In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the sol...In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.展开更多
The Fourier transform spectrometer(FTS)is a core instrument for solar observation with high spectral resolution,especially in the infrared.The Infrared System for the Accurate Measurement of Solar Magnetic Field(AIMS)...The Fourier transform spectrometer(FTS)is a core instrument for solar observation with high spectral resolution,especially in the infrared.The Infrared System for the Accurate Measurement of Solar Magnetic Field(AIMS),working at 10-13μm,will use an FTS to observe the solar spectrum.The Bruker IFS-125 HR,which meets the spectral resolution requirement of AIMS but simply equips with a point source detector,is employed to carry out preliminary experiment for AIMS.A sun-light feeding experimental system is further developed.Several experiments are taken with them during 2018 and 2019 to observe the solar spectrum in the visible and near infrared wavelength,respectively.We also proposed an inversion method to retrieve the solar spectrum from the observed interferogram and compared it with the standard solar spectrum atlas.Although there is a wavelength limitation due to the present sun-light feeding system,the results in the wavelength band from 0.45-1.0μm and 1.0-2.2μm show a good consistency with the solar spectrum atlas,indicating the validity of our observing configuration,the data analysis method and the potential to work in longer wavelength.The work provided valuable experience for the AIMS not only for the operation of an FTS but also for the development of its scientific data processing software.展开更多
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
In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for S...In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for Schrodingerlike equation in time.(ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization.(iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.展开更多
Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the add...Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.展开更多
The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary elem...The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.展开更多
In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential e...In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential equations with initial boundary value (IBVP). According to boundary condition, the initial condition is expanded into a Fourier series. After that, the IBVP is transformed to an iterative relation in K-domain. The series solution or exact solution can be obtained. The rationality and practicability of the algorithm FDTM are verified by comparisons of the results obtained by FDTM and the existing analytical solutions.展开更多
Conventional frequency domain method used in random noise attenuation singular value decomposition （SVD） filtering processing causes bending event damage. To mitigate this problem, we present a mixed Cadzow filterin...Conventional frequency domain method used in random noise attenuation singular value decomposition （SVD） filtering processing causes bending event damage. To mitigate this problem, we present a mixed Cadzow filtering method based on fractional Fourier transform to suppress random noise in 3D seismic data. First, the seismic data is transformed to the time-frequency plane via the fractional Fourier transform. Second, based on the Eigenimage filtering method and Cadzow filtering method, the mixed high-dimensional Hankel matrix is built; then, SVD is performed. Finally, random noise is eliminated effectively by reducing the rank of the matrix. The theoretical model and real applications of the mixed filtering method in a region of Sichuan show that our method can not only suppress noise effectively but also preserve the frequency and phase of effective signals quite well and significantly improve the signal-to-noise ratio of 3D post-stack seismic data.展开更多
With the increasing accuracy requirements of satellite magnetic detection missions,reducing low-frequency noise has become a key focus of satellite magnetic cleanliness technology.Traditional satellite magnetic simula...With the increasing accuracy requirements of satellite magnetic detection missions,reducing low-frequency noise has become a key focus of satellite magnetic cleanliness technology.Traditional satellite magnetic simulation methods have matured in static magnetic dipole simulations,but there is still significant room for optimization in the simulation and computation of low-frequency magnetic dipole models.This study employs the Gauss-Newton method and Fourier transform techniques for modeling and simulating low-frequency magnetic dipoles.Compared to the traditional particle swarm optimization(PSO)algorithm,this method achieves significant improvements,with errors reaching the order of10^(-13)%under noise-free conditions and maintaining an error level of less than 0.5%under 10%noise.Additionally,the use of Fourier transform and the Gauss-Newton method enables high-precision magnetic field frequency identification and rapid computation of the dipole position and magnetic moment,greatly enhancing the computational efficiency and accuracy of the model.展开更多
文摘In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.
基金supported by the National Natural Science Foundation of China(Grant Nos.11873062,11427901,11673038,11803002,11973056,11973061,12003051 and 12073040)supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant Nos.XDA15320102 and XDA15052200)。
文摘The Fourier transform spectrometer(FTS)is a core instrument for solar observation with high spectral resolution,especially in the infrared.The Infrared System for the Accurate Measurement of Solar Magnetic Field(AIMS),working at 10-13μm,will use an FTS to observe the solar spectrum.The Bruker IFS-125 HR,which meets the spectral resolution requirement of AIMS but simply equips with a point source detector,is employed to carry out preliminary experiment for AIMS.A sun-light feeding experimental system is further developed.Several experiments are taken with them during 2018 and 2019 to observe the solar spectrum in the visible and near infrared wavelength,respectively.We also proposed an inversion method to retrieve the solar spectrum from the observed interferogram and compared it with the standard solar spectrum atlas.Although there is a wavelength limitation due to the present sun-light feeding system,the results in the wavelength band from 0.45-1.0μm and 1.0-2.2μm show a good consistency with the solar spectrum atlas,indicating the validity of our observing configuration,the data analysis method and the potential to work in longer wavelength.The work provided valuable experience for the AIMS not only for the operation of an FTS but also for the development of its scientific data processing software.
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Supported by the National Natural Science Foundation of China under Grant No.11571181
文摘In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for Schrodingerlike equation in time.(ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization.(iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.
基金supported by the National Natural Science Foundation of China (No. 10671154)the Na-tional Basic Research Program (No. 2005CB321703)the Science and Technology Foundation of Guizhou Province of China (No. [2008]2123)
文摘Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.
基金This project is supported by National Natural Science Foundation of China
文摘The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.
文摘In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential equations with initial boundary value (IBVP). According to boundary condition, the initial condition is expanded into a Fourier series. After that, the IBVP is transformed to an iterative relation in K-domain. The series solution or exact solution can be obtained. The rationality and practicability of the algorithm FDTM are verified by comparisons of the results obtained by FDTM and the existing analytical solutions.
基金sponsored by the major science and technology special topic of CNPC(No.2013E-38-08)
文摘Conventional frequency domain method used in random noise attenuation singular value decomposition （SVD） filtering processing causes bending event damage. To mitigate this problem, we present a mixed Cadzow filtering method based on fractional Fourier transform to suppress random noise in 3D seismic data. First, the seismic data is transformed to the time-frequency plane via the fractional Fourier transform. Second, based on the Eigenimage filtering method and Cadzow filtering method, the mixed high-dimensional Hankel matrix is built; then, SVD is performed. Finally, random noise is eliminated effectively by reducing the rank of the matrix. The theoretical model and real applications of the mixed filtering method in a region of Sichuan show that our method can not only suppress noise effectively but also preserve the frequency and phase of effective signals quite well and significantly improve the signal-to-noise ratio of 3D post-stack seismic data.
基金supported by the National Key Research and Development Program of China(Grant No.2023YFC2206003)。
文摘With the increasing accuracy requirements of satellite magnetic detection missions,reducing low-frequency noise has become a key focus of satellite magnetic cleanliness technology.Traditional satellite magnetic simulation methods have matured in static magnetic dipole simulations,but there is still significant room for optimization in the simulation and computation of low-frequency magnetic dipole models.This study employs the Gauss-Newton method and Fourier transform techniques for modeling and simulating low-frequency magnetic dipoles.Compared to the traditional particle swarm optimization(PSO)algorithm,this method achieves significant improvements,with errors reaching the order of10^(-13)%under noise-free conditions and maintaining an error level of less than 0.5%under 10%noise.Additionally,the use of Fourier transform and the Gauss-Newton method enables high-precision magnetic field frequency identification and rapid computation of the dipole position and magnetic moment,greatly enhancing the computational efficiency and accuracy of the model.
