A fast algorithm for full non-linear transient waves

The transient surface wave motion is studied by a method which transfers the computational region into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analytical function is used. The coefficients of the series are determined by FFT. The numerical filtration is accomplished in the Fourier domain. The project supported by National Natural Science Foundation of China     

Measurement of decay time based on FFT

Decay time is an important parameter in fluorescence temperature and pH value measurement. Many approaches are developed based on different principles. The decay acquisition and estimation method is one of them. A novel estimation method is given in this paper, based on the fast Fourier transform (FFT). The decay time can be calculated from the frequent items of the FFT. The advantages of this method include high accuracy, quick processing, independence on base offset etc. A set of experiment results is obtained based on this method.     

Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment

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Accelerating electrostatic interaction calculations with graphical processing units based on new developments of ewald method using non‐uniform fast fourier transform

We present new algorithms to improve the performance of ENUF method (F. Hedman, A. Laaksonen, Chem. Phys. Lett. 425, 2006, 142) which is essentially Ewald summation using Non‐Uniform FFT (NFFT) technique. A NearDistance algorithm is developed to extensively reduce the neighbor list size in real‐space computation. In reciprocal‐space computation, a new algorithm is developed for NFFT for the evaluations of electrostatic interaction energies and forces. Both real‐space and reciprocal‐space computations are further accelerated by using graphical processing units (GPU) with CUDA technology. Especially, the use of CUNFFT (NFFT based on CUDA) very much reduces the reciprocal‐space computation. In order to reach the best performance of this method, we propose a procedure for the selection of optimal parameters with controlled accuracies. With the choice of suitable parameters, we show that our method is a good alternative to the standard Ewald method with the same computational precision but a dramatically higher computational efficiency. © 2015 Wiley Periodicals, Inc.     

A fast algorithm for numerical solutions to Fortet's equation

A fast algorithm for computation of default times of multiple firms in a structural model is presented. The algorithm uses a multivariate extension of the Fortet's equation and the structure of Toeplitz matrices to significantly improve the computation time. In a financial market consisting of M1 firms and N discretization points in every dimension the algorithm uses O(nlogn·M·M!·N^M(M-1)/2) operations, where n is the number of discretization points in the time domain. The algorithm is applied to firm survival probability computation and zero coupon bond pricing.     

Convex Optimization and Feasible Circulant Matrix Embeddings in Synthesis of Stationary Gaussian Fields

Circulant matrix embedding is one of the most popular and efficient methods for the exact generation of Gaussian stationary univariate series. Although the idea of circulant matrix embedding has also been used for the generation of Gaussian stationary random fields, there are many practical covariance structures of random fields where classical embedding methods break down. In this work, we propose a novel methodology that adaptively constructs feasible circulant embeddings based on convex optimization with an objective function measuring the distance of the covariance embedding to the targeted covariance structure over the domain of interest. The optimal value of the objective function will be zero if and only if there exists a feasible embedding for the a priori chosen embedding size.     

一维谐振子量子运动中的经典特性

利用量子力学的态叠加原理和算符劈裂法,对处于一维谐振子势中的初始态为高斯波包的中心位置的量子运动进行了研究.结果表明:其中心位置的量子运动呈现出经典谐振子的运动特性;波包的初始位置和初始时刻所加动量对波包中心位置量子动力学的影响与经典谐振子类似条件对运动的影响有相同的性质.本结果对理解复杂量子运动中的高斯波方法有一定的启示作用.     

复合夹层梁瞬态响应的谱有限元法

采用谱有限元法进行复合夹层梁的瞬态响应分析．该方法基于复合夹层梁的六阶运动微分方程,以其波动解作为动力位移形函数,根据标准有限元策略来构建复合夹层梁的动刚度矩阵．在频域内,夹心粘弹性材料的频率相关性采用复模量模型来模拟,进而利用快速傅立叶变换技术(FFT),得到时域内复合夹层梁的瞬态响应分析结果．最后以两端固支夹层梁为例,对其进行了矩形脉冲荷载下的动力响应分析,并与通用有限元程序NASTRAN的计算结果进行了对比,两者吻合良好．