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Stability of Perfectly Matched Layers for Time Fractional Schrödinger Equation
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作者 Tingting Zhang Xiangkun Li 《Engineering(科研)》 CAS 2023年第1期1-12,共12页
It is an important issue to numerically solve the time fractional Schrödinger equation on unbounded domains, which models the dynamics of optical solitons propagating via optical fibers. The perfectly matched lay... It is an important issue to numerically solve the time fractional Schrödinger equation on unbounded domains, which models the dynamics of optical solitons propagating via optical fibers. The perfectly matched layer approach is applied to truncate the unbounded physical domain, and obtain an initial boundary value problem on a bounded computational domain, which can be efficiently solved by the finite difference method. The stability of the reduced initial boundary value problem is rigorously analyzed. Some numerical results are presented to illustrate the accuracy and feasibility of the perfectly matched layer approach. According to these examples, the absorption parameters and the width of the absorption layer will affect the absorption effect. The larger the absorption width, the better the absorption effect. There is an optimal absorption parameter, the absorption effect is the best. 展开更多
关键词 Time Fractional Schrödinger Equation perfectly matched Layer STABILITY
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A study of perfectly matched layers for joint multicomponent reverse-time migration 被引量:3
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作者 杜启振 秦童 +1 位作者 朱钇同 毕丽飞 《Applied Geophysics》 SCIE CSCD 2010年第2期166-173,194,195,共10页
Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equat... Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equations in vertical transversely isotropic media and the idea of the conventional split perfectly matched layer(PML),the PML wave equations in reverse-time migration are derived in this paper and then the high order staggered grid discrete schemes are subsequently given.Aiming at the"reflections"from the boundary to the computational domain,as well as the effect of seismic event's abrupt changes at the two ends of the seismic array,the PML arrangement in reverse-time migration is given.The synthetic and real elastic,prestack,multi-component,reverse-time depth migration results demonstrate that this method has much better absorbing effects than other methods and the joint migration produces good imaging results. 展开更多
关键词 perfectly matched layer(PML) absorbing boundary reverse-time migration velocity-stress equation MULTI-COMPONENT
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A study of damping factors in perfectly matched layers for the numerical simulation of seismic waves 被引量:3
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作者 杨皓星 王红霞 《Applied Geophysics》 SCIE CSCD 2013年第1期63-70,118,共9页
When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially trtmcated boundaries. In this paper, a damping factor refer... When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially trtmcated boundaries. In this paper, a damping factor referred to as the Gaussian dmping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers (PMLs). This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models: a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio (SNR) than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR. 展开更多
关键词 simulation of seismic wave perfectly matched layer (PML) damping factor
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A FINITE ELEMENT METHOD WITH RECTANGULAR PERFECTLY MATCHED LAYERS FOR THE SCATTERING FROM CAVITIES 被引量:3
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作者 Deyue Zhang Fuming Ma Heping Dong 《Journal of Computational Mathematics》 SCIE CSCD 2009年第6期812-834,共23页
We develop a finite element method with rectangular perfectly matched layers (PMLs) for the wave scattering from two-dimensional cavities. The unbounded computational domain is truncated to a bounded one by using of... We develop a finite element method with rectangular perfectly matched layers (PMLs) for the wave scattering from two-dimensional cavities. The unbounded computational domain is truncated to a bounded one by using of a rectangular perfectly matched layer at the open aperture. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. Numerical experiments are carried out to illustrate the competitive behavior of the proposed method. 展开更多
关键词 CAVITY perfectly matched layers Finite element method.
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Finite-difference modeling of Maxwell viscoelastic media developed from perfectly matched layer
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作者 Ruo-Long Song 《Petroleum Science》 SCIE EI CSCD 2023年第5期2759-2772,共14页
In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.Ho... In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.However,convolution operator is intractable in finite-difference time-domain(FDTD)method.A great deal of progress has been made in using time stepping instead of convolution in FDTD.To incorporate PML into viscoelastic media,more memory variables need to be introduced,which increases the code complexity and computation costs.By modifying the nonsplitting PML formulation,I propose a viscoelastic model,which can be used as a viscoelastic material and/or a PML just by adjusting the parameters.The proposed viscoelastic model is essentially equivalent to a Maxwell model.Compared with existing PML methods,the proposed method requires less memory and its implementation in existing finite-difference codes is much easier.The attenuation and phase velocity of P-and S-waves are frequency independent in the viscoelastic model if the related quality factors(Q)are greater than 10.The numerical examples show that the method is stable for materials with high absorption(Q=1),and for heterogeneous media with large contrast of acoustic impedance and large contrast of viscosity. 展开更多
关键词 Finite difference Viscoelastic model Nonsplitting perfectly matched layer
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Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers
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作者 Yu Du Jiwei Zhang 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2022年第2期387-414,共28页
We consider the computation of a nonlocal Helmholtz equation by using perfectly matched layer(PML).We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal opera... We consider the computation of a nonlocal Helmholtz equation by using perfectly matched layer(PML).We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal operator of integral form.After that,we give stability estimates of some weighted-average values of the nonlocal Helmholtz solution and prove that(i)the weighted-average value of the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the weighted-average value of the nonlocal Helmholtz solution itself decays exponentially outside some domain.Particularly for a typical kernel functionγ_(1)(s)=1/2 e^(−|s|),we obtain the Green’s function of the nonlocal Helmholtz equation,and use the Green’s function to further prove that(i)the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the nonlocal Helmholtz solution itself decays exponentially outside some domain.Based on our theoretical analysis,the truncated nonlocal problems are discussed and an asymptotic compatibility scheme is also introduced to solve the resulting truncated problems.Finally,numerical examples are provided to verify the effectiveness and validation of our nonlocal PML strategy and theoretical findings. 展开更多
关键词 Nonlocal wave propagation Helmholtz equation perfectly matched layer asymptotic compatibility scheme Green’s function
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DISCRETE SINGULAR CONVOLUTION METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY PERIODIC STRUCTURES
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作者 Feng Lixin Jia Niannian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第2期138-152,共15页
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is uti... A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem. 展开更多
关键词 Maxwell's equations periodic structures perfect matched layer (PMI) discrete singular convolution (DSC)
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The Application of the Nonsplitting Perfectly Matched Layer in Numerical Modeling of Wave Propagation in Poroelastic Media 被引量:4
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作者 宋若龙 马俊 王克协 《Applied Geophysics》 SCIE CSCD 2005年第4期216-222,共7页
The nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC) was first provided by Wang and Tang (2003) for the finite-difference simulation of elastic wave propagation in solids. In this p... The nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC) was first provided by Wang and Tang (2003) for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot's equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical twolayer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber (DW) method. 展开更多
关键词 FINITE-DIFFERENCE numerical simulation absorbing boundary condition and perfectly matched layer.
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Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations 被引量:3
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作者 赵建国 史瑞其 《Applied Geophysics》 SCIE CSCD 2013年第3期323-336,359,共15页
The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-eleme... The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media. 展开更多
关键词 Absorbing boundary condition elastic wave equation perfectly matched layer finite-element modeling
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An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems 被引量:4
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作者 Zhiming Chen Xinming Wu 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第2期113-137,共25页
The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in deal- ing with problems involving anisotropic scatterers.In t... The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in deal- ing with problems involving anisotropic scatterers.In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is devel- oped.The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates.The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equa- tion which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorb- ing layer.Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method.In particular,it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields. 展开更多
关键词 Adaptivity uniaxial perfectly matched layer a posteriori error analysis acoustic scattering problems
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A Uniaxial Optimal Perfectly Matched Layer Method for Time-harmonic Scattering Problems 被引量:5
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作者 YANG XIAO-YING MA FU-MING +1 位作者 ZHANG DE-YUE Du XIN-WEI 《Communications in Mathematical Research》 CSCD 2010年第3期255-268,共14页
We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. W... We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. With this choice, the solution of the optimal PML problem not only converges exponentially to the solution of the original scatting problem, but also is insensitive to the thickness of the PML layer for sufficiently small parameter ε0. Numerical experiments are included to illustrate the competitive behavior of the proposed optimal method. 展开更多
关键词 uniaxial optimal perfectly matched layer time-harmonic scattering CONVERGENCE
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Perfectly matched layer implementation for ADI-FDTD in dispersive media 被引量:2
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作者 Wang Yu Yuan Naichang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第1期80-84,共5页
Alternating direction implicit finite difference time domain (ADI-FDTD) method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Co... Alternating direction implicit finite difference time domain (ADI-FDTD) method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer (PML) absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution(RC) method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced. 展开更多
关键词 perfectly matched layer alternating direction implicit finite difference time domain dispersive media
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An improved convolution perfectly matched layer for elastic second-order wave equation 被引量:2
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作者 Yang Ling-Yun Wu Guo-Chen +1 位作者 Li Qing-Yang Liang Zhan-Yuan 《Applied Geophysics》 SCIE CSCD 2021年第3期317-330,432,共15页
A convolution perfectly matched layer(CPML)can efficiently absorb boundary reflection in numerical simulation.However,the CPML is suitable for the first-order elastic wave equation and is difficult to apply directly t... A convolution perfectly matched layer(CPML)can efficiently absorb boundary reflection in numerical simulation.However,the CPML is suitable for the first-order elastic wave equation and is difficult to apply directly to the second-order elastic wave equation.In view of this,based on the first-order CPML absorbing boundary condition,we propose a new CPML(NCPML)boundary which can be directly applied to the second-order wave equation.We first systematically extend the first-order CPML technique into second-order wave equations,neglecting the space-varying characteristics of the partial damping coefficient in the complex-frequency domain,avoiding the generation of convolution in the time domain.We then transform the technique back to the time domain through the inverse Fourier transform.Numerical simulation indicates that the space-varying characteristics of the attenuation factor have little influence on the absorption effect and increase the memory at the same time.A number of numerical examples show that the NCPML proposed in this study is effective in simulating elastic wave propagation,and this algorithm is more efficient and requires less memory allocation than the conventional PML absorbing boundary. 展开更多
关键词 Convolutional perfectly matched layer absorbing boundary conditions second-order elastic wave equation numerical simulation
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Application of perfectly matched layer to soil-foundation interaction analysis 被引量:1
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作者 Mohammad Davoodi Abbas Pourdeilami +1 位作者 Hosein Jahankhah Mohammad Kazem Jafari 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2018年第4期753-768,共16页
Despite of the limitation in modeling infinite space, the finite element method(FEM) is one of the most used tools to numerically study the geotechnical problems regarding the capacity of simulating different geometri... Despite of the limitation in modeling infinite space, the finite element method(FEM) is one of the most used tools to numerically study the geotechnical problems regarding the capacity of simulating different geometries, conditions and material behaviors. A kind of absorbing layer named perfectly matched layer(PML) has been applied to modeling the radiation damping using FEM, which makes the dynamic analysis of soil-structure interaction more accurate. The PML is capable of absorbing incident waves under any angle and frequency, ensuring them to pass through the model boundaries without reflection.In this context, a new FEM program has been written and the PML formula has been implemented by rewriting the dynamic equation of motion and deriving new properties for the quadrilateral elements.The analysis of soil-foundation interaction by applying the PML is validated by the evaluation of impedance/compliance functions for different ground conditions. The results obtained from the PML model match the extended mesh results, even though the domain is small enough that other types of absorbing boundaries can reflect waves back to the foundation. The mechanism of the wave propagation in the region shows that the forced vibrations can be fully absorbed and damped by the boundaries surrounded by PMLs which is the role of radiation damping in FEM modeling. 展开更多
关键词 perfectly matched layer (PML) Finite element method (FEM) Wave propagation Impedance/compliance
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Finite Element Analysis in Combination with Perfectly Matched Layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials 被引量:1
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作者 Dbich Karim Sylvain Ballandras +3 位作者 Thierry Laroche Karl Wagner Jean-Michel Brice Xavier Perois 《Applied Mathematics》 2013年第5期64-71,共8页
The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the me... The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the mesh. In fact, these ones do not contribute in practice to the corresponding experimental response. The Perfectly Matched Layer (PML) method, allows to suppress the boundary reflections. In this work, we first demonstrate the basis of PML adapted to FEA formalism. Next, the results of such a method are depicted allowing a discussion on the behavior of finite acoustic resonators. 展开更多
关键词 Finite Element Method perfectly matched Layer Surface Acoustic Wave Piezoelcetric Numerical Modeling
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A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer
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作者 刘亚文 陈亦望 +1 位作者 张品 刘宗信 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期166-176,共11页
A higher-order finite-difference time-domain(HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spheric... A higher-order finite-difference time-domain(HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain(FDTD) and the multiresolution time-domain(MRTD) schemes with respect to memory requirements and CPU time. Moreover, the Berenger's perfectly matched layer(PML) is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML. 展开更多
关键词 higher-order finite-difference time-domain spherical coordinates STABILITY numerical dispersion perfectly matched layer
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Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation
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作者 李宁 谢礼立 翟长海 《Acta Seismologica Sinica(English Edition)》 CSCD 2007年第6期684-695,共12页
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The co... The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary. 展开更多
关键词 perfectly matched layer multi-transmitting formula elastodynamic wave artificial boundary hybrid finite element
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Numerical investigation of the effects of soil-structure and granular material-structure interaction on the seismic response of a flat-bottom reinforced concrete silo
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作者 Sonia Benkhellat Mohammed Kadri Abdelghani Seghir 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2024年第3期609-623,共15页
In this work,a numerical study of the effects of soil-structure interaction(SSI)and granular material-structure interaction(GSI)on the nonlinear response and seismic capacity of flat-bottomed storage silos is conducte... In this work,a numerical study of the effects of soil-structure interaction(SSI)and granular material-structure interaction(GSI)on the nonlinear response and seismic capacity of flat-bottomed storage silos is conducted.A series of incremental dynamic analyses(IDA)are performed on a case of large reinforced concrete silo using 10 seismic recordings.The IDA results are given by two average IDA capacity curves,which are represented,as well as the seismic capacity of the studied structure,with and without a consideration of the SSI while accounting for the effect of GSI.These curves are used to quantify and evaluate the damage of the studied silo by utilizing two damage indices,one based on dissipated energy and the other on displacement and dissipated energy.The cumulative energy dissipation curves obtained by the average IDA capacity curves with and without SSI are presented as a function of the base shear,and these curves allow one to obtain the two critical points and the different limit states of the structure.It is observed that the SSI and GSI significantly influence the seismic response and capacity of the studied structure,particularly at higher levels of PGA.Moreover,the effect of the SSI reduces the damage index of the studied structure by 4%. 展开更多
关键词 reinforced concrete silo perfectly matched layers soil-structure interaction granular material-structure interaction effective seismic input method damage index
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Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma
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作者 WEN Yi WANG Junxiang XU Hongbing 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2024年第1期65-73,共9页
Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is ... Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation. 展开更多
关键词 anisotropic magnetized plasma body-of-revolution(BOR) Crank-Nicolson Douglas-Gunn(CNDG) finite-difference time-domain(FDTD) perfectly matched layer(PML) rotationally symmetric multi-scale problems
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Borehole-GPR numerical simulation of full wave field based on convolutional perfect matched layer boundary 被引量:7
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作者 朱自强 彭凌星 +1 位作者 鲁光银 密士文 《Journal of Central South University》 SCIE EI CAS 2013年第3期764-769,共6页
The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) appr... The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR. 展开更多
关键词 borehole-GPR numerical simulation convolutional perfect match layer finite-difference time-domain method
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