查询词典 galerkin equations

Based on the magneticelasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magneticelasticity kinetic buckling equation of a currentcarrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magneticelasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

Since the different dynamics methods such as Newton-Euler method, Lagrange's equations and other methods can be used to develop the dynamic equations of global system, the two different forms of the dynamic equations are ordinary differential equations and differential algebra equations.

通过结合有限段法和多体系统动力学离散时间传递矩阵法，形成了非线性梁有限段离散时间传递矩阵法，该方法保留了有限段法适用于几何非线性大变形分析、自动考虑动力刚度项等优势，又保留了DT-TMM-MS建模方便灵活的特点。

The main contents of this course include: the elementary solution of first order differential equations, the theory of existence, uniqueness and continuity dependency of initial value problem of first order differential equations, the structure theory of higher order linear differential equation and the solution of constant coefficient equations, the structure theory of system of linear equations, basic solution matrix and the solution of system of constant coefficient equations.

本课程内容有：一阶微分方程初等解法，一阶微分方程初值问题的存在性、唯一性、连续依赖性理论，高阶线性微分方程解的结构理论和常系数方程解法，线性方程组的结构理论、基解矩阵和常系数方程组的解法。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

In the dissertation, meshless element free Galerkin method which utilizes moving least square is used for solving heat transfer problems. Lagrange multiplier method is used to deal with the essential boundary condition. Some parameters in element free Galerkin method, which influence the precision, are also discussed in the numerical simulation. The adaptive method of meshless method is also stated.

本文采用了基于移动最小二乘近似的无网格伽辽金法计算了热传导问题，采用拉格朗日乘子处理本征边界条件；讨论了无网格伽辽金法各个计算参数在数值模拟中对计算精度的影响；并对无网格的自适应方法进行了研究。

Results show that radial basis function and point interpolation methods possess Kronecker Delta function property, but the robustness is poor in some cases; the MLS approximation function does not possess Kronecker Delta function property, but it has good robustness. Differences among the three discretization schemes of meshless method are as follows:the collocation method requires no numerical integration and very little computational time while its robustness is poor; Galerkin method is not a truly meshless method due to the background meshes required for integration; the Petrov-Galerkin method is a truly meshless method and need numerical integration in each sub-domain, so it needs more computational time.

分析结果显示：径向基函数和点插值法均具有d 函数属性，但计算稳定性差；移动最小二乘近似函数不具有d 函数属性，但计算比较稳定；无网格方法中的3种离散方法不同之处在于：配点法不需要积分，计算量小，计算稳定性差；Galerkin方法需要借助背景网格进行积分，它不是真正的无网格方法；Petrov-Galerkin方法，是一种真正的无网格方法，它需要对每个子域进行积分，计算工作量较大。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

In this thesis including six chapters,we presents a combinatorial stabilized/(first or-der equation)Galerkin least-square finite element method for viscous incompressible flowproblem to circumvent inf-sup condition necessary for the classic Galerkin mitred finiteelement method.

在由六章组成的论文中，我们为粘性不可压缩流动问题提出一种消除了经典混合元中离散inf-sup条件约束的组合稳定/最小平方有限元格式。

In this paper, combining the moving Kriging interpolation method and meshless local Petrov-Galerkin method, an improved meshless local Petrov-Galerkin method is presented, in which the Heaviside step function is used as test function over the local weak form.

本文将滑动Kriging插值方法与无网格局部Petrov-Galerkin法相结合，采用Heaviside分段函数作为局部弱形式的权函数，提出一种改进的无网格局部Petrov-Galerkin法，进一步将这种无网格法应用于位势问题，并推导出相应的离散方程。

The Galerkin's method was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary differential equations with time dependent coefficients,which can be solved with numerical methods.

对于电梯工业来说，目前世界上绝大部分电梯仍然是依靠钢丝绳提升的曳引式电梯。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。