A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

大牛地气田气井无阻流量的确定方法研究

大牛地气田气井试井大多采用一点法，由于气层渗透性差，测试时间短，流压很难达到稳定，计算的无阻流量往往偏高，且无法获得正确的产能方程。通过气田多口井修正等时试井数据进行统计分析，获得了一点法试井在不同生产时间下计算无阻流量的经验公式；利用气田修正等时试井的二项式方程系数曰，计算惯性阻力系数并经过曲线回归处理获得了经验关系式，很好地解决了一点法试井计算产能方程的问题。     

波动方程数值模拟的隐式差分法

在有限差分波动方程数值模拟中,通常采用高阶差分方法来提高空间导数的数值逼近精度,以实现降低数值频散,提高数值模拟精度的目的。首先对差分频散进行了理论分析;然后讨论了估计一阶空间导数的隐式差分格式,并与通常采用的高阶精度显式差分格式进行了对比分析,结果表明,隐式差分格式能够在更宽的波数范围使差分频散控制在可接受的水平,如8阶精度的显式差分格式所适应的波数带宽约为O．55kmax,而隐式差分格式所适应的波数带宽约为0．7kmax;最后通过模型试算,对隐式差分格式的有效性进行了验证。模拟结果表明,用隐式差分格式在一定程度上降低了差分频散,提高了模拟精度。     

A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow

 A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest. Sponsored by The Research Council of Norway, project number 125676/410 Dedicated to the memory of Prof. Mike Crisfield, a respected colleague     

透水坡面降雨径流过程的运动波近似解析解

本文从坡面流运动波理论的基本方程出发，利用运动波特征线法和分级叠加法，推导出了实验条件下考虑净雨强随时间变化的坡面流运动波方程近似解析解。用实验实测资料对模拟计算结果进行了验证。结果表明，坡面漫流过程的模拟计算结果与实测资料符合良好。     

一种二元域上的快速计算哈希函数

论文从映射的角度,将哈希函数分为三类:严格哈希函数、计算哈希函数和实用哈希函数。在此基础上,根据二元域上二次方程x2 x c=0的部分不可解的性质,构造了一种计算哈希函数,它满足单向性和一一对应性,同时具有运算速度快的优点。     

分析介质光波导传播特性的Cole—Hopf变换法

采用Cole-Hopf变换法，将平板光波导导模所满足的二阶常微分方程（Helmholtz方程）变换成一阶常微分方程（Riccati方程），用较简单且有效的方法分析导模的特性。给出了多层阶跃型及渐变型平板波导导模的精确解析解和数值解法及实例；给出了非线性平板波导传播特性的数值计算法及实例。     

卷积码的线性系统

介绍了卷积码的线性离散时不变系统模型。从建立卷积码的状态变量方程出发,研究了卷积码的代数结构,并详细论述了基于状态变量方程描述的迭代译码算法。     

A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. Finally, an application of the method to a plane problem involving complete contact is presented.     

声光效应拉曼-内斯方程矩阵级数解法及声光调制器优化设计

提出一种求解正常声光相互作用拉曼 内斯 (Raman Nath)方程的矩阵级数解法 ,该解法直观方便且具有普遍性。计算结果表明 ,对Q =4 1π ,Bragg衍射的效率只有 97 5 % ;对非对称入射 ,以往的Raman Nath近似解误差较大 ;指出提高Bragg衍射效率的有效途径在于提高声光频率比并给出计算声光器件最优长度的计算公式。