面波前的数值演化,得到一些有趣的波斑图．     

广义神经传播方程的A.D.I.有限元分析

广义神经传播方程是神经传播方程的更一般形式，是一类非常重要的非线性发展方程，在生物、力学诸领域有实际背景．有关其解的性质，已有许多讨论I‘－‘］，但数值计算和数值分析方面，还没有研究．而实际当中，研究模型的数值方法和定量计算，往往是非常重要的．本文着重讨论一类具有非线性边值条件的广义神经传播方程的交替方向有限元方法及其数值分析．算法上，采用交替方向有限元，化高维问题为低维问题，在缩减计算量的同时，保持高精确度．分析上，采用Sobolev投影，简化论证，得到理想的稳定性和收敛性结果．1方程模型及有限元数值…     

短纤维复合材料的本征应变边界积分方程计算模型

提出了短纤维复合材料的本征应变边界积分方程计算模型,并采用新发展的边界点法进行了求解．模型依据Eshelby等效夹杂物的概念并借助Eshelby张量,采用迭代方法来计算基体中各种性能短纤维的本征应变,其中所需的Eshelby张量不难通过解析或数值方法获得．由于未知量只出现在边界上,与已有的有限元和边界元模型相比,提出的计算模型可极大地减小异质体问题的求解规模,提高计算效率．通过数值算例计算了代表性体积单元上各种短纤维复合材料的整体弹性性能,验证了计算模型和求解方法的正确性和有效性．     

服从OldroydB型微分模型的粘弹性流体问题的数值解法

本文对服从OldroydB型微分模型的粘弹性流体问题给出了一种数值逼近算法．该算法对压力方程采用标准混合有限元方法,对速度方程采用并行非重叠区域分解方法和特征线法．这种并行算法在子区域上用Galerkin方法,通过积分平均方法显式地给出内边界的数值流．在本文最后还给出了该算法的最优L^2。一误差估计．     

Navier—Stokes方程区域分解法的收敛性

０引言区域分解方法是近年来迅速发展的偏微分方程数值方法．区域分解方法及其收敛性的研究大多是在线性偏微分方程下得到的,对于非线性问题,经典的技巧在收敛性证明时遇到了困难．流体计算是一个较为复杂的非线性问题,数值模拟过程中因节点多．网格复杂,所以计算量很大．由于区域分解方法不但可以缩小求解规模,进行并行计算,而且可以在不同区域选取不同离散方法和模型,因此对Ｎ－Ｓ方程区域分解方法的研究会有较高的实用价值,也可以对其它非线性问题数值方法研究提供新的途径．本文首先给出了Ｎ－Ｓ方程的最优控制方法以及一些重要…     

微分本构粘弹性轴向运动弦线横向振动分析的差分法

给出了微分本构粘弹性轴向运动弦线横向振动数值仿真的一种差分法．文中建立了具有微分本构的粘弹性运动弦线的横向振动模型;通过对系统的控制方程和本构方程在不同的分数节点离散,得到一种新的差分方法．利用这一方法,弦线振动方程的数值计算过程可以交替地显式进行,且有较小的截断误差和好的数值稳定性．与通用的方法比较,新的方法计算简单、方便．文中利用方程的不变量检验了数值结果的可靠性,并利用这一方法给出了一类弦线模型的参数振动分析．     

渗流问题灰色数值模型的解法研究

灰色数值模型的求解是研究灰色数值模型的一个重要问题 .本文根据灰集合、灰数及其灰色运算规则 ,在渗流系统的基本灰色数值模型的基础上 ,分析了求解这类模型的一整套灰色数值算法 ,并对灰色数值算法、普通算法和经典数值方法的计算结果进行了全面比较 ,论证了灰色数值算法对灰信息传递的正确性和对渗流系统描述的合理性 .     

Identification of constitutive parameters for fractional viscoelasticity

This paper develops a numerical model to identify constitutive parameters in the fractional viscoelastic field. An explicit semi-analytical numerical model and a finite difference (FD) method based numerical model are derived for solving the direct homogenous and regionally inhomogeneous fractional viscoelastic problems, respectively. A continuous ant colony optimization (ACO) algorithm is employed to solve the inverse problem of identification. The feasibility of the proposed approach is illustrated via the numerical verification of a two-dimensional identification problem formulated by the fractional Kelvin–Voigt model, and the noisy data and regional inhomogeneity etc. are taken into account.     

Interactive Solution Approach to a Multiobjective Optimization Problem in a Paper Machine Headbox Design

A successful application of the interactive multiobjective optimization method NIMBUS to a design problem in papermaking technology is described. Namely, an optimal shape design problem related to the paper machine headbox is studied. First, the NIMBUS method, the numerical headbox model, and the associated multiobjective optimization problem are described. Then, the results of numerical experiments are presented.     

Parameter identification in multistage population dynamics model

We present a numerical analysis to solve a parameter identification problem. We identify the demographical parameters of a multistage population dynamics model (Ainseba et al., 2011 [12]). Our nonlinear optimization problem with constraints is solved by a Quasi-Newton method. The convergence proof of this numerical method is performed here. Some numerical applications of it are also given at the end of the paper.     

Exact controllability of a spherical cap: Numerical implementation of HUM

This paper deals with the numerical implementation of the exact boundary controllability of the Reissner model for shallow spherical shells (Ref. 1). The problem is attacked by the Hilbert uniqueness method (HUM, Refs. 2–4), and we propose a semidiscrete method for the numerical approximation of the minimization problem associated to the exact controllability problem. The numerical results compare well with the results obtained by a finite difference and conjugate gradient method in Ref. 5.This work was done when the first two authors were at CNR-IAC, Rome, Italy as Graduate Students.     

Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology

In this work adaptive and high resolution numerical discretization techniques are demonstrated for solving optimal control of the monodomain equations in cardiac electrophysiology. A monodomain model, which is a well established model for describing the wave propagation of the action potential in the cardiac tissue, will be employed for the numerical experiments. The optimal control problem is considered as a PDE constrained optimization problem. We present an optimal control formulation for the monodomain equations with an extra-cellular current as the control variable which must be determined in such a way that excitations of the transmembrane voltage are damped in an optimal manner.The focus of this work is on the development and implementation of an efficient numerical technique to solve an optimal control problem related to a reaction-diffusions system arising in cardiac electrophysiology. Specifically a Newton-type method for the monodomain model is developed. The numerical treatment is enhanced by using a second order time stepping method and adaptive grid refinement techniques. The numerical results clearly show that super-linear convergence is achieved in practice.     

振动杆有限差分模型的一类特征值反问题

1引言杆是重要的工程构件之一,具有分布质量的杆的纵向振动由下面的偏微分方程描述:     

离散椭球分布下两阶段WCVaR风险利润优化模型及应用

本文研究随机变量非完全分布下的两阶段风险-利润优化问题。采用最坏情况下条件风险(Worst-case Conditional Value-at-Risk:WCVaR) 度量指标,在离散椭球分布下建立了两阶段WCVaR 约束下利润期望最大优化模型,运用优化对偶方法将复杂的Max-Min 结构化简,理论上证明了简化模型和原模型的同解性,以发电商电能分配组合优化为数值实例,验证了模型和计算方法的有效性。     

Spectral Method for the Black-Scholes Model of American Options Valuation

In this paper, we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model. The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocation method based on graded meshes. For the other spatial domain boundary, an artificial boundary condition is applied to the pricing problem for the effective truncation of the semi-infinite domain. Then, the front-fixing and stretching transformations are employed to change the truncated problem in an irregular domain into a one-dimensional parabolic problem in [−1,1]. The Chebyshev spectral method coupled with fourth-order Runge-Kutta method is proposed for the resulting parabolic problem related to the options. The stability of the semi-discrete numerical method is established for the parabolic problem transformed from the original model. Numerical experiments are conducted to verify the performance of the proposed methods and compare them with some existing methods.     

Direct solution method for the equilibrium problem for elastic stents

We are interested in numerical methods for approximating vector‐valued functions on a metric graph. As a model problem, we formulate and analyze a numerical method for the solution of the stationary problem for the one‐dimensional elastic stent model. The approximation is built using the mixed finite element method. The discretization matrix is a symmetric saddle‐point matrix, and we discuss sparse direct methods for the fast and robust solution of the associated equilibrium system. The convergence of the numerical method is proven and the error estimate is obtained. Numerical examples confirm the theoretical estimates.