改进力法计算的研究

针对传统力法的缺点, 利用VBA进行了Excel电子表格的编制, 对传统力法 进行了改进. 在保持传统力法的基本原理和计算过程的基础上, 解决了力法计算繁琐的问题, 提高了计算速度和学习效率, 增强了结构力学课程与实际的联系, 对工科课程的教学具有一 定的指导意义.     

三阶非线性发展方程的线性化有理逼近方法

研究了三阶非线性发展方程的初边值问题的解。采用基于Sinc函数的微分求积法发展了线性化有理逼近方法。通常的配点法不适用于上述三阶问题的求解。本文把提出的方法用于求解KdV方程,取得了良好的效果。     

QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.     

解非定常不可压缩N-S方程的迭代压力Poisson方程法

１．引 言 数值求解不可压缩流体流动问题可以采用原始变量的方程作为控制方程,也可以用涡量一流函数方程作为控制方程．直接求解原始变量的不可压缩 Ｎａｖｉｅｒ—Ｓｔｏｋｅｓ方程存在一个主要困难：速度向量在每一时刻都必须满足零散度约束条件,即不可压缩性连续方程．用涡量一流函数方程求解时,连续方程自动满足,所以不存在约束条件的问题,但涡量的边界条件比较难处理,且不易应用于三维问题和带有自由表面或其它流体交界面的问题． 解决上述速度向量必须满足零散度约束条件的困难的方法有：人工压缩法［３,１７］;压力Ｐｏｉｓ…     

蒙特卡罗模拟法在边坡可靠性分析中的运用

江永红．蒙特卡罗模拟法在边坡可靠性分析中的运用．数理统计与管理，１９９８，１７（１），１３～１６．可靠性分析是边坡工程及滑坡治理中的重要研究课题。鉴于决定边坡可靠性的诸变量多为随机变量，本文论述了用蒙特卡罗模拟法计算边坡可靠度的基本原理，对模拟次数确定、计算误差估计等问题提出了解决办法，并结合具体运用说明该方法的实施步骤     

红黑排序混合算法收敛速度分析

The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.     

浅析波谱分析课程教学改革

根据在波谱分析课程教学中遇到的一些实际问题,本文探讨了便于波谱分析课程教学的几种方法,并收到了较好的教学效果.     

自旋因式化法推求同科电子组态原子光谱项

以同科电子i3组态光谱项推求为例,提出了用自旋因式化方法推求同科电子光谱项的一般方法.该法较为简单、适用,易于推广,可求出任一基态或激发态原子或离子光谱项.     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.     

Nonsmooth analysis of vector-valued mappings with contributions to nondifferentiable programming

We define order Lipschitz mappings from a Banach space to an order complete vector lattice and present a nonsmooth analysis for such functions. In particular, we establish properties of a generalized directional derivative and gradient and derive results concerning a calculus of generalized gradients (i.e., calculation of the generalized gradient of f when f = f₁ + f₂, f = f · ₂, etc.). We show the relevance of the above analysis to nondifferentiaile programming by deriving optimality conditions for problems of the form min f(x) subject to x [euro] S. For S arbitrary we state the results in terms of cones of displacement of the feasible region at the optimal point; when S ={x ? A|g(x) ? B}, we obtain Kuhn-Tucker type results.