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 paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibi...In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.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
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
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
The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces o...The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.展开更多
In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this...In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations: the first-order (velocity-stress) and the second- order (displacement-stress) separate elastic wave equa- tions, with the first-order (velocity-stress) and the second- order (displacement-stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.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
The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the tim...The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.展开更多
Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element method...Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green's function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.展开更多
The entropy split method is based on the physical entropies of the thermally perfect gas Euler equations.The Euler flux derivatives are approximated as a sum of a conservative portion and a non-conservative portion in...The entropy split method is based on the physical entropies of the thermally perfect gas Euler equations.The Euler flux derivatives are approximated as a sum of a conservative portion and a non-conservative portion in conjunction with summation-by-parts(SBP)difference boundary closure of(Gerritsen and Olsson in J Comput Phys 129:245-262,1996;Olsson and Oliger in RIACS Tech Rep 94.01,1994;Yee et al.in J Comp Phys 162:33-81,2000).Sj?green and Yee(J Sci Comput)recently proved that the entropy split method is entropy conservative and stable.Stand-ard high-order spatial central differencing as well as high order central spatial dispersion relation preserving(DRP)spatial differencing is part of the entropy stable split methodol-ogy framework.The current work is our first attempt to derive a high order conservative numerical flux for the non-conservative portion of the entropy splitting of the Euler flux derivatives.Due to the construction,this conservative numerical flux requires higher oper-ations count and is less stable than the original semi-conservative split method.However,the Tadmor entropy conservative(EC)method(Tadmor in Acta Numerica 12:451-512,2003)of the same order requires more operations count than the new construction.Since the entropy split method is a semi-conservative skew-symmetric splitting of the Euler flux derivative,a modified nonlinear filter approach of(Yee et al.in J Comput Phys 150:199-238,1999,J Comp Phys 162:3381,2000;Yee and Sj?green in J Comput Phys 225:910934,2007,High Order Filter Methods for Wide Range of Compressible flow Speeds.Proceedings of the ICOSAHOM09,June 22-26,Trondheim,Norway,2009)is proposed in conjunction with the entropy split method as the base method for problems containing shock waves.Long-time integration of 2D and 3D test cases is included to show the com-parison of these new approaches.展开更多
Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three trans...Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.展开更多
The piecewise linear recursive convolution (PLRC) finite-different time-domain (FDTD) method improves accuracy over the original recursive convolution (RC) FDTD approach and current density convolution (JEC) b...The piecewise linear recursive convolution (PLRC) finite-different time-domain (FDTD) method improves accuracy over the original recursive convolution (RC) FDTD approach and current density convolution (JEC) but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.展开更多
Objective In order to find early latent faults and prevent catastrophic failures, diagnosis of insulation condition by measuring technique of partial discharge(PD) in gas insulated switchgear (GIS) is applied in this ...Objective In order to find early latent faults and prevent catastrophic failures, diagnosis of insulation condition by measuring technique of partial discharge(PD) in gas insulated switchgear (GIS) is applied in this paper, which is one of the most basic ways for diagnosis of insulation condition. Methods Ultra high frequency(UHF) PD detection method by using internal sensors has been proved efficient, because it may avoid the disturbance of corona, but the sensor installation of this method will be limited by the structure and operation condition of GIS. There are some of electromagnetic (E-M) waves leak from the place of insulation spacer, therefore, the external sensors UHF measuring PD technique is applied, which isn't limited by the operation condition of GIS. Results This paper analyzes propagated electromagnetic (E-M) waves of partial discharge pulse excited by using the finite-difference time-domain (FDTD) method. The signal collected at the outer point is more complex than that of the inner point, and the signals' amplitude of outer is about half of the inner, because it propagates through spacer and insulation slot. Set up UHF PD measuring system. The typical PD in 252kV GIS bus bar was measured using PD detection UHF technique with external sensors. Finally, compare the results of UHF measuring technique using external sensors with the results of FDTD method simulation and the traditional IEC60270 method detection. Conclusion The results of experiment shows that the UHF technique can realize the diagnosis of insulation condition, the results of FDTD method simulation and the result UHF method detection can demonstrate each other, which gives references to further researches and application for UHF PD measuring technique.展开更多
In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is i...In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.展开更多
The characteristics of a cylindrical conformal microstrip patch antenna are analyzed by using the characteristic-based time domain (CBTD) method. A governing equation in the cylindrical coordinate system is formulat...The characteristics of a cylindrical conformal microstrip patch antenna are analyzed by using the characteristic-based time domain (CBTD) method. A governing equation in the cylindrical coordinate system is formulated directly to facilitate the analysis of cylindrically conformal microstrip patch antennas. The algorithm has second-order accuracy both in time and space domain and has the potential to eliminate the spurious wave reflection from the numerical boundaries of the computational domain, Numerical results demonstrate the important merits and accuracy of the proposed technique in computational electromagnetics,展开更多
This paper proposes a hybrid full-wave analysis using Finite-Difference Time-Domain (FDTD) and Wave Concept Iterative Process (WCIP) methods, developed to analyze locally arbitrarily shaped microwave structures and Mu...This paper proposes a hybrid full-wave analysis using Finite-Difference Time-Domain (FDTD) and Wave Concept Iterative Process (WCIP) methods, developed to analyze locally arbitrarily shaped microwave structures and Multilayer Planar structure. Using the equivalence principle, the original problem can be decomposed into two sub regions and solve each sub region separately. An interpolation scheme is proposed for communicating between the FDTD fields and WCIP wave, which will not require the effort of fitting the WCIP mesh to the FDTD cells in the interface region. This method is applied to calculate the scattering parameters of arbitrary (3-D) microwave structures. Applying FDTD to 3D discontinuity and WCIP to the remaining region preserves the advantages of both WCIP flexibility and FDTD efficiency. A comparison of the results with the FDTD staircasing data verifies the accuracy of the proposed method.展开更多
Conventional gradient-based full waveform inversion (FWI) is a local optimization, which is highly dependent on the initial model and prone to trapping in local minima. Globally optimal FWI that can overcome this limi...Conventional gradient-based full waveform inversion (FWI) is a local optimization, which is highly dependent on the initial model and prone to trapping in local minima. Globally optimal FWI that can overcome this limitation is particularly attractive, but is currently limited by the huge amount of calculation. In this paper, we propose a globally optimal FWI framework based on GPU parallel computing, which greatly improves the efficiency, and is expected to make globally optimal FWI more widely used. In this framework, we simplify and recombine the model parameters, and optimize the model iteratively. Each iteration contains hundreds of individuals, each individual is independent of the other, and each individual contains forward modeling and cost function calculation. The framework is suitable for a variety of globally optimal algorithms, and we test the framework with particle swarm optimization algorithm for example. Both the synthetic and field examples achieve good results, indicating the effectiveness of the framework. .展开更多
In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approxim...In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.展开更多
The approach to optimization of finite-difference(FD)schemes for the linear advection equation(LAE)is proposed.The FD schemes dependent on the scalar dimensionless parameter are considered.The parameter is included in...The approach to optimization of finite-difference(FD)schemes for the linear advection equation(LAE)is proposed.The FD schemes dependent on the scalar dimensionless parameter are considered.The parameter is included in the expression,which approximates the term with spatial derivatives.The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter.For the proper choice of the parameter,these functions are minimized.The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term.The cases of schemes from first to fourth approximation orders are considered.The optimal values of the parameter are obtained.Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions.Also,schemes are used in the FD-based lattice Boltzmann method(LBM)for modeling of the compressible gas flow.The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.展开更多
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the National Natural Science Foundation of China(No.40774056)Program of Excellent Team in Harbin Institute of Technology
文摘In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.
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.
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Taif University Researchers Supporting Project Number(TURSP-2020/164),Taif University,Taif,Saudi Arabia.
文摘The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.
基金partially supported by China National Major Science and Technology Project (Subproject No:2011ZX05024-001-03)
文摘In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations: the first-order (velocity-stress) and the second- order (displacement-stress) separate elastic wave equa- tions, with the first-order (velocity-stress) and the second- order (displacement-stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.
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 Joint Fund of Seismological Science(Grant No.U1839206)the National R&D Program on Monitoring,Early Warning and Prevention of Major Natural Disaster(Grant No.2017YFC1500301)+2 种基金supported by IGGCAS Research Start-up Funds(Grant No.E0515402)National Natural Science Foundation of China(Grant No.E1115401)supported by National Natural Science Foundation of China(Grant No.11971258).
文摘The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.
基金supported by the National Natural Science Foundation of China (No. 41130418)the Strategic Leading Science and Technology Programme (Class B) of the Chinese Academy of Sciences (No. XDB10010400)
文摘Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green's function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.
基金support from the NASA TTT/RCA program for the second author is grate-fully acknowledged.
文摘The entropy split method is based on the physical entropies of the thermally perfect gas Euler equations.The Euler flux derivatives are approximated as a sum of a conservative portion and a non-conservative portion in conjunction with summation-by-parts(SBP)difference boundary closure of(Gerritsen and Olsson in J Comput Phys 129:245-262,1996;Olsson and Oliger in RIACS Tech Rep 94.01,1994;Yee et al.in J Comp Phys 162:33-81,2000).Sj?green and Yee(J Sci Comput)recently proved that the entropy split method is entropy conservative and stable.Stand-ard high-order spatial central differencing as well as high order central spatial dispersion relation preserving(DRP)spatial differencing is part of the entropy stable split methodol-ogy framework.The current work is our first attempt to derive a high order conservative numerical flux for the non-conservative portion of the entropy splitting of the Euler flux derivatives.Due to the construction,this conservative numerical flux requires higher oper-ations count and is less stable than the original semi-conservative split method.However,the Tadmor entropy conservative(EC)method(Tadmor in Acta Numerica 12:451-512,2003)of the same order requires more operations count than the new construction.Since the entropy split method is a semi-conservative skew-symmetric splitting of the Euler flux derivative,a modified nonlinear filter approach of(Yee et al.in J Comput Phys 150:199-238,1999,J Comp Phys 162:3381,2000;Yee and Sj?green in J Comput Phys 225:910934,2007,High Order Filter Methods for Wide Range of Compressible flow Speeds.Proceedings of the ICOSAHOM09,June 22-26,Trondheim,Norway,2009)is proposed in conjunction with the entropy split method as the base method for problems containing shock waves.Long-time integration of 2D and 3D test cases is included to show the com-parison of these new approaches.
基金This research is supported by the National Natural Science Foundation of China(grant No.U1839208).
文摘Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.
基金National Natural Science Foundation of China (No. 60471002) and the Natural Science Foundation ofJiangxi Province (No. 0412014)
文摘The piecewise linear recursive convolution (PLRC) finite-different time-domain (FDTD) method improves accuracy over the original recursive convolution (RC) FDTD approach and current density convolution (JEC) but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.
文摘Objective In order to find early latent faults and prevent catastrophic failures, diagnosis of insulation condition by measuring technique of partial discharge(PD) in gas insulated switchgear (GIS) is applied in this paper, which is one of the most basic ways for diagnosis of insulation condition. Methods Ultra high frequency(UHF) PD detection method by using internal sensors has been proved efficient, because it may avoid the disturbance of corona, but the sensor installation of this method will be limited by the structure and operation condition of GIS. There are some of electromagnetic (E-M) waves leak from the place of insulation spacer, therefore, the external sensors UHF measuring PD technique is applied, which isn't limited by the operation condition of GIS. Results This paper analyzes propagated electromagnetic (E-M) waves of partial discharge pulse excited by using the finite-difference time-domain (FDTD) method. The signal collected at the outer point is more complex than that of the inner point, and the signals' amplitude of outer is about half of the inner, because it propagates through spacer and insulation slot. Set up UHF PD measuring system. The typical PD in 252kV GIS bus bar was measured using PD detection UHF technique with external sensors. Finally, compare the results of UHF measuring technique using external sensors with the results of FDTD method simulation and the traditional IEC60270 method detection. Conclusion The results of experiment shows that the UHF technique can realize the diagnosis of insulation condition, the results of FDTD method simulation and the result UHF method detection can demonstrate each other, which gives references to further researches and application for UHF PD measuring technique.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education(No.20010614003)
文摘In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.
文摘The characteristics of a cylindrical conformal microstrip patch antenna are analyzed by using the characteristic-based time domain (CBTD) method. A governing equation in the cylindrical coordinate system is formulated directly to facilitate the analysis of cylindrically conformal microstrip patch antennas. The algorithm has second-order accuracy both in time and space domain and has the potential to eliminate the spurious wave reflection from the numerical boundaries of the computational domain, Numerical results demonstrate the important merits and accuracy of the proposed technique in computational electromagnetics,
文摘This paper proposes a hybrid full-wave analysis using Finite-Difference Time-Domain (FDTD) and Wave Concept Iterative Process (WCIP) methods, developed to analyze locally arbitrarily shaped microwave structures and Multilayer Planar structure. Using the equivalence principle, the original problem can be decomposed into two sub regions and solve each sub region separately. An interpolation scheme is proposed for communicating between the FDTD fields and WCIP wave, which will not require the effort of fitting the WCIP mesh to the FDTD cells in the interface region. This method is applied to calculate the scattering parameters of arbitrary (3-D) microwave structures. Applying FDTD to 3D discontinuity and WCIP to the remaining region preserves the advantages of both WCIP flexibility and FDTD efficiency. A comparison of the results with the FDTD staircasing data verifies the accuracy of the proposed method.
文摘Conventional gradient-based full waveform inversion (FWI) is a local optimization, which is highly dependent on the initial model and prone to trapping in local minima. Globally optimal FWI that can overcome this limitation is particularly attractive, but is currently limited by the huge amount of calculation. In this paper, we propose a globally optimal FWI framework based on GPU parallel computing, which greatly improves the efficiency, and is expected to make globally optimal FWI more widely used. In this framework, we simplify and recombine the model parameters, and optimize the model iteratively. Each iteration contains hundreds of individuals, each individual is independent of the other, and each individual contains forward modeling and cost function calculation. The framework is suitable for a variety of globally optimal algorithms, and we test the framework with particle swarm optimization algorithm for example. Both the synthetic and field examples achieve good results, indicating the effectiveness of the framework. .
基金partially supported by the NASA Nebraska Space Grant Program and UCRCA at the University of Nebraska at Omaha.
文摘In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.
文摘The approach to optimization of finite-difference(FD)schemes for the linear advection equation(LAE)is proposed.The FD schemes dependent on the scalar dimensionless parameter are considered.The parameter is included in the expression,which approximates the term with spatial derivatives.The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter.For the proper choice of the parameter,these functions are minimized.The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term.The cases of schemes from first to fourth approximation orders are considered.The optimal values of the parameter are obtained.Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions.Also,schemes are used in the FD-based lattice Boltzmann method(LBM)for modeling of the compressible gas flow.The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.