Interaction between a circular inclusion and a symmetrically branched crack

The interaction problem between a circular inclusion and a symmetrically branched crack embedded in an infinite elastic medium is solved. The branched crack is modeled as three straight cracks which intersect at a common point and each crack is treated as a continuous contribution of edge dislocations. Green's functions are used to reduce the problem into a system of singular equations consisting of the distributions of Burger's dislocation vectors as unknown functions through the superposition technique. The resulting integral equations are solved numerically by the method of Gauss-Chebychev quadrature. The proposed integral equation approach is first verified for two limiting cases against the literature. More effort is paid on the effect of inclusion on both the Mode I and Mode lI stress intensity factors at the branch tips. The effect of inclusion on the branching path is also investigated.     

具有高阶剪切效应的粘弹性板准静态分析的DQ法

本文对基于Reddy的高阶剪切理论及线性粘弹性材料的Boltzmann本构定律建立的高阶剪切粘弹性板准静态分析的数学模型，在空域上应用推广的DQ技术对模型进行简化，求得了问题的DQ近似解析解；得到了横向阶跃载荷作用下的粘弹性简支板的准静态响应；考察了几何、材料参数及横向剪切效应对粘弹性板拟静态弯曲行为的影响。为说明该方法的可靠性和有效性，将考虑剪切变形及不计剪切变形的DQ数值结果与粘弹性薄板精确解进行了比较，同时研究了数值结果的收敛性。结果表明该方法具有收敛性好，计算精度高，计算量少等优点。     

饱和土一维动力响应分析的弱式微分求积元法

基于伽辽金加权残值法，本文首先建立一维饱和土动力学控制微分方程的弱形式，而后分别采用微分求积法和有限元法将其空间坐标离散，得到以土体骨架位移、流体-土骨架相对位移和孔隙流体压力为自由度的单元离散方程，从而采用Crank-Nicolson 法求解．数值算例一方面通过与解析解的对比，验证了离散方程和数值程序的正确性．另一方面，通过地表位移和基底孔隙压力的收敛性分析，检验了求积元和有限元法的收敛效率．数值结果表明：所建立的弱式微分求积法在饱和土动力分析中不仅具有显著优于常规有限元法的收敛效率，而且还具有可变阶的收敛性能，为今后高效率分析提供了一种可能．     

集中载荷作用下梯度复合材料梁的小波-微分求积法分析

将梯度复合材料梁作为平面应力问题处理,采用小波和微分求积混合法,对集中荷载作用下结构的响应进行了分析.考虑材料特性参数沿高度方向呈梯度分布,在该方向上采用广义微分求积法进行离散;鉴于广义微分求积法求解集中荷载问题精度不高的缺点,在梁的长度方向上引入对突变信号敏感的小波插值函数.数值计算表明,小波-微分求积混合法不仅保留了广义微分求积法高效的优点,而且能够很好地模拟结构局部化特征.     

Error estimates to smooth solutions of semi‐discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws

In this article, we focus on error estimates to smooth solutions of semi‐discrete discontinuous Galerkin (DG) methods with quadrature rules for scalar conservation laws. The main techniques we use are energy estimate and Taylor expansion first introduced by Zhang and Shu in (Zhang and Shu, SIAM J Num Anal 42 (2004), 641–666). We show that, with (piecewise polynomials of degree k) finite elements in 1D problems, if the quadrature over elements is exact for polynomials of degree , error estimates of are obtained for general monotone fluxes, and optimal estimates of are obtained for upwind fluxes. For multidimensional problems, if in addition quadrature over edges is exact for polynomials of degree , error estimates of are obtained for general monotone fluxes, and are obtained for monotone and sufficiently smooth numerical fluxes. Numerical results validate our analysis. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 467–488, 2017     

A differential quadrature based numerical method for highly accurate solutions of Burgers' equation

In this article, we introduce a new, simple, and accurate computational technique for one‐dimensional Burgers' equation. The idea behind this method is the use of polynomial based differential quadrature (PDQ) for the discretization of both time and space derivatives. The quasilinearization process is used for the elimination of nonlinearity. The resultant scheme has simulated for five classic examples of Burgers' equation. The simulation outcomes are validated through comparison with exact and secondary data in the literature for small and large values of kinematic viscosity. The article has deduced that the proposed scheme gives very accurate results even with less number of grid points. The scheme is found to be very simple to implement. Hence, it applies to any domain requires quick implementation and computation.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2023–2042, 2017     

Valuation of variable annuities with Guaranteed Minimum Withdrawal Benefit under stochastic interest rate

This paper develops an efficient direct integration method for pricing of the variable annuity (VA) with guarantees in the case of stochastic interest rate. In particular, we focus on pricing VA with Guaranteed Minimum Withdrawal Benefit (GMWB) that promises to return the entire initial investment through withdrawals and the remaining account balance at maturity. Under the optimal (dynamic) withdrawal strategy of a policyholder, GMWB pricing becomes an optimal stochastic control problem that can be solved using backward recursion Bellman equation. Optimal decision becomes a function of not only the underlying asset but also interest rate. Presently our method is applied to the Vasicek interest rate model, but it is applicable to any model when transition density of the underlying asset and interest rate is known in closed-form or can be evaluated efficiently. Using bond price as a numéraire the required expectations in the backward recursion are reduced to two-dimensional integrals calculated through a high order Gauss–Hermite quadrature applied on a two-dimensional cubic spline interpolation. The quadrature is applied after a rotational transformation to the variables corresponding to the principal axes of the bivariate transition density, which empirically was observed to be more accurate than the use of Cholesky transformation. Numerical comparison demonstrates that the new algorithm is significantly faster than the partial differential equation or Monte Carlo methods. For pricing of GMWB with dynamic withdrawal strategy, we found that for positive correlation between the underlying asset and interest rate, the GMWB price under the stochastic interest rate is significantly higher compared to the case of deterministic interest rate, while for negative correlation the difference is less but still significant. In the case of GMWB with predefined (static) withdrawal strategy, for negative correlation, the difference in prices between stochastic and deterministic interest rate cases is not material while for positive correlation the difference is still significant. The algorithm can be easily adapted to solve similar stochastic control problems with two stochastic variables possibly affected by control. Application to numerical pricing of Asian, barrier and other financial derivatives with a single risky asset under stochastic interest rate is also straightforward.     

Legendre spectral collocation method for volterra-hammerstein integral equation of the second kind

This paper is concerned with obtaining the approximate solution for VolterraHammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function ω(x) = 1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L~2 norm and L~∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.     

基于System Generator的GMSK调制器仿真设计

GMSK由于具有优良的频谱效率和功率效率等特性,因而作为一种重要的调制技术被广泛地应用。传统的GMSK调制器需要在硬件中进行高斯滤波和相位积分计算,会出现各种截取误差,并且造成硬件资源浪费。本文是基于System Generator的GMSK正交调制器的仿真设计,采用了一种新的全数字基于相位路径的算法产生正交调制查找表,生成GMSK正交调制信号,该算法降低了计算复杂度与硬件实现难度。     

基于25GHz信道间隔和30Gbaud的28.8Tbit/s Nyquist-WDM系统性能研究

为了提高奈奎斯特波分复用(Nyquist-WDM)系统的 频谱效率和传输距离,利用改进型多元低密度奇偶校验(NB-LDPC)码对Nyquist-WDM系 统进行信道编码,并结合偏振复用64进制正交幅度调制(PM-64QAM) 技术对28.8Tbit/s Nyquist-WDM相干检测系统进行性能研究。仿真结 果表明,经单模光纤(SMF)传输4900km之后, 与未采用编码的系统相比,在波特率为30Gbaud、信道间隔为25GHz 时,Nyquist-WDM系统通过采用改进型NB-LDPC码可以有效抑制符号间干扰,使误码性能改 善2.58dB, 频谱效率达到11.63bit/s/Hz;同时,通过采用NB-LDPC码可增加系 统的传输距离,改善系统对非线性效应的容忍度。