拉普拉斯方程

基于Darcy渗流定律及质量守恒原理对渗流场进行了理论分析，研究了稳定渗流连续性方程，建立了稳定渗流的一般基本微分方程，对于均质各向同性坝体，上述方程变为著名的拉普拉斯方程。

We will have Darcy law application to continuity equation to stabilize the normally basic differential equation of the influent fields , for quality isotropy dam body , above-mentioned equation is famous Laplace equation ;

非规则区域中拉普拉斯方程的有限分析5点格式

The 5-point finite analytic schemes for laplace equation in irregular domains

关于p－拉普拉斯方程径向解的一点注记

A note on the existence for radial solution of the p-Laplacian equation

另外，我们还给出了拉普拉斯方程和一般方程的Pinching-估计以及Hamilton张量极大值原理的一个应用。

Furthermore , we shall give Pinching-estimate for general equation and the proof of n-dimensional for the Laplace equation and an application of Hamilton tensor maximum principle .

分析V形槽静电超声传感器微气隙结构研究静电场不均匀性，用解拉普拉斯方程的方法解的单个V形槽面电荷密度。

In this paper , by analyzing micro air-gap structure for electrostatic ultrasonic transducers with V-grooved backplates , a research on electrostatic field asymmetry of ultrasonic transducers is indicated . A single V-grooved surface charge density is solved by solving Laplace 's equation .

对拉普拉斯方程及典型的大变形成形过程进行了分析，通过与拉普拉斯方程解析解和相应的商品化刚塑性有限元软件Deform的分析结果进行对比，验证了处理方案的正确性。

A Laplace problem and some metal forming processes were analyzed , through the comparisons with theoretical results of the Laplace problem and the commercial software Deform simulation data , the effectiveness of the methods developed here is demonstrated .

在拉氏变换域内将线性化的Navierstokes方程转化为求解相应的势函数和流函数，前者满足拉普拉斯方程，后者满足Helmholtz方程。

The linearized Navier Stokes equation of 2 D viscous incompressible fluid is transformed into resolving the corresponding potential function and stream function in Laplace domain , while the former satisfies the Laplace equation and the latter satisfies the Helmholtz equation .

拟周期小波边界元法求解拉普拉斯方程

To Solve Laplace Equations with Periodic Quasi Wavelet Boundary Element Method

用复变函数理论求解拉普拉斯方程，得出电流密度和洛伦茨力的解析式，并从计算中，找到了产生环电流的足够条件。

The conditions causing circular electric current are found by the calculation .

拉普拉斯方程边值问题的一种数值解法

Numerical solutions of boundary value problems for Laplace equations

拉普拉斯方程在静电选矿中的应用

Application of laplace 's equation to electrostatic ore dressing

通过求解拉普拉斯方程，得出非均匀电场对矿粒吸引力的表示式。

The expression of this attraction is obtained by solving Laplace 's equation .

平面静电场拉普拉斯方程的简捷解及其应用

A simple method of solutions of two-dimensional Laplace equation in electrostatics and Its Applications

应用求解拉普拉斯方程的边值问题建立有限元网格

Application of solving boundary problems of Laplace equation to generate the mesh of finite element

由于该方法的数值计算是基于拉普拉斯方程的正问题进行的，具有易于处理复杂边界、收敛性好、精度高的特点。

The algorithm has characteristics of capability of dealing with complex boundary and high astringency and precision .

通过拉普拉斯方程求解有特殊电荷分布的空间电势

Solution of the Electric Potential in the Space with Free Electric Charge Special Distribution by Laplace 's Equation

拉普拉斯方程有限差分表达式之改进&隔点取元公式

An Improvement on Finite Difference Expressions in Laplace Equation & the Formula of Taking Element by Every Other Point

根据拉普拉斯方程计算可知，在尺寸不变的前提下其屏蔽效果由材料的磁导率所决定。

Theoretical calculation found that the shielding effectiveness is determined by the permeability of the materials with the same size .

它是在物理坐标面上，对一组拉普拉斯方程进行数值解而得到的。

The grids on the physical coordinate plane areobtained from the numerical solutions of a set of Laplace 's equations .

研究电极的位移形变所产生的误差时，需要在不规则边界条件下求解拉普拉斯方程。

With the thought of " perturbation ", this paper analyes the solution of Laplace equation for poles having irregular boundary .

论文首先以三维拉普拉斯方程作为基本控制方程，应用第二格林定理，建立线性频域内的积分方程。

Taking 3D Laplace equation as governing equation and applying to the second-order Green identity , an integration equation is founded in linear frequency-domain .

在研究精密电容器的几何尺寸误差引起的电容量误差时，往往需在不规则边界的边值条件下求解拉普拉斯方程。

In evaluation of errors of precise capacitors due to geometric , imperfection , one has to solve Laplace equation subject to irregular boundary condition .

使用边界积分方法求解已知第二类边界条件的拉普拉斯方程或泊松方程时，理论上解是不唯一的。

Theoretically the numerical solution of Poisson 's equation or Laplace 's equation plus Neumann boundary condition calculated by the boundary integration method is not unique .

得到了用级数表示的满足控制拉普拉斯方程和可导通边界条件的基本解及应力强度因子。

A general solution and the stress intensity factor are obtained in term of series expansion , which satisfies both Laplace equation and the permeable boundary condition .

在成形砂轮电解修整电场模型的基础上，应用有限元法求解电场中拉普拉斯方程几何反问题。

The finite element method was applied to solve the inverse boundary problem of Laplace 's equation according to electric field model of profile wheel dressing processes .

利用边界积分方程解拉普拉斯方程的数学方法，解扭转问题中的挠曲函数，求边界剪应力和扭转刚度。

In this paper , boundary integral equation method is used to work out warping functions , torsional rigidity and shear stresses along boundaries in torsional problems .

本文还求解了磁标量满足的拉普拉斯方程，电磁矢量满足的亥姆霍兹方程，利用边值问题求解电磁场，并且应用麦克斯韦应力张量来计算某些电磁作用力。

This paper also solves the electromagnetic field through the use of boundary value problem and calculates certain electromagnetic force through the application of Maxwell stress tensor .

轴流式水轮机流场状况虽然比较复杂，但经过一些合理简化后就能用拉普拉斯方程来描述它。

Although the flow pattern in Kaplan turbine parts is very complex , it allows to be described in the form of the Laplace equation through reasonable simplification .

本文利用拉普拉斯方程的基本解作为权函数，给出求解交系数非齐次亥姆霍茨方程的迭代格式，进而得到求解这类方程的边界元迭代法。

In the time varying electromagnetic field , we have solved Helmholtz equation of a scalar potential under the spherical polar coordinate , and obtained its general solution .

本文从求解拉普拉斯方程入手，利用极限条件和边界条件推出了半无穷大空间中的双层导电介质在点源电流场中产生的电势分布规律，推出了几种特殊情况下的电势分布规律。

Based on the limit and boundary conditions , Laplace Equation was used to calculate the field distribution produced by point sources with an infinite double-layer conductive medium .