Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these met...Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.展开更多
3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic m...3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.展开更多
In this work, we treat scattering objects, water, surface and bottom in a truly unified manner in a parallel finitedifference time-domain (FDTD) scheme, which is suitable for distributed parallel computing in a mess...In this work, we treat scattering objects, water, surface and bottom in a truly unified manner in a parallel finitedifference time-domain (FDTD) scheme, which is suitable for distributed parallel computing in a message passing interface (MPI) programming environment. The algorithm is implemented on a cluster-based high performance computer system. Parallel computation is performed with different division methods in 2D and 3D situations. Based on analysis of main factors affecting the speedup rate and parallel efficiency, data communication is reduced by selecting a suitable scheme of task division. A desirable scheme is recommended, giving a higher speedup rate and better efficiency. The results indicate that the unified parallel FDTD algorithm provides a solution to the numerical computation of acoustic scattering.展开更多
Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer(CPML) is given for solving the truncation problem of the open...Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer(CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain(ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor(PEC) waveguide.The algorithm has the same numerical stability as the ECT-CFDTD method.For the long-time propagation problems of an evanescent wave in a waveguide,several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML.Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide.展开更多
This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the...This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo's amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^(3+):YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp(α'L),which is previously employed to describe the relationship between echo's efficiency and thickness,should be modified as 1.3 · 0.09 exp(2.4 ·α'L) with the propagation of echo considered.展开更多
Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modu...Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modulus and combining the dynamic skeleton curve and the damping degradation coefficient,the constitutive equation of the logarithmic dynamic skeleton can be obtained,which considers the damping effect in a soil dynamics problem.Based on the finite difference method and the multi-transmitting boundary condition,a 1D site seismic response analysis program called Soilresp1D has been developed herein and used to analyze the time-domain seismic response in three types of sites.At the same time,this study also provides numerical simulation results based on the hyperbolic constitutive model and the equivalent linear method.The results verify the rationality of the new soil dynamic constitutive model.It can analyze the mucky soil site nonlinear seismic response,reflecting the deformation characteristics and damping effect of the silty soil.The hysteresis loop area is more extensive,and the residual strain is evident.展开更多
Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time st...Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.展开更多
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ...The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell's equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.展开更多
A higher-order finite-difference time-domain(HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spheric...A higher-order finite-difference time-domain(HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain(FDTD) and the multiresolution time-domain(MRTD) schemes with respect to memory requirements and CPU time. Moreover, the Berenger's perfectly matched layer(PML) is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.展开更多
Metallic ring-shaped nanotube arrays are proposed and its optical transmission properties are studied by using finite-difference time-domain (FDTD) method. Compared with the transmission spectra of conventional circ...Metallic ring-shaped nanotube arrays are proposed and its optical transmission properties are studied by using finite-difference time-domain (FDTD) method. Compared with the transmission spectra of conventional circular nanotube arrays, two photonic band gaps are emerged in the transmission spectra offing-shaped nanotube arrays, the two band gaps and transmission spectra are adjusted by the length, inner radius, intertube spacing and the dielectric constants of the core and embedding medium, and magnitude modification, redshift and blueshift of the resonance modes are observed. A metallic ring-shaped nanotube arrays for subwavelength band-stop filter in the range of visible light can be achieved. To understand its physical origin, field-interference mechanism was suggested by the field distributions. The proposed nanostructures and results may have great potential applications in subwavelength near-field optics.展开更多
The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order sy...The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite- difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.展开更多
An efficient conformal locally one-dimensional finite-difference time-domain(LOD-CFDTD) method is presented for solving two-dimensional(2D) electromagnetic(EM) scattering problems. The formulation for the 2D tra...An efficient conformal locally one-dimensional finite-difference time-domain(LOD-CFDTD) method is presented for solving two-dimensional(2D) electromagnetic(EM) scattering problems. The formulation for the 2D transverse-electric(TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit(ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field(TF/SF) boundary and the perfectly matched layer(PML), the radar cross section(RCS) of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.展开更多
An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness wav...An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness waveguide. ILC-FDTD not only removes tile instability of the original locally conformal FDTD algorithm, but also improves the computational accuracy by locally modifying magnetic field update equations and the virtual iterative electric fields accordlng to the complexity of tile slot fringe fields. The mutual coupling between two edge inclined slots can also be analyzed by ILC-FDTD effectively.展开更多
To deal with the staircase approximation problem in the standard finite-difference time-domain(FDTD) simulation,the two-dimensional boundary condition equations(BCE) method is proposed in this paper.In the BCE met...To deal with the staircase approximation problem in the standard finite-difference time-domain(FDTD) simulation,the two-dimensional boundary condition equations(BCE) method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.展开更多
The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes.Particularly,a high-aspect-ratio flexible flying wing is pr...The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes.Particularly,a high-aspect-ratio flexible flying wing is prone to body freedomflutter(BFF),which is a result of coupling of the rigid body short-periodmodewith 1st wing bendingmode.Accurate prediction of the BFF characteristics is helpful to reflect the attitude changes of the vehicle intuitively and design the active flutter suppression control law.Instead of using the rigid body mode,this work simulates the rigid bodymotion of the model by using the six-degree-of-freedom(6DOF)equation.A dynamicmesh generation strategy particularly suitable for BFF simulation of free flying aircraft is developed.An accurate Computational Fluid Dynamics/Computational Structural Dynamics/six-degree-of-freedom equation(CFD/CSD/6DOF)-based BFF prediction method is proposed.Firstly,the time-domain CFD/CSD method is used to calculate the static equilibrium state of the model.Based on this state,the CFD/CSD/6DOF equation is solved in time domain to evaluate the structural response of themodel.Then combinedwith the variable stiffnessmethod,the critical flutter point of the model is obtained.This method is applied to the BFF calculation of a flyingwing model.The calculation results of the BFF characteristics of the model agree well with those fromthe modalmethod andNastran software.Finally,the method is used to analyze the influence factors of BFF.The analysis results show that the flutter speed can be improved by either releasing plunge constraint or moving the center ofmass forward or increasing the pitch inertia.展开更多
The problem for calculating EM energy absorption by lossy dielectric scatterer ir-radiated by plane wave are discussed.The factors affecting the accuracy of computation arediscussed.The calculated results of EM energy...The problem for calculating EM energy absorption by lossy dielectric scatterer ir-radiated by plane wave are discussed.The factors affecting the accuracy of computation arediscussed.The calculated results of EM energy absorption and its distribution in homogeneousand layered homogenous lossy dielectric spheres are presented,and a comparison of these resultswith analytical solution is given.The calculation is carried out for dielectric cylinder on conduct-ing ground as well,and the results are compared with the image theory.All the computationsshew that the finite-difference time-domain method can give satisfactory results.展开更多
Prestack reverse time migration (RTM) is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of t...Prestack reverse time migration (RTM) is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference (FD) method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.展开更多
Generally, FD coefficients can be obtained by using Taylor series expansion (TE) or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a...Generally, FD coefficients can be obtained by using Taylor series expansion (TE) or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares (LS) can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional (2D) forward modeling to three-dimensional (3D) and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.展开更多
To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of ...To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.展开更多
During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surface-wave phenomenon. To accurately determine the effects o...During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surface-wave phenomenon. To accurately determine the effects of this interface on surface-wave propagation, the boundary conditions must be accurately modeled. In this paper, we present a numerical approach based on the dynamic poroelasticity for a space–time-domain staggered-grid finite-difference simulation in porous media that contain a free-surface boundary. We propose a generalized stess mirror formulation of the free-surface boundary for solids and fluids in porous media for the grid mesh on which lays the free-surface plane. Its analog is that used for elastic media, which is suitable for precise and stable Rayleigh-type surface-wave modeling. The results of our analysis of first kind of Rayleigh (R1) waves obtained by this model demonstrate that the discretization of the mesh in a similar way to that for elastic media can realize stable numerical solutions with acceptable precision. We present numerical examples demonstrating the efficiency and accuracy of our proposed method.展开更多
基金This research is supported by the National Natural Science Foundation of China(NSFC)under contract no.42274147.
文摘Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.
基金The authors thank the funds supported by the China National Nuclear Corporation under Grants Nos.WUQNYC2101 and WUHTLM2101-04National Natural Science Foundation of China(42074132,42274154).
文摘3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.
基金Project supported by the National Defense Laboratory Foundation (Grant No.51444020103QT0601)the Shanghai Leading Academic Discipline Project (Grant No.T0102)
文摘In this work, we treat scattering objects, water, surface and bottom in a truly unified manner in a parallel finitedifference time-domain (FDTD) scheme, which is suitable for distributed parallel computing in a message passing interface (MPI) programming environment. The algorithm is implemented on a cluster-based high performance computer system. Parallel computation is performed with different division methods in 2D and 3D situations. Based on analysis of main factors affecting the speedup rate and parallel efficiency, data communication is reduced by selecting a suitable scheme of task division. A desirable scheme is recommended, giving a higher speedup rate and better efficiency. The results indicate that the unified parallel FDTD algorithm provides a solution to the numerical computation of acoustic scattering.
基金supported by the National Natural Science Foundation of China(Grant No.61231003)
文摘Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer(CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain(ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor(PEC) waveguide.The algorithm has the same numerical stability as the ECT-CFDTD method.For the long-time propagation problems of an evanescent wave in a waveguide,several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML.Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide.
基金Project supported by Tianjin Research Program Application Foundation and Advanced Technology,China(Grant No.15JCQNJC01100)
文摘This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo's amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^(3+):YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp(α'L),which is previously employed to describe the relationship between echo's efficiency and thickness,should be modified as 1.3 · 0.09 exp(2.4 ·α'L) with the propagation of echo considered.
基金Major Program of the National Natural Science Foundation of China under Grant No.52192675 and the 111 Project of China under Grant No.D21001。
文摘Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modulus and combining the dynamic skeleton curve and the damping degradation coefficient,the constitutive equation of the logarithmic dynamic skeleton can be obtained,which considers the damping effect in a soil dynamics problem.Based on the finite difference method and the multi-transmitting boundary condition,a 1D site seismic response analysis program called Soilresp1D has been developed herein and used to analyze the time-domain seismic response in three types of sites.At the same time,this study also provides numerical simulation results based on the hyperbolic constitutive model and the equivalent linear method.The results verify the rationality of the new soil dynamic constitutive model.It can analyze the mucky soil site nonlinear seismic response,reflecting the deformation characteristics and damping effect of the silty soil.The hysteresis loop area is more extensive,and the residual strain is evident.
基金supported by National Natural Science Foundation of China(41504109,41404099)the Natural Science Foundation of Shandong Province(BS2015HZ008)the project of "Distinguished Professor of Jiangsu Province"
文摘Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304074,61475042,and 11274088)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2015202320 and GCC2014048)the Key Subject Construction Project of Hebei Province University,China
文摘The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell's equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61301063 and 41305017)
文摘A higher-order finite-difference time-domain(HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain(FDTD) and the multiresolution time-domain(MRTD) schemes with respect to memory requirements and CPU time. Moreover, the Berenger's perfectly matched layer(PML) is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.
基金Projects(11164007,61275174)supported by the National Natural Science Foundation of ChinaProject(20100162110068)supported by the Doctoral Program of Higher Education of China+1 种基金Project(20132BAB212007)supported by the Natural Science Foundation of Jiangxi Province,ChinaProject(GJJ11107)supported by Scientific Foundation of Jiangxi Education Department,China
文摘Metallic ring-shaped nanotube arrays are proposed and its optical transmission properties are studied by using finite-difference time-domain (FDTD) method. Compared with the transmission spectra of conventional circular nanotube arrays, two photonic band gaps are emerged in the transmission spectra offing-shaped nanotube arrays, the two band gaps and transmission spectra are adjusted by the length, inner radius, intertube spacing and the dielectric constants of the core and embedding medium, and magnitude modification, redshift and blueshift of the resonance modes are observed. A metallic ring-shaped nanotube arrays for subwavelength band-stop filter in the range of visible light can be achieved. To understand its physical origin, field-interference mechanism was suggested by the field distributions. The proposed nanostructures and results may have great potential applications in subwavelength near-field optics.
基金supported by the National Natural Science Foundation of China(Grant Nos.60931002 and 61101064)the Universities Natural Science Foundation of Anhui Province,China(Grant Nos.KJ2011A002 and 1108085J01)
文摘The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite- difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.
基金supported by the National Natural Science Foundation of China(Grant Nos.61331007 and 61471105)
文摘An efficient conformal locally one-dimensional finite-difference time-domain(LOD-CFDTD) method is presented for solving two-dimensional(2D) electromagnetic(EM) scattering problems. The formulation for the 2D transverse-electric(TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit(ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field(TF/SF) boundary and the perfectly matched layer(PML), the radar cross section(RCS) of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.
基金Supported by the National Natural Science Fbundation of China(No.69931030)
文摘An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness waveguide. ILC-FDTD not only removes tile instability of the original locally conformal FDTD algorithm, but also improves the computational accuracy by locally modifying magnetic field update equations and the virtual iterative electric fields accordlng to the complexity of tile slot fringe fields. The mutual coupling between two edge inclined slots can also be analyzed by ILC-FDTD effectively.
基金Project supported by the National Natural Science Foundation of China(Grant No.51025622)
文摘To deal with the staircase approximation problem in the standard finite-difference time-domain(FDTD) simulation,the two-dimensional boundary condition equations(BCE) method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.
基金This work was supported by the National Natural Science Foundation of China(No.11872212)and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes.Particularly,a high-aspect-ratio flexible flying wing is prone to body freedomflutter(BFF),which is a result of coupling of the rigid body short-periodmodewith 1st wing bendingmode.Accurate prediction of the BFF characteristics is helpful to reflect the attitude changes of the vehicle intuitively and design the active flutter suppression control law.Instead of using the rigid body mode,this work simulates the rigid bodymotion of the model by using the six-degree-of-freedom(6DOF)equation.A dynamicmesh generation strategy particularly suitable for BFF simulation of free flying aircraft is developed.An accurate Computational Fluid Dynamics/Computational Structural Dynamics/six-degree-of-freedom equation(CFD/CSD/6DOF)-based BFF prediction method is proposed.Firstly,the time-domain CFD/CSD method is used to calculate the static equilibrium state of the model.Based on this state,the CFD/CSD/6DOF equation is solved in time domain to evaluate the structural response of themodel.Then combinedwith the variable stiffnessmethod,the critical flutter point of the model is obtained.This method is applied to the BFF calculation of a flyingwing model.The calculation results of the BFF characteristics of the model agree well with those fromthe modalmethod andNastran software.Finally,the method is used to analyze the influence factors of BFF.The analysis results show that the flutter speed can be improved by either releasing plunge constraint or moving the center ofmass forward or increasing the pitch inertia.
文摘The problem for calculating EM energy absorption by lossy dielectric scatterer ir-radiated by plane wave are discussed.The factors affecting the accuracy of computation arediscussed.The calculated results of EM energy absorption and its distribution in homogeneousand layered homogenous lossy dielectric spheres are presented,and a comparison of these resultswith analytical solution is given.The calculation is carried out for dielectric cylinder on conduct-ing ground as well,and the results are compared with the image theory.All the computationsshew that the finite-difference time-domain method can give satisfactory results.
基金This research was supported by the National Nature Science Foundation of China (No. 41074100) and the Program for NewCentury Excellent Talents in the University of the Ministry of Education of China (No. NCET- 10-0812).
文摘Prestack reverse time migration (RTM) is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference (FD) method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.
基金supported by the National Natural Science Foundation of China(No.41474110)Shell Ph.D. Scholarship to support excellence in geophysical research
文摘Generally, FD coefficients can be obtained by using Taylor series expansion (TE) or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares (LS) can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional (2D) forward modeling to three-dimensional (3D) and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.
文摘To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.
基金sponsed by National Natural Science Foundation of China(NSFC,Grant No.41304077)the Natural Basic Research Program of China(the“973 Project,”Grant No.2013CB733303)Postdoctoral Science Foundation of China(Grant No.2014T70740)
文摘During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surface-wave phenomenon. To accurately determine the effects of this interface on surface-wave propagation, the boundary conditions must be accurately modeled. In this paper, we present a numerical approach based on the dynamic poroelasticity for a space–time-domain staggered-grid finite-difference simulation in porous media that contain a free-surface boundary. We propose a generalized stess mirror formulation of the free-surface boundary for solids and fluids in porous media for the grid mesh on which lays the free-surface plane. Its analog is that used for elastic media, which is suitable for precise and stable Rayleigh-type surface-wave modeling. The results of our analysis of first kind of Rayleigh (R1) waves obtained by this model demonstrate that the discretization of the mesh in a similar way to that for elastic media can realize stable numerical solutions with acceptable precision. We present numerical examples demonstrating the efficiency and accuracy of our proposed method.