An analytical technique by way of partial differential equations is presented in this paper to analysis the magnetic field in air gap of the surface mounted permanent magnet motors.
解析法计算精度高，易于在计算机上实现，为永磁电动机的设计和优化提供了有力的工具。
This is a basic point, The mass conservative interpolation function is deduced in this thesis and the method to solve the stream surface expression from the partial differential equation of flow field is proposed.
本文首先推导了正确的基于质量守恒的单元插值函数，并提出从流场的偏微分方程直接求解流面方程的方法。
The general expressions of the elastic field of quasicrystals are achieved by introducing a displacement potential function, namely, the displacement and stress components can be expressed in terms of the derivatives of the function, which satisfies a partial differential equation with higher order, the huge numbers of complicated basic equations involving elasticity of quasicrystals can be reduced to solution of a single higher-order partial differential equation, this simplifies extremely the solution procedure.
利用位移势函数表示的一般解，应用Fourier分析和对偶积分方程理论，我们分别对八次对称二维准晶含有直位错和裂纹、三维立方准晶含有圆盘状裂纹及接触问题等情况进行了研究，主要结果有：得到了含有直位错及含有裂纹的八次对称二维准晶的弹性场的精确分析表达式，并给出了含有裂纹情形时的脆性断裂判据，应变能及应变能释放率。
The 3D nonlinear partial differential equations of the annular flow field are simplified by this model firstly, and then the zero-order perturbation equations are derived by the perturbation method and the static characteristics are finally obtained with a numerical method.
首先采用该模型简化了大间隙环流三维流场非线性偏微分控制方程，然后采用摄动方法推导了零阶摄动方程，并采用数值方法求解了大间隙环流的静特性。
Consequently, the finite element description of Partial differential equation for the rock mass heat conduction differential equation is given. Furthermore, the numerical simulation of distribution of the two-dimensional steady temperature field of fracture rock mass is established based on FEPG software.
给出了岩体导热偏微分方程的有限元描述，应用FEPG软件对裂隙岩体二维稳定温度场分布进行了数值模拟。
To overcome the disadvantages, A freeform reflector design method, which is mainly based on a first-order quasi-linear partial differential equation, is proposed in this article for uniform rectangular illuminance distribution in the field of LED illumination.
为了克服该设计方法的缺点，本论文在文献调研的基础上，建立了点光源的非成像光学设计模型，提出了一种基于一阶拟线性偏微分方程的自由曲面反射器设计方法。
But most physical simulations, for example computational fluid dynamics simulation or partial differential equations, generate data field which is nonuniform. Us-ing regular datasets will bring about accuracy problem and redundant storage.
但是大部分物理模拟计算（如计算流体力学或偏微分方程求解）生成的三维数据场分布极不均匀，如果采用规则数据表示，将会产生精度问题和极大的存储冗余。
The partial differential equations of stator temperature field model are dispersed with thermal equilibrium equation and are coupled with the temperature equations of water or hydrogen of cooling system.
采用热平衡方程对定子温度场的偏微分方程进行离散化处理，与冷却系统中水温及氢温的计算相耦合，形成联立方程组。
It uses electrostatic model to simulate the electric potential distribution, single phase laminar incompressible Navier-Stokes model to simulate the flow field distribution and coefficient model of partial differential equations to simulate charge transport.
利用其静电模块模拟电势分布；利用单相层流不可压缩纳维-斯托克斯方程模块模拟气流场分布；利用系数型偏微分方程模块模拟电荷输运。
Based on the turbulent bulk flow theory and Moody wall friction coefficients equation, 3D non linear partial differential equations of large gap annular flow field are simplified, and zero order perturbation equations derived. The static characteristics of eccentric rotor have been investigated with numerical method.
基于紊流整体流动模型和Moody壁面摩擦系数方程简化了大间隙环流三维流非线性偏微分控制方程组，推导了零阶摄动方程并采用数值方法对大间环流中偏心转子静特性进行了深入研究。
The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. The exact expressions for field quantities are obtained in transform domain.
利用现代控制理论中状态空间法求解了偏微分控制方程，获得了拉普拉斯变换域内的精确解。
The eigenvalues of ridge waveguide are solved with the matching of electric and magnetic field on the multiple virtual boundaries by partial differential operator theory and the property of ridge waveguide is discussed.
该文用电磁场算子理论通过多个虚拟边界的电场和磁场的耦合求解脊波导的本征值，在此基础上讨论了脊波导的的传输特性。
This paper researches the method of typhoon wind field retrieval based on the techniques of partial differential equation, machine learning and so on. The main work of this paper includes four aspects as follows: (1) Typhoon eye extraction by partial differential equations.
本文结合偏微分方程和机器学习等智能信息处理技术研究台风风场的反演方法，主要包括以下四个方面的研究工作：（1）基于偏微分方程的台风眼提取。
Finite control volume integral approach was developed to discrete elliptic partial differential equation of electromagnetic field, and successive over relaxation method was introduced to expedite numerical converging.
采用有限控制容积积分方法离散求解椭圆型偏微分电磁场方程，并采用逐点超松弛迭代方法加快收敛速度。
The partial differential equations are established in all the sub-domains, and the general solutions of the magnetic vector potential are obtained. With the boundary conditions between the adjacent sub-domains, the magnetic field is solved, and the electromagnetic performance is calculated.
对该电机进行了子域划分，并建立磁场的偏微分方程，得到了矢量磁位及磁场强度表达式，进而根据各子域间的边界条件建立了方程组，对电机电磁性能进行了计算。
Numerical method for solving the free boundary plasma equilibrium equation (a nonlinear partial differential equation of elliptic type) during the evolution of the external maintaining, field is presented.
本文介绍了外维持场随时间变化条件下等离子体平衡方程（非线性椭圆型偏微分方程）的数值求解方法。
An algorithm based on the control theory of partial differential equations is proposed. It is also shown that the Null field method originally developed in the problem of acoustic scattering can be used to solve the corresponding adjoint problem of the optimal problem.
提出基于偏微分方程控制方法的一种算法，并证明原用于处理散射问题的Null-fieldmethod可用来求解优化问题的随伴问题。
It is a partial differential equation satisfied by the electric field E.
这是一个，由电场E确定的偏微分方程。
Nowadays, the PDE (partial differential equation) has been widely applied in the optical image processing field, such as image segmentation, image smoothing, edge detection and so on.
偏微分方程（PartialDifferentialEquation，PDE）是一种数学处理方法，最初应用于光学图像领域，在图像分割、图像平滑、边缘检测等图像处理领域得到了广泛的应用。
Among the simulation in temperature field, it uses the PDE toolboxes of Matlab through inputting initial conditions in the borders to solve Partial Differential Equation of Heat transfer, calculate and display the temperature distribution situations of section of the plate.
在对温度场的模拟中，运用MATLAB中的PDE工具箱，通过输入边界条件和初始条件求解传热偏微分方程，直接计算出温度在轧件横断面上的分布情况。