求积

While calculating tensor Green's functions, the algorithm of secondary division is adopted to solve the singular problem. The Gaussian quadrature and continued fraction is adopted to calculate the integral with Bessel function. This method not only can ensure the right calculation of tensor Green's functions but also can get high precision.

求取张量格林函数积分时，采用二次剖分算法解决计算中奇异值问题，对于含有贝塞尔函数的积分项，利用结合连分式展开的高斯求积代替常规的快速汉克尔变换方法，确保了张量格林函数的正确计算并提高了计算精度。

It is also shown for the first time that DQEM could be regarded as the combinations of the sub-domain method with the special mixed collocation method.

微分求积法和微分求积单元法是在近年里发展起来，并正在进一步发展的一种数值计算方法，本文对这两种方法的原理和它们在结构力学中的应用进行了较深入系统地研究。

Under the higher-dimensional situation, it introduces mainly the multiple integrals formulas on some standard areas, the multiple integrals formula by the methods of sampling, the reduction of dimensions and the boundary type cubature with a certain algebraic precision, and calculate multiple integrals with the methods of number theoretical net and so on.

在高维情形下，主要介绍了一些标准区域上的多重积分公式，用抽样法来求多重积分，具有代数精度的降维展开式和边界型求积公式，以及用数论网格的方法来计算高维积分等。

The author of this text has put out a kind of new-type quadrature formula by using the Gaussian quadrature formula and the orthogonality of Per Kai polynomial.

应用Gauss型求积法则和Per Kai多项式的正交性质，本文作者推导出了一种新型的求积公式—Gauss-Per Kai积分公式。

We proposed theautomatic and semi-automatic inverse Laplace transform methods and acriteriar for the optimal choice of transform parameters.24 numerical inverseLaplace transform formulas are compared for 16 different problems that haveexact solutions.

利用流行的数值积分方法，如Newton-Cotes求积公式、Gauss求积公式和振荡函数求积公式，共构造了24种Laplace逆变换方法。然后以16个有工程应用背景的Laplace逆变换问题为例，比较了这24种方法的优劣，得到了一些新的结论。

Plot --- composite numerical quadrature formula to solve the problem of integration functions for composite tr...

数值积---复合求积公式对积分问题的求解功能用复合梯形求积公式和复合抛物线公式，对给定的积分问题进行计算。

Plot --- composite numerical quadrature formula to solve the problem of integration functions for composite trapezoidal plot formula and compound parabolic formula, the right to issue integral calculation.

数值积---复合求积公式对积分问题的求解功能用复合梯形求积公式和复合抛物线公式，对给定的积分问题进行计算。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

As using Gaussian numerical integration, this paper uses Gauss-Legendre quadrature formula instead of Gauss-Chebyshev quadrature formula in order to avoid the precision decrease due to the singularity of cut-off error at both end points.

在利用高斯型求积公式进行数值积分时，本文采用高斯—勒让德求积公式取代高斯一切比雪夫求积公式，以避免因截断误差在端点出现奇异而导致的精度下降。

It also introduces the discrete ordinates couple-solving method (DOT-BSTP-DOT) which uses the half-symmetric angular quadratures for core geometry and the quadratic S〓 biasing angular quadratures for duct geometry. Calibrations for several types of duct are carried out and the schemes of XPR epithermal neutron filter are successfully designed. The other international popular code ANISN is also exploited and modified.

本论文首先开发、修改了其它国际通用屏蔽计算程序DOT/4.2和MCNP/4B，编制了边界源转换程序BSTP，首次建立深穿透屏蔽计算的临界源方向偏倚与指数变换相结合的蒙特卡罗耦合抽样方法，以及堆芯几何采用半对称求积基、孔道几何采用二阶S〓偏向求积基的离散坐标耦合求解法（DOT-BSTP-DOT），并对不同孔道进行了数值校算，成功地得到了西安脉冲堆超热中子过滤器的设计方案。

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。