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
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
The Z-Axis tiPPer eiectromagnetic （ZTEM） technique is based on a frequency-domain airbome electromagnetic system that measures the natural magnetic field. A survey area was divided into several blocks by using the M...The Z-Axis tiPPer eiectromagnetic （ZTEM） technique is based on a frequency-domain airbome electromagnetic system that measures the natural magnetic field. A survey area was divided into several blocks by using the Maxwell＇s equations, and the magnetic components at the center of each edge of the grid cell are evaluated by applying the staggered-grid finite-difference method. The tipper and its divergence are derived to complete the 3D ZTEM forward modeling algorithm. A synthetic model is then used to compare the responses with those of 2D finite-element forward modeling to verify the accuracy of the algorithm. ZTEM offers high horizontal resolution to both simple and complex distributions of conductivity. This work is the theoretical foundation for the interpretation of ZTEM data and the study of 3D ZTEM inversion.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
The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip lines.The key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle states...The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip lines.The key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle states.In this paper,we solve the RHB equation with the Woods-Saxon-type mean-field and Delta-type pairing-field potentials by using the finite-difference method(FDM).We inevitably obtain spurious states when using the common symmetric central difference formula(CDF)to construct the Hamiltonian matrix,which is similar to the problem resulting from solving the Dirac equation with the same method.This problem is solved by using the asymmetric difference formula(ADF).In addition,we show that a large enough box is necessary to describe the continuum quasi-particle states.The canonical states obtained by diagonalizing the density matrix constructed by the quasi-particle states are not particularly sensitive to the box size.Part of the asymptotic wave functions can be improved by applying the ADF in the FDM compared to the shooting method with the same box boundary condition.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 fluid-structure interaction(FSI)in aircraft hydraulic pipeline systems is of great concern because of the damage it causes.To accurately predict the vibration characteristic of long hydraulic pipelines with curved...The fluid-structure interaction(FSI)in aircraft hydraulic pipeline systems is of great concern because of the damage it causes.To accurately predict the vibration characteristic of long hydraulic pipelines with curved segments,we studied the frequency-domain modeling and solution method for FSI in these pipeline systems.Fourteen partial differential equations(PDEs)are utilized to model the pipeline FSI,considering both frequency-dependent friction and bending-flexibility modification.To address the numerical instability encountered by the traditional transfer matrix method(TMM)in solving relatively complex pipelines,an improved TMM is proposed for solving the PDEs in the frequency domain,based on the matrix-stacking strategy and matrix representation of boundary conditions.The proposed FSI model and improved solution method are validated by numerical cases and experiments.An experimental rig of a practical hydraulic system,consisting of an aircraft engine-driven pump,a Z-shaped aero-hydraulic pipeline,and a throttle valve,was constructed for testing.The magnitude ratio of acceleration to pressure is introduced to evaluate the theoretical and experimental results,which indicate that the proposed model and solution method are effective in practical applications.The methodology presented in this paper can be used as an efficient approach for the vibrational design of aircraft hydraulic pipeline systems.展开更多
Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse ...Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.展开更多
The use of columns on elastic foundation is very common in Civil Engineering, like bridge pier, the foundation of the buildings etc. So, it will be useful to find the critical load for the structure, the problem in th...The use of columns on elastic foundation is very common in Civil Engineering, like bridge pier, the foundation of the buildings etc. So, it will be useful to find the critical load for the structure, the problem in this paper will be solved by Finite-Difference Mode, that＇ s simple and has an extensive use. The way it works is that by dividing the component into many units. Finite-difference methods （FDM） are numerical methods for anoroximating, the solutions to differential eauations usine finite difference equations to approximate derivatives.展开更多
The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, e...The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.展开更多
We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular...We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.展开更多
With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） meth...With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.展开更多
Seismic anisotropy has been extensively acknowledged as a crucial element that influences the wave propagation characteristic during wavefield simulation,inversion and imaging.Transversely isotropy(TI)and orthorhombic...Seismic anisotropy has been extensively acknowledged as a crucial element that influences the wave propagation characteristic during wavefield simulation,inversion and imaging.Transversely isotropy(TI)and orthorhombic anisotropy(OA)are two typical categories of anisotropic media in exploration geophysics.In comparison of the elastic wave equations in both TI and OA media,pseudo-acoustic wave equations(PWEs)based on the acoustic assumption can markedly reduce computational cost and complexity.However,the presently available PWEs may experience SV-wave contamination and instability when anisotropic parameters cannot satisfy the approximated condition.Exploiting pure-mode wave equations can effectively resolve the above-mentioned issues and generate pure P-wave events without any artifacts.To further improve the computational accuracy and efficiency,we develop two novel pure qP-wave equations(PPEs)and illustrate the corresponding numerical solutions in the timespace domain for 3D tilted TI(TTI)and tilted OA(TOA)media.First,the rational polynomials are adopted to estimate the exact pure qP-wave dispersion relations,which contain complicated pseudo-differential operators with irrational forms.The polynomial coefficients are produced by applying a linear optimization algorithm to minimize the objective function difference between the expansion formula and the exact one.Then,the developed optimized PPEs are efficiently implemented using the finite-difference(FD)method in the time-space domain by introducing a scalar operator,which can help avoid the problem of spectral-based algorithms and other calculation burdens.Structures of the new equations are concise and corresponding implementation processes are straightforward.Phase velocity analyses indicate that our proposed optimized equations can lead to reliable approximation results.3D synthetic examples demonstrate that our proposed FD-based PPEs can produce accurate and stable P-wave responses,and effectively describe the wavefield features in complicated TTI and TOA media.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 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supported by the Natural Science Foundation of China(No.41374078)Geological Survey Projects of Ministry of Land and Resources of China(No.12120113086100 and 12120113101300)
文摘The Z-Axis tiPPer eiectromagnetic （ZTEM） technique is based on a frequency-domain airbome electromagnetic system that measures the natural magnetic field. A survey area was divided into several blocks by using the Maxwell＇s equations, and the magnetic components at the center of each edge of the grid cell are evaluated by applying the staggered-grid finite-difference method. The tipper and its divergence are derived to complete the 3D ZTEM forward modeling algorithm. A synthetic model is then used to compare the responses with those of 2D finite-element forward modeling to verify the accuracy of the algorithm. ZTEM offers high horizontal resolution to both simple and complex distributions of conductivity. This work is the theoretical foundation for the interpretation of ZTEM data and the study of 3D ZTEM inversion.
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(11775119,2175109)the Natural Science Foundation of Tianjin,China(19JCYBJC30800)。
文摘The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip lines.The key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle states.In this paper,we solve the RHB equation with the Woods-Saxon-type mean-field and Delta-type pairing-field potentials by using the finite-difference method(FDM).We inevitably obtain spurious states when using the common symmetric central difference formula(CDF)to construct the Hamiltonian matrix,which is similar to the problem resulting from solving the Dirac equation with the same method.This problem is solved by using the asymmetric difference formula(ADF).In addition,we show that a large enough box is necessary to describe the continuum quasi-particle states.The canonical states obtained by diagonalizing the density matrix constructed by the quasi-particle states are not particularly sensitive to the box size.Part of the asymptotic wave functions can be improved by applying the ADF in the FDM compared to the shooting method with the same box boundary condition.
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supported by the National Natural Science Foundation of China(Nos.51975025 and 51890822)the Young Elite Scientists Sponsorship Program by China Association for Science and Technology(No.2016QNRC001)the National Key Research and Development Program of China(No.2019YFB2004500)。
文摘The fluid-structure interaction(FSI)in aircraft hydraulic pipeline systems is of great concern because of the damage it causes.To accurately predict the vibration characteristic of long hydraulic pipelines with curved segments,we studied the frequency-domain modeling and solution method for FSI in these pipeline systems.Fourteen partial differential equations(PDEs)are utilized to model the pipeline FSI,considering both frequency-dependent friction and bending-flexibility modification.To address the numerical instability encountered by the traditional transfer matrix method(TMM)in solving relatively complex pipelines,an improved TMM is proposed for solving the PDEs in the frequency domain,based on the matrix-stacking strategy and matrix representation of boundary conditions.The proposed FSI model and improved solution method are validated by numerical cases and experiments.An experimental rig of a practical hydraulic system,consisting of an aircraft engine-driven pump,a Z-shaped aero-hydraulic pipeline,and a throttle valve,was constructed for testing.The magnitude ratio of acceleration to pressure is introduced to evaluate the theoretical and experimental results,which indicate that the proposed model and solution method are effective in practical applications.The methodology presented in this paper can be used as an efficient approach for the vibrational design of aircraft hydraulic pipeline systems.
基金Supported by the National Natural Science Foundation of China (69983005)
文摘Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.
文摘The use of columns on elastic foundation is very common in Civil Engineering, like bridge pier, the foundation of the buildings etc. So, it will be useful to find the critical load for the structure, the problem in this paper will be solved by Finite-Difference Mode, that＇ s simple and has an extensive use. The way it works is that by dividing the component into many units. Finite-difference methods （FDM） are numerical methods for anoroximating, the solutions to differential eauations usine finite difference equations to approximate derivatives.
基金financially supported by the Key Program of National Natural Science Foundation of China(No.41530320)China Natural Science Foundation for Young Scientists(No.41404093)+1 种基金Key National Research Project of China(Nos2016YFC0303100 and 2017YFC0601900)China Natural Science Foundation(No.41774125)
文摘The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(No.41304082)the China Postdoctoral Science Foundation(No.2016M590731)+2 种基金the Young Scientists Fund of the Natural Science Foundation of Hebei Province(No.D2014403011)the Program for Young Excellent Talents of Higher Education Institutions of Hebei Province(No.BJ2016046)the Geological survey project of China Geological Survey(No.1212011121197)
文摘We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.
基金The National Natural Science Foundation of China(No.60702027)the Free Research Fund of the National Mobile Communications Research Laboratory of Southeast University (No.2008B07)the National Basic Research Program of China(973 Program)(No.2007CB310603)
文摘With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.
基金supported by the National Key R&D Program of China(2021YFA0716902)National Natural Science Foundation of China(NSFC)under contract number 42374149 and 42004119National Science and Technology Major Project(2024ZD1002907)。
文摘Seismic anisotropy has been extensively acknowledged as a crucial element that influences the wave propagation characteristic during wavefield simulation,inversion and imaging.Transversely isotropy(TI)and orthorhombic anisotropy(OA)are two typical categories of anisotropic media in exploration geophysics.In comparison of the elastic wave equations in both TI and OA media,pseudo-acoustic wave equations(PWEs)based on the acoustic assumption can markedly reduce computational cost and complexity.However,the presently available PWEs may experience SV-wave contamination and instability when anisotropic parameters cannot satisfy the approximated condition.Exploiting pure-mode wave equations can effectively resolve the above-mentioned issues and generate pure P-wave events without any artifacts.To further improve the computational accuracy and efficiency,we develop two novel pure qP-wave equations(PPEs)and illustrate the corresponding numerical solutions in the timespace domain for 3D tilted TI(TTI)and tilted OA(TOA)media.First,the rational polynomials are adopted to estimate the exact pure qP-wave dispersion relations,which contain complicated pseudo-differential operators with irrational forms.The polynomial coefficients are produced by applying a linear optimization algorithm to minimize the objective function difference between the expansion formula and the exact one.Then,the developed optimized PPEs are efficiently implemented using the finite-difference(FD)method in the time-space domain by introducing a scalar operator,which can help avoid the problem of spectral-based algorithms and other calculation burdens.Structures of the new equations are concise and corresponding implementation processes are straightforward.Phase velocity analyses indicate that our proposed optimized equations can lead to reliable approximation results.3D synthetic examples demonstrate that our proposed FD-based PPEs can produce accurate and stable P-wave responses,and effectively describe the wavefield features in complicated TTI and TOA media.
