查询词典 discretization

The alternating direction implicit method is used to solve discretization equation and supplement block iteration method to quickening convergence.

本文选择交替方向隐式迭代法，并补以块修正技术以促进收敛。

The basic approach of protecting people from being hurt or killed in an accident is to improve crashworthiness of vehicles. This paper starts with discussing theories and methods for vehicle passive safety design, which included experiential methods, analytic methods, multi-body dynamics methods, crash test methods and the finite element method. Emphasis will be paid to the basic FEM theories and algorithms of impact problems. Topics discussed include the governing equation, element discretization, hourglass control, time integration, material model, shell element algorithms and contact-impact algorithms. For more reliable simulation results, this paper then conducts study on how to accurately get material model parameters by combining the FEM method with experimental method, and develops relevant material test machine and parameter calculating software. Based on that, basic typical impact simulation and test validation study are conducted. On the basis of the above work, the paper studies the thin-shell structures'crashworthiness, which was affected by the following factors: spot-weld features, shell thickness, cross-section and pre-deformation. As to vehicle parts'crashworthiness, the paper conducts simulation study of designing energy-absorbing steering system and adaptive airbag system. A practical energy-absorbing steering wheel is designed as an example. In further depth research, the paper suggests several inverse quantificational methods for vehicle crashworthiness design based on the ideal crash characteristics. The above theories and methods are applied with good results through several practical vehicles' crashworthiness design and improvement.

文中对汽车碰撞安全性的设计理论和方法进行了归类和总结，其中包括经验法、解析法、多刚体动力学法、试验法以及有限元方法等；重点介绍了碰撞有限元法的基本理论和有关算法，涉及到有限元求解控制方程、单元离散、沙漏模态控制、时间积分、材料模型和应力修正、薄壳单元算法以及接触碰撞界面算法等，探讨了有限元计算中的材料模型参数获取技术，开发了相应的材料试验装置及材料模型参数反求软件，在此基础上进行了基本的碰撞仿真算例和试验对比研究；文中通过应用有限元方法研究了薄壁构件的碰撞吸能特性，指出了设计薄壁吸能构件时需要考虑的几个主要影响因素，即焊点、壁厚、横截面和预变形等；在关于车辆部件的碰撞安全性能设计中进行了吸能转向机构和自适应安全气囊的仿真研究，提出了吸能转向机构和自适应安全气囊的仿真研究方法；文中最后探讨了整车碰撞性能的设计与改进方法，提出了以理想碰撞特性为目标，采用分段加速度或者根据碰撞时间进行设计的反推设计法、部件吸能仿真优化设计法等量化设计方法，并通过综合应用文中所讨论的相关技术进行了整车碰撞性能的设计与改进实例研究，所选定的车型是大众化的普通轿车和碰撞安全性基础较差的微型面包车，研究结果表明，本文所提出的设计与改进方法是适用而有效的，具有重要的工程实用意义和价值。

The unique advantage of this halfanalytical numerical method is that the analytical process of Conformal Mapping can transform an irregular area into a regular one such as a rectangle. Therefore, the discretization error of numerical methods on the boundary can be avoided, and the numerical algorithm can be implemented more easily, with the computing efficiency improved.

这种保角变换的半解析数值方法的突出优点是：利用前期的保角变换解析处理将不规则的场域转化为规则的矩形域，从而避免了纯数值技术对复杂边界的离散化误差，降低了后期数值计算的算法复杂度，并提高了计算效率。

This section presents two kinds of characteristic schemes, one is the natural use of the usual backward Euler characteristic difference scheme ( [60] ) onto the triangular mesh, the other replaces the backward Euler's method by modified Euler formula to approximate the characteristic differential equation, so that the discretization for characteristic curve can get up to second order accuracy.

本节给出了两种三角形网格上的特征差分格式，第一种是通常的向后Euler型特征差分格式（[60]）在三角形网格上的自然运用，第二种采用§3.3、§3.4的离散思想，使用改进的Euler公式代替向后Euler公式来近似特征微分方程，使其对特征线的离散达到了二阶精度。

The approximate method of discretization may be used to calculate the persistent spin current in mesoscopic ring.

用离散化的近似方法也可以计算介观环中的持续自旋流。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

In the process of discretization of the auxiliary function, the traditional central difference formula is replaced by the backward difference formula, and numerical results show the method is of good stability.

在辅助函数的离散过程中用后向差分公式代替传统的中心差分公式，数值结果显示出良好的稳定性。

In Section 3, the BEM and the corresponding constant-element discretization is presented.

在第3条中，边界元法和相应的常数元离散。

Major research work and conclusions are summarized as follows:1 The development of molecular distillation are reviewed in respect of the principle, model research and application; The technical and structure parameters are analyzed with respect to the evaporation rate and separation factor.2 Based on analysis of heat transfer and mass transfer process in WFMD, the discretization forms of bow wave ordinary differential equations and film partial differential equations are obtained with Runge-Kutta method and finite difference method respectively.

主要工作与研究结果如下： 1 综述分子蒸馏技术的应用及其发展现状，从分子蒸馏技术的原理、模型研究及其应用的发展等进行了系统评述；并结合蒸发速率和分离效率这两个评价分子蒸馏效果的重要指标，对刮膜分子蒸馏器工艺参数与结构参数进行了分析与讨论。

It is shown that in Jameson's algorithm is not an orthogonal stream-lines coordinate system, but a local stream-lines coordinate system instead. Nevetheless, because of the finite-difference discretization in Jameson's scheme is not carried out along the direction of s and n, but along the Cartesian coordinates, the analysis on all terms of the full potential equation in Cartesian coordinates reveals that his scheme does take a back-ward difference along the streamwise exactly at all points in the supersonic flow region.

表明其所采用的坐标系不是真正的正交流线坐标系，而是局部流线坐标系；同时由于Jameson方法并不对s，n进行差分离散，而是在原笛卡尔坐标系下作差分离散，对笛卡尔坐标系下的全位势方程中的各项的分析表明，Jameson方法恰好能做到在超音速点沿真正的流线方向作后差分。

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。