利用高斯求积和连分式展开计算电磁张量格林函数积分

针对于利用快速汉克尔变换求解电磁张量格林函数中含有贝塞尔函数积分项时，积分核函数不总是随贝塞尔函数（Jv(λr)）参数λ的增大而趋于收敛，从而产生错误结果的问题，我们利用一种直接数值积分——结合连分式展开的高斯求积方法进行计算，通过对不同模型的试算表明这种方法总能够保证电磁张量格林函数积分的正确计算.     

基于谱域球谐展开的多层快速多极子算法

介绍了基于谱域球谐函数展开的多层快速多极子算法，通过处理三维金属体的散射问题，验证了算法参数选取的经验公式，并对算法性能做出了理论分析，得出该算法具有内存占用少、迭代速度快的优点，数值结果显示了该方法的高效性。     

A semi-analytical model in time domain for moving loads

A model for investigations of ground motions due to continuously moving loads with constant and time-varying amplitudes is presented. The vertical displacements excited by moving load areas are obtained at a fixed observation point at the surface of the three-dimensional halfspace in time domain. The load is moving along a straight line with constant speed. To solve this nonaxisymmetric, initial boundary value problem a semi-analytical, discretized model is developed. It is based on Green's functions for a suddenly applied, stationary surface point load with Heaviside time dependency. These functions, also called influence functions of the halfspace, are valid for any homogeneous, isotropic and linear-elastic medium. The principle of superposition is used. Results are shown for the transient and the steady-state ground motions, and they are compared with analytical solutions. The load speed is varied in the subcritical range up to the propagation velocity of Rayleigh-waves.     

Semi-analytical evaluation of integral forms associated with Lamb's problem

The present work gives solutions of integrals resulting from Lamb's problem solution by an accurate and efficient approximation procedure. The formulation of the solutions requires the study of Green's function of Lamb problem solution. Unfortunately, this problem is associated to great mathematical difficulties and needs the evaluation of some complex integrals. We handled these integrals by an appropriate strategy based on decoupling their effects mathematically and solved by using the least squares method. The present solutions can be applied to study the dynamical interaction between soil and structures, to be used to determine the transient wave fields caused by a seismic source, and also to assess numerical computations with a different numerical methods program.     

APPROXIMATING RAINFALL-RUNOFF MODELLING RESPONSE USING A STOCHASTIC INTEGRAL EQUATION

Rainfall-runoff modelling uncertainty can be analysed by the use of a stochastic integral formulation. The stochastic integral equation can be based on the rainfall–runoff model input of model rainfall or model rainfall excess. Similarly, the stochastic integral equation can be based on the rainfall–runoff model output of the modelled runoff hydrograph. The residual between actual measured runoff data and modelled runoff (from the rainfall–runoff model) is analysed here by the use of a stochastic integral equation. This approach is used to develop a set of convolution integral transfer function realizations that represent the chosen rainfall–runoff modelling error. The resulting stochastic integral component is a distribution of possible residual outcomes that may be directly added to the rainfall–runoff model's deterministic outcome, to develop a distribution of probable runoff hydrograph realizations from the chosen rainfall–runoff model.     

Viscoelastic functionally graded finite element method with recursive time integration and applications to flexible pavements

The finite‐element (FE) method is used for modeling geotechnical and pavement structures exhibiting significant non‐homogeneity. Property gradients generated due to non‐homogeneous distributions of moisture is one such example for geotechnical materials. Aging and temperature‐induced property gradients are common sources of non‐homogeneity for asphalt pavements. Investigation of time‐dependent behavior combined with functionally graded property gradation can be accomplished by means of the non‐homogeneous viscoelastic analysis procedure. This paper describes the development of a generalized isoparametric FE formulation to capture property gradients within elements, and a recursive formulation for solution of hereditary integral equations. The formulation is verified by comparison with analytical and numerical solutions. Two application examples are presented: the first describes stationary crack‐tip fields for viscoelastic functionally graded materials, and the second example demonstrates the application of the proposed procedures for efficient and accurate simulations of interfaces between layers of flexible pavement. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical computation of incomplete elliptic integrals of a general form

We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.     

Elements of spin motion

For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial values of a modification of the Andoyer canonical variables. A computational procedure is obtained for determining these elements from the combination of the spin angular momentum vector and a triad defining the orientation of the rigid body. A numerical experiment shows that the errors of transformation between the elements and variables are sufficiently small. The errors increase linearly with time for some elements and quadratically for some others.     

非奇变换与地形校正中央区积分

利用非奇变换，将地形校正诸奇异积分转化为一组非奇异积分。理论分析和数值计算都表明，奇异积分非奇异后，可有效地提高地形校正中央区积分的精确度。     

Rayleigh wave group velocity in a spherically symmetric gravitating earth model

Expressions for kinetic energy, elastic potential energy and gravitational potential energy for the spheroidal oscillations of a spherically symmetric, self-gravitating, elastic earth model have been obtained. Some inconsistencies in the expressions given by earlier authors have been pointed out. The principle of equipartition of energy and the Rayleigh principle have been used to derive a formula for Rayleigh wave group velocity in terms of energy integrals. This formula can be used to compute the group velocity without the numerical differentiation implied in its definition