数值方程

The basic equations of structure are derived from Hamilton variational principle and the constitution of material utilizes the increment theory.

基于Hamilton变分原理导出圆柱壳的运动方程，本构关系采用增量理论，借助增量数值算法求解动力方程组。

The paper have two parts, one is numerical solution of partial di?erential equation,another is submanifold.

本文分两部分，第一部分是偏微分方程数值解内容，第二部分是子流形几何内容。

The numerical tests show that, DSR equation migration methods such as common azimuth migration have a promising prospect in areas with strong variations of velocity, e.g., subsalt, reef and buried hill, etc.

数值试验表明，共方位角偏移等DSR方程叠前深度偏移方法在盐体或礁体、古潜山等强横向变速地区具有很好的应用前景。

To review the numerical methods of the multibody systems dynamics and applications of the symplectic methods

多体系统动力学方程数值方法的发展历程及探讨辛算法的应用

Assume also that point corresponds the value of parameter t, then the equation of the tangent line to the curve L at point M is given by

假设对应到参数值，则L在点M的切线方程为。

The threshold of lithium tantalite under single-shot is found to be 1.84J /cm 2 and the avalanche rate was determined to be 1.01 cm 2 /J by calculation. We found that avalanche dominates the ablation process, while photoionization serves as a free electron provider.

在800nm飞秒激光脉冲作用下，钽酸锂晶体单脉冲烧蚀阈值为1.84 J /cm 2；在此基础上，我们通过建立钽酸锂晶体中导带电子密度演化微分方程，并数值求解，得到了钽酸锂的碰撞电离速率系数为1.01 cm 2 /J ，并得出在钽酸锂表面烧蚀中，光致电离提供种子电子，雪崩电离起主导作用的结论。

After summarizing the waveform relaxation methods and domain decomposition, we finish some research on optimal Schwarz waveform relaxation algorithm as follows: In the first part, we apply Schwarz waveform relaxation methods on telegraph equation system to get optimal transmission conditions to speed up the algorithm.

在对波形松弛算法以及区域分解进行了综述性介绍后，本文对Schwarz波形松弛迭代算法具体进行了以下研究：首先，本文将在电报方程系统上应用Schwarz波形松弛迭代算法，通过强制加入新的局部传输条件分别给出了两种加速算法并通过定理保证了其优化后的收敛性，进而得到优化Schwarz波形松弛算法，然后通过数值试验对传统Schwarz波形松弛算法与优化Schwarz波形松弛算法进行了比较，研究了收敛率与优化系数的关系，找到了使算法最优的系数取值；最后得出优化后的Schwarz波形松弛算法优于常规Schwarz波形松弛算法的结论。

High order symplectic schemes of three-dimensional time-domain Maxwell's equations are constructed with symplectic integrator technique combined with high order staggered difference. The method is used to analyzing stability and numerical dispersion of high order time-domain methods and symplectic schemes with matrix analysis and tensor product.

利用辛积分技术与高阶交错差分技术，建立求解三维时域Maxwell方程的高阶辛算法；结合电磁场中的物理概念，借助矩阵分析和张量分析理论，获得高阶时域方法及高阶辛算法的稳定性和数值色散性的统一处理新方法。

According to the discrete material balance equation of control volume,a new numerical scheme based on PEBI grid and CVFE grid is provided,where absolute permeability is in tensor form.

根据所建立的单个控制体离散形式的物质平衡方程，基于 PEBI和 CVFE网格，采用任意形式的渗透率张量，建立了相应的数值算法。

According to the discrete material balance equation of control-volume,a new numerical scheme based on PEBI grid and CVFE grid is provided,where absolute permeability is in tensor form.

摘 要：根据所建立的单个控制体离散形式的物质平衡方程，基于PEBI和CVFE网格，采用任意形式的渗透率张量，建立了相应的数值算法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。