边界元法

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

Absorbing boundary condition ; wave equation ; spectral element ; central difference method

吸收边界条件；波动方程；谱元；中心差分法

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

RCS of facetsof targets coated RAM was resolved by combining Impedance Boundary Condition and Geometric Optics and RCS of those edges were approximated by computing the RCS of edges of impedance wedge through Method of Equivalent Currents.

其中，涂覆目标面元的散射场是通过结合阻抗边界条件和几何光学法而得到；而涂覆目标棱边的散射场则是通过等效电磁流法求解阻抗劈的边缘绕射场近似得到的。

RCS of facets of targets coated RAM was resolved by combining Impedance Boundary Condition and Geometric Optics and RCS of those edges were approximated by computing the RCS of edges of impedance wedge through Method of Equivalent Currents.

其中，涂覆目标面元的散射场是通过结合阻抗边界条件和几何光学法而得到；而涂覆目标棱边的散射场则是通过等效电磁流法求解阻抗劈的边缘绕射场近似得到的。

And the conservation laws of moment and momentum are obtained by the combining the tiny element analysis method in continua mechanics with variation principle in analytical mechanics.

论文摘要：本文在建立时变边界挠性体的动力学方程时，将并入的质量对挠性体的作用当作时变边界上的表面力，并将连续介质力学中的微元分析法和分析力学中的变分原理相结合，导出了时变边界的变质量刚体的动量和动量矩矩方程。

First, we extract the boundaries between two different materials by weighting with gray-level gradient,and only voxels on these boundaries participate in the generation of each image, so it drastically reduces the rendering time. Second. We think the voxels on boundaries as the mixture of different materials,so in every voxel there is a surface. We use the oriented cube-interpolation technique to get the intersection point of viewing orientation and the surface in the voxel, then compute the surface normal of the intersection point. We use the normal to shade the voxel in order to improve the image quality.

首先，采用灰度梯度加权提取出三维数据场中不同物质间的边界，根据显示的需要只对这些边界上的体元赋予相应的阻光度并进行光亮度合成计算，因而可大大减少计算量，提高显示的速度；将边界上的体元作为不同物质的混合体，采用与方向有关的三线性插值来计算视线方向与体素内等值面的交点，根据交点的法向量进行光照效应计算以提高显示图像的质量；最后用投影成像法显示最终的图像。

Based on the cellular automaton made up of regular hexagon cells, the nearest neighbor type and periodic boundary condition, equiaxial microstructure as parent phase was obtained.

文章采用正六边形网格划分法、最近邻邻居关系以及周期性边界条件的元胞自动机方法，获得等轴的母相微观组织。

So, some research on plane steering six-bar linkage has been done in this project as follows: based on the condition equation of correct steering and the equations of two closed loop of steering mechanism, a set of three equations in three variables can be obtained after a variable is expurgated with the elimination method.

本课题对平面转向六杆机构进行了如下的研究：根据转向条件方程，与转向机构的两个闭环方程，采用消元法消去一个未知变量，得出了转向六杆机构关于输入角的目标函数方程；利用边界条件，得出一个包含三个变量、三个方程的方程组

Firstly, the lake water quality model is developed under the condition of both internal and external pollution by using the method of microelement analysis, then homogenizes the non-cylindrical boundary condition and utilizes the methods of vector expending and pseudomonotone of the variational operator, and last the existence and uniqueness of the solution for a type free initial-boundary value problem is obtained.

本文首先运用微元分析法导出在外源和内源双重污染下湖泊水质模型，然后对一类自由初边值问题通过对非柱形边界条件的齐次约化，运用变分型算子的向量扩张和拟单调方法获得解的存在性、唯一性。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。