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
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
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
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
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
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
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
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
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
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
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
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
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
We present a well-posed and discretely stable perfectly matched layer for the anisotropic(and isotropic)elastic wave equations without first re-writing the governing equations as a first order system.The new model is ...We present a well-posed and discretely stable perfectly matched layer for the anisotropic(and isotropic)elastic wave equations without first re-writing the governing equations as a first order system.The new model is derived by the complex coordinate stretching technique.Using standard perturbation methods we show that complex frequency shift together with a chosen real scaling factor ensures the decay of eigen-modes for all relevant frequencies.To buttress the stability properties and the robustness of the proposed model,numerical experiments are presented for anisotropic elastic wave equations.The model is approximated with a stable node-centered finite difference scheme that is second order accurate both in time and space.展开更多
Consider the diffraction of a time-harmonic wave incident upon a periodic chiral structure. The diffraction problem may be simplified to a two-dimensional one. In this paper, the diffraction problem is solved by a fin...Consider the diffraction of a time-harmonic wave incident upon a periodic chiral structure. The diffraction problem may be simplified to a two-dimensional one. In this paper, the diffraction problem is solved by a finite element method with perfectly matched absorbing layers (PMLs). We use the PML technique to truncate the unbounded domain to a bounded one which attenuates the outgoing waves in the PML region. Our computational experiments indicate that the proposed method with complicated chiral grating structures. is efficient, which is capable of dealing展开更多
We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into ...We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into the bounded domain.The parameters in the uniaxial PML method are determined by sharp a posteriori error estimates developed by Chen and Wu[8].An hp-adaptive finite element strategy is proposed to solve the uniaxial PML equation.Numerical experiments are included which indicate the desirable exponential decay property of the error.展开更多
We derive a perfectly matched layer(PML)for the Schrödinger equation using a modal ansatz.We derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the disc...We derive a perfectly matched layer(PML)for the Schrödinger equation using a modal ansatz.We derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the discretization in the layer and show how to choose layer parameters so that these errors are matched and optimal performance of the PML is obtained.Numerical computations in 1D and 2D demonstrate that the optimized PML works efficiently at a prescribed accuracy for the zero potential case,with a layer of width less than a third of the de Broglie wavelength corresponding to the dominating frequency.展开更多
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
Parallel acceleration of convolution perfectly matched layer (CPML) algorithm suffers from massive division operation which is widely accepted as one of the most expensive operations for the equipment such as graphi...Parallel acceleration of convolution perfectly matched layer (CPML) algorithm suffers from massive division operation which is widely accepted as one of the most expensive operations for the equipment such as graphic processing unit (GPU), field programmable gate array (FPGA) etc. In pursuit of higher efficiency and lower power consumption, this article revisited the CPML theory and proposed a new fast division-free parallel CPML structure. By optimally rearranging the CPML inner iteration process, all the division operators can be eliminated and replaced by recalculating the related field updating coefficients offline. Experiments show that the proposed division-free structure can save more than 50% arithmetic instructions and 25% execution time of the traditional parallel CPML structure without any accuracy loss.展开更多
We consider the anisotropic uniaxial formulation of the perfectly matched layer(UPML)model for Maxwell’s equations in the time domain.We present and analyze a mixed finite element method for the discretization of the...We consider the anisotropic uniaxial formulation of the perfectly matched layer(UPML)model for Maxwell’s equations in the time domain.We present and analyze a mixed finite element method for the discretization of the UPML in the time domain to simulate wave propagation on unbounded domains in two dimensions.On rectangles the spatial discretization uses bilinear finite elements for the electric field and the lowest order Raviart-Thomas divergence conforming elements for the magnetic field.We use a centered finite difference method for the time discretization.We compare the finite element technique presented to the finite difference time domain method(FDTD)via a numerical reflection coefficient analysis.We derive the numerical reflection coefficient for the case of a semi-infinite PML layer to show consistency between the numerical and continuous models,and in the case of a finite PML to study the effects of terminating the absorbing layer.Finally,we demonstrate the effectiveness of the mixed finite element scheme for the UPML by a numerical example and provide comparisons with the split field PML discretized by the FDTD method.In conclusion,we observe that the mixed finite element scheme for the UPML model has absorbing properties that are comparable to the FDTD method.展开更多
文摘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.
文摘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.
基金Supported by the NNSF of China(10626017)the Science Foundation of the Education Committee of Heilongjiang Province(11511276)the Foundation of Heilongjiang Province(LBH-Q05114).
文摘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.
基金The Major State Research Development Program (2005CB321701) of Chinathe NSF(10801063) of China
文摘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.
文摘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.
基金supported by the National Science and Technology Major Special Sub-project of China(No.2016ZX05024-001-008)the National Natural Science Foundation Joint Fund Prcject of China(No.U1562215).
文摘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.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61301063 and 41305017)
文摘A higher-order finite-difference time-domain(HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain(FDTD) and the multiresolution time-domain(MRTD) schemes with respect to memory requirements and CPU time. Moreover, the Berenger's perfectly matched layer(PML) is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.
基金National Natural Science Foundation of China (50608024 and 50538050).
文摘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.
文摘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%.
文摘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.
基金supported by the NSF of China (10801063)Major State Basic Research Development Program of China (Grant No. 2005CB321701)
文摘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.
文摘We present a well-posed and discretely stable perfectly matched layer for the anisotropic(and isotropic)elastic wave equations without first re-writing the governing equations as a first order system.The new model is derived by the complex coordinate stretching technique.Using standard perturbation methods we show that complex frequency shift together with a chosen real scaling factor ensures the decay of eigen-modes for all relevant frequencies.To buttress the stability properties and the robustness of the proposed model,numerical experiments are presented for anisotropic elastic wave equations.The model is approximated with a stable node-centered finite difference scheme that is second order accurate both in time and space.
基金The research was supported by the Special Funds for Major State Basic Research Projects(G1999032802) in Chinathe NNSF(10076006)of China
文摘Consider the diffraction of a time-harmonic wave incident upon a periodic chiral structure. The diffraction problem may be simplified to a two-dimensional one. In this paper, the diffraction problem is solved by a finite element method with perfectly matched absorbing layers (PMLs). We use the PML technique to truncate the unbounded domain to a bounded one which attenuates the outgoing waves in the PML region. Our computational experiments indicate that the proposed method with complicated chiral grating structures. is efficient, which is capable of dealing
文摘We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into the bounded domain.The parameters in the uniaxial PML method are determined by sharp a posteriori error estimates developed by Chen and Wu[8].An hp-adaptive finite element strategy is proposed to solve the uniaxial PML equation.Numerical experiments are included which indicate the desirable exponential decay property of the error.
文摘We derive a perfectly matched layer(PML)for the Schrödinger equation using a modal ansatz.We derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the discretization in the layer and show how to choose layer parameters so that these errors are matched and optimal performance of the PML is obtained.Numerical computations in 1D and 2D demonstrate that the optimized PML works efficiently at a prescribed accuracy for the zero potential case,with a layer of width less than a third of the de Broglie wavelength corresponding to the dominating frequency.
基金supported by the NSFC(Grants No.11771035,12071401,12171376,2020-JCJQ-ZD-029)the Natural Science Foundation of Hunan Province(Grant No.2019JJ50572)+1 种基金the Natural Science Foundation of Hubei Province(Grant No.2019CFA007)the Xiangtan University(Grant No.2018ICIP01)。
文摘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.
基金sponsored by the National Natural Science Foundation of China (30870577)
文摘Parallel acceleration of convolution perfectly matched layer (CPML) algorithm suffers from massive division operation which is widely accepted as one of the most expensive operations for the equipment such as graphic processing unit (GPU), field programmable gate array (FPGA) etc. In pursuit of higher efficiency and lower power consumption, this article revisited the CPML theory and proposed a new fast division-free parallel CPML structure. By optimally rearranging the CPML inner iteration process, all the division operators can be eliminated and replaced by recalculating the related field updating coefficients offline. Experiments show that the proposed division-free structure can save more than 50% arithmetic instructions and 25% execution time of the traditional parallel CPML structure without any accuracy loss.
基金supported in part by Los Alamos National Laboratory,an affirmative action/equal opportunity employer which is operated by the University of California for the United States Department of Energy under contract Nos W-7405-ENG-36,03891-001-99-4G,74837-001-0349,and/or 86192-001-0449in part by the U.S.Air Force Office of Scientific Research under grants AFOSR F49620-01-1-0026 and AFOSR FA9550-04-1-0220.
文摘We consider the anisotropic uniaxial formulation of the perfectly matched layer(UPML)model for Maxwell’s equations in the time domain.We present and analyze a mixed finite element method for the discretization of the UPML in the time domain to simulate wave propagation on unbounded domains in two dimensions.On rectangles the spatial discretization uses bilinear finite elements for the electric field and the lowest order Raviart-Thomas divergence conforming elements for the magnetic field.We use a centered finite difference method for the time discretization.We compare the finite element technique presented to the finite difference time domain method(FDTD)via a numerical reflection coefficient analysis.We derive the numerical reflection coefficient for the case of a semi-infinite PML layer to show consistency between the numerical and continuous models,and in the case of a finite PML to study the effects of terminating the absorbing layer.Finally,we demonstrate the effectiveness of the mixed finite element scheme for the UPML by a numerical example and provide comparisons with the split field PML discretized by the FDTD method.In conclusion,we observe that the mixed finite element scheme for the UPML model has absorbing properties that are comparable to the FDTD method.