数值算法

There are six forming methods throughcombining three different types of elements, among them, thereare four forming methods which have emblematize andpracticability: multi-point die forming、half multi-point die forming、multi-point alternating forming、half multi-point alternating forming.

对有限元模型建立及数值模拟关键算法和参数的研究在进行薄板类件多点成形的有限元分析中，涉及两类边界条件，一类是载荷，另一类是运动约束。

The experimentative result of the three common testing functions shows the validity of the algorithm.

对三个常用测试函数的数值仿真结果显示了该算法的有效性。

A method of computing rifle explorator solid contour curve;2. Real-Time Ensuring Technology in Artillery Rifle Manufacturing;3. It takes a long period to design an electrochemical machining cathode for machining the mixed rifle with large spiral angle and the experiments are difficult.

针对火炮炮管大缠角混合膛线电解加工中阴极研制周期长、设计难度大的问题，采用Visual C++对阴极工作齿按弹道方程运动生成膛线的过程进行了数值模拟，建立了阴极工作齿的三维模型和膛线加工模型，给出了该模型的求解算法。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

In theory, this kind of interferometer can divide the parasitic interferential signal, meanwhile, it has nonlinear error.

在计算过程中，对时域采样数值进行加权，然后采用多步移相算法进行位相计算，可以有效地抑制谐波误差的影响。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

Fast Multipole Algorithm is a newly proposed promising numerical solver for two-and three-dimensional integral equations in ...

快速多极算法是一种十分有前途的适合电大目标电磁特性分析的数值计算方法。

Fast Multipole Algorithm is a newly proposed promising numerical solver for two-and three-dimensional integral equations in electromagnetic scattering problem.

快速多极算法是一种十分有前途的适合电大目标电磁特性分析的数值计算方法。

AQMC algorithm progresses in the nondifferentiable optimization. First, we develop the local search such that the search direction, search radius and number of search points are adjusted according to the previous search result.

首先改进了局部搜索算法，使得搜索方向，搜索半径和搜索所计算的函数值个数根据已有的搜索结果而自适应调整。

CFD-fluent simulation software and measurement are applied to establish the math models of exhaust gas concentration distribution and boundary conditions. Finite volume methods and PISO are used to solve the differential equations of exhaust gas distribution in a kitchen. After the adjustment and comparison with those from the practical measure, the simulation results of CO2 and CO concentration distributions accord with experimental ones.

运用CFD-fluent模拟软件和实测相结合的方法，建立废气的浓度和扩散分布的数学模型与边界条件，利用数值分析法中的有限体积法和PISO算法对厨房内废气分布的微分方程进行离散和求解，对模拟结果进行校正并与实际测试结果进行比较。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。