基于非结构三角网格的两种自适应技术研究

实现两种基于无结构Delaunay三角网格的自适应方法,并且把两种方法分别应用于求解一个典型的二维溃坝问题,同时对两种方法的数值结果和稳定性进行比较。数值结果表明两种方法对提高数值解的精度和调整问题求解区域的剖分起到明显的作用。     

基于快速汉克尔变换数值求解波方程

1．引言波方程是三大类偏微分方程中的一大类方程，即所谓双曲型偏微分方程，在解决实际问题时极为常见，会经常碰到．比如激光和微波在线性或非线性介质中的传播问题、大气中的声学问题等都要用到波方程．虽然对波方程的数值求解已经研究得很多，但在实际应用中有不同的具体情况，因此仍有必要对方程数值求解方法进行探索．差分法和有限元法是数值求解偏微分方程的两种常用方法，对波方程也不例外．在实际应用中，首先考虑到这两种方法，但显式差分格式对步长有较苛刻的要求，而有限元法是比较复杂的，本征模式（拉盖尔一高斯模）展开法对…     

一种基于设计模式的三阶段并行程序设计方法

并行程序的可编程性是并行计算的难点之一，使用传统的方法对非数值问题进行并行求解则更加困难。通过对设计模式概念的扩展，定义了算法模式与结构模式，以此为基础提出了一种基于设计模式的三阶段并行程序设计方法，并通过算法模式库与结构模式库实现对该方法的系统支持，该方法不仅可有于一般的数值问题求解，而且在处理复杂的非数值问题时与传统方法相比要简单得多，通过一个简单的数值问题和一个复杂非数值问题作为实例说明了使用这一方法进行问题并行求解与并行程序设计的过程。     

基于Bang-Bang原理的时间最优控制问题求解

时间最优控制是工程实践中经常遇到的一类最优控制问题。对于较简单的时间最优控制问题可以应用古典变分法和庞特里雅金最大值原理进行分析求解。但在实际问题中，能求得解析解的仅是少数。因此，有必要寻求一种能够有效求解时间最优控制问题的数值方法。在分析时间最优控制问题已有求解方法优缺点的基础上，提出基于Bang—Bang原理和参数最优化方法（遗传算法-单纯形法）相结合求解一类仿射系统的时间最优控制问题的方法。对线性阻尼振子问题进行了数值仿真，结果表明该方法效果良好。     

一种基于Lagrangian松弛法求解化工批处理过程调度的方法

提出一种快速求取化工批处理过程次优调度的方法，通过约束变换，引入操作批量的函数和松弛物料贮存能力，将调度问题分解为一个两层次的优化问题，用动态规划求解下层问题，用次梯度求解上层对偶问题，然后依据对偶问题的解，以启发方式构作原问题的可行解。数值测试结果了该方法的有效性和实用性。     

点电源场中垂直接触带地表节点电位求解分析

节电电位的求解在地球物理正反演中都有重要的作用。作为地球物理计算中常用的两种方法，数值解和解析解各有特点，以求节点电源场中垂直接触带地表节点电位为例，基于FORTRAN语言编写程序，分别用解析计算法和数值计算法进行求解，并对求解结果进行精度比较，以确定解析计算法的准确性和可用性，从而确定了一种效率更高的计算方法。     

Excel在热传导问题数值解法教学中的应用探讨

文章通过实例介绍了应用Excel解决热传导问题数值解法的具体计算方法.给出的实例包括迭代求解和直接求解两种方法.在教学中,利用Excel软件演示热传导问题的数值求解过程,高效直观,这对拓宽学生的视野,提高他们学习软件及传热学知识的兴趣,具有很好的实际应用价值.     

利用计算机仿真与系统辨识求解导弹弹道轨迹

提出了求解某武器系统导弹弹道轨迹的两种方法，计算机仿真和系统辨识方法，详细介绍了导弹系统的计算机仿真模型，并利用控制理论和数值分析的方法对仿真模型求解，根据系统辨识理论，将整个系统看作“黑箱”建立与输入，输出数据等价的模型，引入折息因子对模型进行辨识，最后分别给出了计算机仿真试验曲线和系统辨识试验曲线，证明了两种求解方法的有效性。     

SMB色谱模型数值计算的时空守恒元解元方法

为了探寻出一种求解SMB色谱模型的快速数值求解方法,并试图通过比较得出时空守恒元/解元(CE/SE)方法确实是快速数值求解方法,因而采用该方法对SMB色谱模型进行数值求解,并在数值方法的计算效率和精确度两个方面与有限差分法和正交配置有限元法进行了比较,最终得出了CE/SE方法是具有高计算效率和高精确度特性的快速数值求解方法.通过两个实例的模拟仿真,结果表明了该方法在高计算效率和高精确度方面的优越性.     

有等式约束优化问题的粒子群优化算法

目前大多数粒子群优化算法针对无约束优化问题或不等式约束优化问题，求解有等式约束优化问题的方法是把每个等式约束变成两个不等式约束，这种方法的缺点是在进化过程中粒子位置很难满足等式约束条件，影响了收敛速度和解的精度。提出了求解有等式约束优化问题的两种新粒子群优化算法，数值试验结果表明，算法是有效的。     

一种高数值精度的P3P问题半闭式解法*

根据有限数目的参考点,通过二维单目观测图像估计三维目标的姿态参数(又称PnP问题,perspective-n-point)是计算机视觉研究中的一个经典难题。当参考点的数目n<6时,PnP问题为高度非线性问题并可能存在多个可行解。目前求解PnP问题的方法主要分为迭代解法和闭式解法两类。迭代解法数值精度高,但是只能收敛到多解中的一个解,无法同时得到全部可行解;闭式解法的优点是可以一次得到全部可行解,但是现有算法在数值精度和数值稳定性上要逊于迭代解法。针对以上问题,以P3P问题为研究对象,提出一种可以同时得到全部可行解并具有高数值精度的半闭式解法,并通过详细的实验验证该方法的有效性。     

Dual analysis for heat exchange: Application to thermal bridges

The research presented in this article is a contribution to the characterization of thermal dual analysis.The aim of a dual analysis based on two complementary numerical methods is to calculate the stationary temperature field. The two methods are respectively the classical Kinetically Admissible (KA) finite element or temperature method, and the Statically Admissible (SA) flow method.The originality of this work is twofold. First, it uses a flow approach (SA) in 2D and 3D that naturally respects flow conservation (in contrast to the KA method). Second, calculating the dissipation energy allows the exact solution of a problem to be enclosed, with the lower and upper bounds being calculated respectively by the KA and SA methods.Thermal bridges are areas of risk in the building walls, because they can give rise to uncontrolled increments in heat transfer. A number of studies have looked at thermal bridges, but much of the numerical code for building energy simulations uses heat transfer models based on one-dimensional heat flow analysis. Fabrizio Ascione (2014) showed that this can lead to unreliable results. The originality of this paper is to consider 2D and 3D thermal bridges using dual analysis with mesh sizes smaller than those used in conventional finite element approaches.     

基于结合扩展精度技术的基本解方法的非线性功能梯度材料热传导问题求解

采用基本解方法结合扩展精度技术和Kirchhoff变换求解功能梯度材料的二维热传导问题.在求解瞬态热传导问题时运用Laplace变换处理时间变量,将时域问题转化为频域问题求解;采用基本解方法计算得到高精度的频域数值解,再分别采用Stehfest和Talbot这2种数值Laplace逆变换恢复原瞬态热传导问题的计算结果.通过3个非线性功能梯度材料的稳态和瞬态热传导基准算例,分析结合扩展精度技术的基本解方法的计算精度与扩展精度位数、边界布点数和虚拟边界参数三者之间的关系.比较Stehfest和Talbot这2种数值Laplace逆变换算法的优劣.采用结合扩展精度技术的基本解方法数值研究热传导系数随位置剧烈变化的功能梯度材料热传导行为.数值结果表明该方法具有求解精度高、适用性好等特点,能高效模拟非线性功能梯度材料的二维稳态与瞬态热传导行为.     

New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue

In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.     

Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods

New implicit iterative methods are presented for the efficient numerical solution of non-linear elliptic boundary-value problems. Isomorphic iterative schemes in conjunction with preconditioning techniques are used for solving non-linear elliptic equations in two and three-space dimensions. The application of the derived methods on characteristic 2D and 3D non-linear boundary-value problems is discussed and numerical results are given.     

基于边界元法的二维VLSI版图电容提取

文章中提出了一种用边界元法计算ＶＬＩＳ版图电容的方法，它通过求解二维Ｌａｐｌａｃｅ方程，直接得到包括寄生电容在内的版图电容的值。与其它计算电容的数值方法相比，该方法数据准备简单，占有内存少，计算效率高，并且有较高的精度。     

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier–Stokes equations. Second, it reports numerical simulation results for 1D shock tube problem, 2D impinging jet and 2D/3D broken dam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems.     

Modal Hermite spectral collocation method for solving multi-dimensional hyperbolic telegraph equations

The present research is contemplated proposing a numerical solution of multi-dimensional hyperbolic telegraph equations with appropriate initial time and boundary space conditions. The truncated Hermite series with unknown coefficients are used for approximating the solution in both of the spatial and temporal variables. The basic idea for discretizing the considered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) telegraph equations is based on the collocation method together with the Hermite operational matrices of derivatives. The resulted systems of linear algebraic equations are solved by some efficient methods such as LU factorization. The solution of the algebraic system contains the coefficients of the truncated Hermite series. Numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme. Comparisons of numerical results associated to the proposed method with some of the existing numerical methods confirm that the method is accurate and fast experimentally.     

H∞ Static Output Feedback Control of 2‐D Discrete Systems in FM Second Model

The problem of H_∞ static output feedback (SOF) control of two‐dimensional (2‐D) discrete systems described by the Fornasini‐Marchesini (FM) second model is investigated in this paper. First, by applying the 2‐D Bounded Real Lemma, the 2‐D H_∞ SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). Then, by combining the slack variable technique with two kinds of existing LMI methods, respectively, less conservative sufficient LMI conditions are proposed for the BMI formulation. The relation of these two kinds of LMI conditions are revealed by analyzing the choices of coordinate transformation matrices involved in the first kind of LMI conditions. Finally, a numerical example is provided to demonstrate the effectiveness and merits of the proposed methods.