In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependen...In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L<sub>2</sub> and L<sub>∞</sub> error norms are computed to study the accuracy and the simplicity of the presented method.展开更多
Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harm...Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.展开更多
A base function expressed with Chebyshev polynomials is reached. The relationship between the coefficients of the partial differential equation and the base function is deduced. Using the relationship, one can obtain ...A base function expressed with Chebyshev polynomials is reached. The relationship between the coefficients of the partial differential equation and the base function is deduced. Using the relationship, one can obtain nearly the same results as those calculated by Fast Fourier Transformation (FFT). The pseudo-spectral matrix method is applied in this paper to simulate numerically the incompressible laminar boundary flow on a plate. The simulation proves to be precise and efficient.展开更多
We propose a new scheme for simulation of a high-order nonlinear Schrodinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respec...We propose a new scheme for simulation of a high-order nonlinear Schrodinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.展开更多
This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch curre...This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.展开更多
针对傅里叶分解方法存在过度分解、运算时间长等问题,提出了一种基于循环频谱包络的经验傅里叶分解(CEEFD)算法,并将该算法运用到滚动轴承故障诊断中。首先,对信号进行了快速傅里叶变换(FFT),获得了信号的频谱,对傅里叶频谱进行了循环包...针对傅里叶分解方法存在过度分解、运算时间长等问题,提出了一种基于循环频谱包络的经验傅里叶分解(CEEFD)算法,并将该算法运用到滚动轴承故障诊断中。首先,对信号进行了快速傅里叶变换(FFT),获得了信号的频谱,对傅里叶频谱进行了循环包络,得到了包络曲线,减少了无用极值点的个数,抑制了噪声对分量的干扰;然后,采用改进的局部最大最小值(local max min)分割技术,对频谱包络曲线进行了频带分割;最后,构建了零相位滤波器,采用逆快速傅里叶变换(IFFT)对每个频带进行了信号重构,得到了若干个瞬时频率且具有物理意义的单分量信号;通过对仿真信号和滚动轴承实测信号的分析,并将其与经验模态分解(EMD)、经验小波变换(EWT)、傅里叶分解方法(FDM)、变分模态分解(VMD)和经验傅里叶分解(EFD)进行了实验对比验证。研究结果表明:采用CEEFD方法获得的单分量包含了更准确的故障特征信息,验证了CEEFD方法的有效性,CEEFD方法可用于轴承的故障诊断;相对于上述方法,CEEFD方法具有更高的准确精度和更强的抗噪声干扰能力。展开更多
We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing therma...We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.展开更多
文摘In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L<sub>2</sub> and L<sub>∞</sub> error norms are computed to study the accuracy and the simplicity of the presented method.
基金Project supported by the National Natural Science Foundation of China (No.10172038)
文摘Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.
文摘A base function expressed with Chebyshev polynomials is reached. The relationship between the coefficients of the partial differential equation and the base function is deduced. Using the relationship, one can obtain nearly the same results as those calculated by Fast Fourier Transformation (FFT). The pseudo-spectral matrix method is applied in this paper to simulate numerically the incompressible laminar boundary flow on a plate. The simulation proves to be precise and efficient.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11201169 and 11271195)the Qing Lan Project of Jiangsu Province,China
文摘We propose a new scheme for simulation of a high-order nonlinear Schrodinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.
基金Supported by the National Natural Science Foundation of China
文摘This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.
文摘针对傅里叶分解方法存在过度分解、运算时间长等问题,提出了一种基于循环频谱包络的经验傅里叶分解(CEEFD)算法,并将该算法运用到滚动轴承故障诊断中。首先,对信号进行了快速傅里叶变换(FFT),获得了信号的频谱,对傅里叶频谱进行了循环包络,得到了包络曲线,减少了无用极值点的个数,抑制了噪声对分量的干扰;然后,采用改进的局部最大最小值(local max min)分割技术,对频谱包络曲线进行了频带分割;最后,构建了零相位滤波器,采用逆快速傅里叶变换(IFFT)对每个频带进行了信号重构,得到了若干个瞬时频率且具有物理意义的单分量信号;通过对仿真信号和滚动轴承实测信号的分析,并将其与经验模态分解(EMD)、经验小波变换(EWT)、傅里叶分解方法(FDM)、变分模态分解(VMD)和经验傅里叶分解(EFD)进行了实验对比验证。研究结果表明:采用CEEFD方法获得的单分量包含了更准确的故障特征信息,验证了CEEFD方法的有效性,CEEFD方法可用于轴承的故障诊断;相对于上述方法,CEEFD方法具有更高的准确精度和更强的抗噪声干扰能力。
文摘We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.
