数值方法

Exercise 5 , To find a new method to calculate gravity between any two objects , in which gravitational constant G is required to be taken out of consideration before calculation and by which same result can be obtained as does by Gravitational Law.

习题5，试找到一个新的计算万有引力的方法，使用这种方法可以在不考虑万有引力常数的情况下仍然可以正确地求解出任意两个物体间的万有引力数值。

The advantage is its ability to study spectrum and wave functions beyond the ground state.

蒙特卡罗哈密顿方法是研究量子理论的数值模拟新方法，其优点是可求出超出基态的能谱和波函数。

Main creative points of the thesis are as following:1. It is the first time to apply 2-D and 3-D turbulent model of the air-water two phases flow to the study on hydraulic properties of groyne. It makes description of the turbulent flow field to be possible precisely. This offers a more accurate method to determine the water surface in channel improvement.2. Based on the results of experiment and simulation for 3-D turbulent model of air-water two phases flow, a new formula to compute the height of damming is built.3. Based on the 2-D mode and the formula to compute the height of damming, the subdivision method of 2-D computation for water surface at upstream and downstream.

本文的创新工作主要是：首次将三维水气两相流紊流数学模型应用于丁坝水动力学特性研究，使丁坝附近流场和紊动场的精细描述成为可能，为航道整治中水面线确定提供了一个更为准确的方法；(2)基于水槽实验和三维水气两相流紊流数学模型数值模拟结果，建立了新的丁坝前奎水高度计算公式；(3)基于上述奎水高度计算公式和本文二维水面计算数学模型，首次提出了丁坝上下游二维水面分段计算方法。

Numerical simulation proves that the proposed method is more accurate than conventional harmonic analysis method.

数值模拟试验表明，在适当选取点质量埋深度的情况下，本文的点质量调和分析方法较传统的调和分析方法精度更高。

A quick and correct forecast of tidal current when oil spill occurs is a key step in the forecast of oil spill. Based on the harmonic constant of tidal component of M2, S2, O1 and K1 in Lingshan Island, Laoshantou and Chaolian Island, and by using harmonic method, the thesis first conducts a current forecast in a single point, and then builds up a current field forecast in Jiaozhou Bay and its adjacent seas. The computed results match well with the actual situation. The method reduces greatly the time of real time current forecast by not using numerical stimulation, so it fit to the two requirements of quickness and correctness in oil spill forecast system.

迅速准确地预测出溢油发生时的潮流情况是溢油环境预测的根本保证，因此文中根据灵山岛、崂山头和朝连岛三处M2、S2，、O1和K1四个主要分潮的调和常数资料，采用调和的方法进行单点的潮流预报，进而建立了胶州湾及邻近海域的预报潮流场；该方法的潮流预报结果与实际情况吻合良好，且因避开了数值计算过程而大大减少了流场实时预报的机时，符合溢油应急预报系统所要求的准确与快速。

In sphere approximate, GPS/Gravity-BVP is Neumann problem over exterior spherical domains. Then the natural boundary reduction, suggested by Feng and Yu, is applied to deal with the three dimensional problems. By expansion in spherical harmonics, the natural integral equations of harmonic problems over exterior spherical domains are obtained. Meanwhile, a numerical method for solving geodetic BVP is developed.

在球近似下将GPS-边值问题转化为Neumann外问题，用自然边界元法进行自然边界归化，得到自然边界积分方程，再求自然边界积分方程的数值解，与其他边界元方法相比，自然边界元法的计算量大大减小，并且具有很好的逼近性质，能有效地处理奇异积分，是求解GPS-边值问题有效方法。

Similarly, the new method was applied to analyses three-dimensional entity structures. The hexahedron element with 8 nodes was selected to solve the structures. Some examples were listed, and the results show that cellular element method can solve space problems well.

同时，还应用该方法分析三维实体结构，以8节点六面体等参元为例进行了数值试验和讨论，证明该方法在弹性力学空间问题中的应用同样是有效的。

The theoretical and numerical results show that the hybrid method is efficient.

理论和数值结果表明，此混合型方法是一个有效方法。

The numerical tide prediction in hydrography is investigated and the Prediction and Application System of Tides in Hydrography is developed.

研究了应用于海道测量的潮汐数值预报方法，研制了海道测量潮汐计算与应用软件系统，介绍了该系统的组成与主要功能以及有关数学模型的建立与计算方法。

A method for integrating infinite integrals that occur in solving the fields of source coil and equivalent coils is presented. Subtraction of asymptotic terms is proposed to speed up the truncation process of an infinite integration interval, which greatly improves the infinite integrals.

给出了一种简单有效的数值积分方法计算激励线圈和等效线圈解析解中遇到的无穷积分，提出了一种加速无穷积分收敛的有效方法，显著提高了磁场及涡流场的计算效率。

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。