查询词典 variational method

To one kind of variational inequalities, some researchers give an alternating direction method, which solve a linear variational inequality and a system of nonlinear equations in each iteration.

针对一类变分不等式，有研究者给出了一种交替方向法，在每一步迭代中分别要求解一个线性变分不等式和一个非线性方程。

To variational inequalities with separate structures, the thesis presents a descend method based on the alternating directions method, and some numerical results demonstrate that the new method is effective in practice.

对于结构可分的变分不等式，本文在交替方向法的基础上提出了一种下降方法，并给出了相应的算法收敛性证明与数值试验结果。

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

By means of the difference discrete variational principle, discrete Legendre transformation and discrete version of the E-L cohomology, for a kind of regular meshes we''ve found there is a kind of symplectic/multisymplectic structures with corresponding symplectic/multisymplectic finite element method/mixed finite element method schemes.

利用差分离散变分原理、离散Legendre变换和EL上同调的离散形式，对于正规网格找到一类有限元和混合有限元的辛或多辛结构，以及相应的辛有限元/混合有限元格式。

Nodal and edge elements. Galerkin's method and variational formulations. The Method of Moments.

一维、二维和三维的有限元法，节点和边界单元，Galerkin方法和变分原理。

Part Ⅰ deals with the foundmental theory of variational technique in the lossy electromagnetic fields. In chapter two and three the Green theorem is introduced so the unified method to derive functional is given. Chapter four is devoted to discuss two type of inner product. In chapter five the generialized least function theorem is given and applied in the derivation of variational expressions.

第一篇主要是关于有耗电磁变分的基础理论，由四章组成，前二章引入了以Green定理为核心的边值问题理论，建立了电磁变分的普遍理论，第四章从对称的观点出发讨论了建立泛函的两种内积形式，第五章给出了一般电磁场的广义最小作用量原理，并用之解决变分问题。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

This paper focuses on four important aspects as follows. The first one is the establishment of variational quations which provides the mathematics theories for the finite element method of HMT; the second one is for the study of scalar/node and vector/edge finite element method; the third one is about how to solve faster for the large-sacled matrix system of scalar/node and vector/edge finite element; and the last one is achieving the forward modeling with high precision of HMT method.

主要包括四部分：建立与高频大地电磁法边值问题相等价的变分问题，为有限元数值计算奠定数理基础；标量/矢量有限元方法的研究；加速标量/矢量有限元矩阵系统方程迭代求解技术的研究；实现高频大地电磁参数精确快速正演模拟的研究。

This integral equation is incorporated into a velocity-pressure variational formulation for the interior region, and a finite element method is used to approximate the resulting variational problem.

本文在绪论中简单介绍了边界元的发展历史及其发展现状，并把边界元和有限元做了简单的比较，介绍了它们各自的优缺点。

In this context a genetic algorithm was applied to the four-dimension (4-D) variational data assimilation, which provided a kind of new and effective method in the initial field optimization. The theoretical basis and detailed algorithm were introduced in this paper. At the same time, according to the property of the variational problem itself, we designed the rational genetic coding, operators and parameters.

本文将遗传算法应用于四维变分资料同化问题，提供了一种新的较为有效的NWP初始场优化方法，给出了相应的理论依据和详细算法，并结合变分问题本身的特点，设计了合理的遗传编码、遗传操作和遗传参数。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。