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
Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean latt...Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean lattices with toroidal boundary by applying Tesler's crossing orientations to obtain some Pfaffan orientations and enumerating their Pfaffans.展开更多
Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfe...Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd+1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] + 1 q2d 33 1.展开更多
In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the ab...In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let wi?be a non-isolated vertex of graph Gi?where i=1, 2, …, k. We use Gu(k)?(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H) and G1, G2,…, Gk?by identifying the vertices u (respectively, v) and w1, w2,…, wk. In this paper, we first present a new technique of directly comparing the matching energies of Gu(k)?and Hv(k), which can tackle some quasi-order incomparable problems. As the applications of the technique, then we can determine the unicyclic graphs with perfect matchings of order 2n with the first to the ninth smallest matching energies for all n≥211.展开更多
The perfectly matched layer(PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation(PE) model applying PML technique was previously used to analyze...The perfectly matched layer(PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation(PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide(Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Padé approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer(ABL) both in acoustic and seismo-acoustic sound propagation modeling.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
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
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
Analysis of soil-structure interaction is commonly conducted by dividing the infinite domain of the soil into two domains:interior and exterior domains.The interior domain is bounded in a small region,while the exteri...Analysis of soil-structure interaction is commonly conducted by dividing the infinite domain of the soil into two domains:interior and exterior domains.The interior domain is bounded in a small region,while the exterior domain is replaced by artificial boundary conditions.The choice of artificial boundary conditions is a critical issue in the analysis of soil-structure interaction problems.Perfectly matched discrete layer(PMDL)has been proved as a good approach for modeling the exterior domain.In this study,a modified version of the PMDLs,i.e.PMDLs with analytical wavelengths(AW-PMDLs),is used in the soil-structure interaction analysis in time domain,which essentially can be regarded as an extension of the analysis in frequency domain,being previously proven to be effective.Numerical verifications are implemented.The results demonstrate that the proposed method performs well in the analysis of soilstructure interaction problems in time domain.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
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
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 National Natural Science Foundation of China(Grant No.11471273 11671186)
文摘Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean lattices with toroidal boundary by applying Tesler's crossing orientations to obtain some Pfaffan orientations and enumerating their Pfaffans.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11001166,10971131)the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd+1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] + 1 q2d 33 1.
文摘In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let wi?be a non-isolated vertex of graph Gi?where i=1, 2, …, k. We use Gu(k)?(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H) and G1, G2,…, Gk?by identifying the vertices u (respectively, v) and w1, w2,…, wk. In this paper, we first present a new technique of directly comparing the matching energies of Gu(k)?and Hv(k), which can tackle some quasi-order incomparable problems. As the applications of the technique, then we can determine the unicyclic graphs with perfect matchings of order 2n with the first to the ninth smallest matching energies for all n≥211.
基金supported by the Foundation of State Key Laboratory of Acoustics,Institute of Acoustics,Chinese Academy of Sciences(No.SKLA201303)the National Natural Science Foundation of China(Nos.11104044,11234002,and 11474073)
文摘The perfectly matched layer(PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation(PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide(Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Padé approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer(ABL) both in acoustic and seismo-acoustic sound propagation modeling.
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.
基金Project(41174061) supported by the National Natural Science Foundation of ChinaProject(2011QNZT011) supported by the Free Exploration Program of Central South University,China
文摘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.
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supported by the Korea Institute of Energy Technology Evaluation and Planning(KETEP)the Ministry of Trade,Industry and Energy(MOTIE)of the Republic of Korea(Grant No.20171510101960).
文摘Analysis of soil-structure interaction is commonly conducted by dividing the infinite domain of the soil into two domains:interior and exterior domains.The interior domain is bounded in a small region,while the exterior domain is replaced by artificial boundary conditions.The choice of artificial boundary conditions is a critical issue in the analysis of soil-structure interaction problems.Perfectly matched discrete layer(PMDL)has been proved as a good approach for modeling the exterior domain.In this study,a modified version of the PMDLs,i.e.PMDLs with analytical wavelengths(AW-PMDLs),is used in the soil-structure interaction analysis in time domain,which essentially can be regarded as an extension of the analysis in frequency domain,being previously proven to be effective.Numerical verifications are implemented.The results demonstrate that the proposed method performs well in the analysis of soilstructure interaction problems in time domain.
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.