泊松方程

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。

This paper presents the boundary value problem solved as the biharmonic equation of upper plane and strip domain with Green functional method and it deals with the numerical solution of bihormonic equation, using the Matlab program calculation to realize the visualization of numeric solution.

用Green函数法求解了区域为上半平面和带形区域的双调和泊松方程的边值问题；以及探讨了双调和方程的数值解，并用Matlab编程计算实现了双调和方程数值解的可视化。

In calculation, the discretization of continuity equation is performed in accordance with semi-implicit Scharfetter-Gummel scheme and the electric field is solved by the current conservation instead of the Poisson's equation, so it saves plenty of time for calculation.

在计算中，对于粒子的连续性方程我们采用Scharferter和Gummel提出的有限差分方法，并用电流守恒方程代替泊松方程来求解电场，从而节省了大量的计算时间。

And electric equation to study electric double layer, streaming potential and electroviscous effects

本文综合电解质溶液离子输运方程，流体运动方程和电场泊松方程研究微扩散管的双

In calculation, the discretization of continuity equation is performed in accordance with semi-implicit Scharfetter-Gummel scheme and the electric field is solved by the current conservation instead of the Poissons equation, so it saves plenty of time for calculation.

在计算中，对于粒子的连续性方程我们采用Scharferter和Gummel提出的有限差分方法，并用电流守恒方程代替泊松方程来求解电场，从而节省了大量的计算时间。

In calculation, the discretization of continuity equation is performed in accordance with semi-implicit and the electric field is solved by the current conservation instead of the Poissons equation.

在计算过程中，对于粒子的连续性方程我们采用有限差分方法，并用电流守恒方程代替泊松方程来求解电场。

A function was set up to deduce a second kind of Fredholm integral equation by using the basic solution of Poisson＇s equation.

将弹性扭转问题看成为泊松方程的边值问题，利用泊松方程的基本解构造了一个函数，推导出第二类Fredholm积分方程。

The functional by variational calculus leads to a set of elliptic partial differential equations,in particular,Poisson equations,which is possibly solved by numerical methods.

利用变分法可以从这个二次误差指标函数导出一组椭圆形偏微分方程泊松方程，这类方程有相当成熟的数值解法。

On the basic of NNLSE and the Poisson equation, using the Green function approach, we obtain the response function of the lead glass of finite-size, which is a strong nonlocal medium. Starting with the paraxial ray equation, we obtain the analytical solutions of the oscillation trajectory and period of the beam.

基于非局域非线性薛定谔方程以及热传导的泊松方程，采用格林函数法求出了强非局域介质铅玻璃的响应函数和临界功率；从光线方程出发得到了偏离材料中心入射的光束中心振荡轨迹以及周期的解析解。

Our approach to energy subbands in the active region of QCL is k · p method. Electron eigenvalues and eigenstates are calculated by solving Schrodinger and Poisson equations self-consistently.

k·p微扰方法下，利用有限差分法求解了化合物半导体的有效质量方程，在计算中考虑了超晶格界面处电子有效质量不连续性，自洽求解了掺杂有源区在不同外加电场下的薛定谔方程和泊松方程。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。