粘性Burgers方程的高阶隐式WCNS格式

JFNK (Jacobian-free Newton-Krylov)方法是由外层Newton迭代法和内层Krylov子空间迭代法构成的嵌套迭代方法.本文提出了一种基于JFNK方法的高阶隐式WCNS (weighted compact nonlinear scheme)格式,并用于求解一维、二维粘性Burgers方程.外层迭代法采用含参数的多步Newton迭代法,给出了收敛性分析,内层迭代法采用无矩阵GMRES迭代法.粘性Burgers方程的非线性对流项采用五阶WCNS格式计算.为提高方法精度和计算效率,时间离散采用三阶隐式的DIRK (diagonal implicit Runge-Kutta)方法.数值结果表明基于JFNK方法的隐式WCNS格式在时间上能达到三阶精度,与显式TVD Runge-Kutta WCNS方法相比,计算效率更高.此外,基于JFNK方法的隐式WCNS格式稳定性好,且具有良好的激波捕捉能力.     

求解非线性方程组的一种并行算法

提出了一种在分布式环境下求解非线性方程组的并行算法,该算法将Newton迭代法中的Jacobi矩阵进行适当的分裂,使得Newton迭代法具有很好的并行性。并在理论上进行了收敛性分析。在HP rx2600集群上进行的数值实验结果表明并行效率达70%以上。     

基于牛顿迭代法的电力系统非线性谐波状态估计

谐波状态估计为电力系统的谐波监控、抑制和治理提供了依据.在同步相量量测装置配置不可观的条件下,引入数据采集与监控系统量测到的谐波有功功率作为量测量,建立基于混合量测的非线性谐波状态估计的灵敏度数学模型,应用牛顿迭代法进行求解.算例分析表明,谐波状态估计的灵敏度数学模型和牛顿迭代法求解有效,混合量测数据能提高系统谐波状态估计的精度.     

物料平衡及其在炼油企业的应用

物料平衡是炼油企业生产运行和统计的主要业务之一,通过物料平衡,能够清楚地了解全厂物流的走向和收率.炼油企业的物料平衡主要包括生产运行管理需要的装置级平衡和全厂平衡,以及满足生产统计管理需要的物料统计平衡.在现场仪表测量实时数据和手工录入数据的基础上,依据工艺流程、物料路由等条件建立数学模型,通过一定的工具和算法,求解平衡方程,得到平衡结果.通过不同层次平衡结果的应用,可以及时掌握企业生产情况,更好地调整生产和优化生产,降低成本,提高效益.     

一种求解非线性方程组的混合优化算法及程序实现

非线性方程组求解是工程实践与理论研究中的一个典型问题。传统的方法主要有梯度法、Newton迭代法等。该文综合修正Newton法与梯度法的各自优势,对非线性方程组的求解问题提出了一种混合方法并用C语言编码实现该算法。将两种方法相结合,使其相互取长补短,在迭代初始值不太好的情况下也能保证收敛性,同时加快收敛速度,数值结果表明该算法是有效的。     

Newton型方法的推广与改进

对解非线性方程组Newton迭代格式进行了改进,得到了两种比Newton法较为宽松的并且收敛速度较快的新的迭代格式.从而构造了两种新的Newton型迭代法.理论分析和数值实验证明这两种方法是稳定且有效的.     

三聚氰胺工艺的动态仿真

三聚氰胺工艺是化工领域中比较复杂的工艺流程,由于过程的复杂性和不稳定性,实际生产中难以控制,很难建立数学模型进行计算.为解决上述问题,对尿素高压法制备三聚氰胺的过程进行模型化和动态仿真的研究.通过对体系进行物料平衡和能量平衡分析,在可靠的热力学和反应动力学基础上,建立了数学模型,并根据模型的形式选取了适当的数值计算方法求解模型体系,最后完成了本工艺流程的动态仿真.仿真结果与实际生产的工艺参数吻合得较好,验证了模型的正确性.     

月壤力学参数在线估计算法研究

提出了一种基于Guass-Legendre数值积分法和Newton迭代法的新的月壤力学参数估计算法;首先分析行驶在月壤环境下的月球车刚性驱动轮的力/力矩情况,推导出用于力学参数的求解模型;然后采用两点Guass-Legendre数值积分法对模型进行简化;最后结合Newton迭代法和最速下降法求解非线性方程组,依据虚拟六维力/力矩传感器和其它车载传感设备的输出计算出月壤关键力学参数内摩擦角和压陷系数;仿真实验显示该方法是正确和有效的,在高噪声干扰下依然具有较高的准确度,并且该方法具有低计算复杂度,适于月球车进行在线地形参数估计。     

卷烟企业能源平衡调度模型与应用

为实现卷烟企业能源的供需平衡调度,研究了卷烟企业能源平衡调度方法与数学模型.在考虑卷烟企业能源种类多、分时段供应等条件下,建立了以最小化单位最终产品综合能耗和单位最终产品总能源消耗成本为目标的卷烟企业能源平衡调度模型,并构建了一种分段实数编码和基因中间重组操作的改良遗传算法来求解数学模型.某卷烟厂蒸汽平衡调度案例表明:建立的模型和求解算法能较好地解决卷烟企业能源平衡调度,并能有效降低卷烟生产能源2%左右. (Kunming University of Science and Technology, Kunming 650093,China)     

基于遗传算法的电子元器件优化布局

用微元体热平衡法建立电路板上元件温度场求解的数学模型,采用高斯-赛德尔迭代法求解热平衡方程组。用改进的遗传算法对元件布局进行优化设计,仿真实验表明全局优化大大降低了系统的温度应力,提高了系统的可靠性。此外,用Flotherm软件模拟了电路板的温度场,验证了优化布局模型和算法的有效性。     

Approximation of the Crank-Nicholson method by the iterated dynamic-theta method

Choptuik's iterated Crank-Nicholson method has become a popular algorithm for solving partial differential equations in computational physics. We generalize Choptuik's explicit iteration approach to implicit finite difference schemes, by the introduction of a novel method with an iteration step dependent parameter and analyze its stability and computational efficiency.     

Combination of the boundary integral equation method and the extrapolation method

Many numerical methods including the boundary integral equation method start with division of the domain of calculation into intervals. The accuracy of their results can be improved considerably by extrapolation. To be able to apply the extrapolation method it is necessary to know the asymptotic expansion of the error.In this paper the principle of the extrapolation method and subjects important for its application are described. Above all it is shown how to determine the asymptotic expansions numerically by trial and error. In the first sections the matter is explained in a general manner to encourage users of various numerical methods—among them users of the finite element method—to try to extrapolate their results. Then the investigations are exemplified in detail by the boundary integral equation method. The accuracy of approximate solutions of integral equations for plane elastostatic problems with prescribed boundary tractions and displacements is improved by extrapolation. Particular attention is paid to boundary tractions and displacements with discontinuous derivatives.To induce also practically orientated readers without specialized mathematical knowledge to think about applying the extrapolation method the basic topics are represented in an extensive manner and illustrated by simple examples. (For a survey of this paper see end of Section 1.)     

Proof of the equivalence of the Hillert analytical method and the method of orthogonal projection

In this short paper, the equivalence of the Hillert analytical method with the method of orthogonal projection (or the Muggianu method) is rigorously proven.     

Empirical column selection method in the simplex method

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 182–186, July–August, 1995.     

Complexity of the bisection method

The bisection method   is the consecutive bisection of a triangle by the median of the longest side. In this paper we prove a subexponential asymptotic upper bound for the number of similarity classes of triangles generated on a mesh obtained by iterative bisection, which previously was known only to be finite. The relevant parameter is γ/σ$\gamma /\sigma$, where γ$\gamma$ is the biggest and σ$\sigma$ is the smallest angle of the triangle. We get this result by introducing a taxonomy of triangles that precisely captures the behaviour of the bisection method. We also prove that the number of directions on the plane given by the sides of the triangles generated is finite. Additionally, we give purely geometrical and intuitive proofs of classical results for the bisection method.     

New numerical method for the solutions of the MCDF equations based on the CIP method

A new numerical method based on the constrained interpolation profile (CIP) method to solve the Multiconfiguration Dirac-Fock (MCDF) equations is presented. The radial wave functions are represented by the values and the spatial derivatives on an arbitrary grid system, and approximated by cubic polynomials. Owing to this representation, the values and the spatial derivatives of the effective charge distribution and inhomogeneous term are calculated using the previous cycle's wave functions. Then the homogeneous MCDF equations are integrated to obtain two linearly independent solutions, which are used to construct the Green function, by the adaptive stepsize controlled Runge-Kutta method controlling the truncation errors within a prescribed accuracy. The radial wave function is improved by taking the convolution of the Green function and the inhomogeneous term. The effectiveness of this numerical procedure is investigated after implementing it into the relativistic atomic structure code GRASP92.     

A comparison of the balanced matrix method and the aggregation method of model reduction

The balanced matrix method and the aggregation method for model reduction are compared. It is shown that there is a "natural" choice for the aggregated reduced model output matrix that makes the aggregated model comparable to the balanced matrix reduced-order model. This assumes that the eigenvalues retained in the aggregated model are truly dominant and that the orders of the two models are equal. However, there are situations in which the choice of the eigenvalues to be retained in an aggregated model is not obvious. In these cases the balanced matrix method may be superior. The models are compared in two numerical examples.     

Iterative methods improving newton's method by the decomposition method

In this paper, we present a sequence of iterative methods improving Newton's method for solving nonlinear equations. The Adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses. The orders of convergence are derived analytically, and then rederived by applying symbolic computation of Maple. Some numerical illustrations are given.     

Constructing the Lyee method with a method engineering approach

This paper proposes an Evolution driven ME approach aiming to support the evolution of an existing method (the As–Is method) in order to obtain a new method (the To–Be method) better adapted to a given engineering situation and/or satisfying new methodogical requirements. The proposed approach is used in order to evolve the existing Lyee method into a Lyee user driven method.¹