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
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
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
In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer （PML） is introduced to enclose the cavity, and the PML formulati...In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer （PML） is introduced to enclose the cavity, and the PML formulations for both TM and TE polarizations are presented. Existence, uniqueness and convergence of the PML solutions are considered. Numerical experiments demonstrate that the PML method is efficient and accurate for solving cavity scattering problems.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 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 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
In this paper,we are concerned about the stability analysis for a Perfectly Matched Layer(PML)recently developed by Becache et al.[5]for simulating wave propagation in the Drude metamaterial.This PML is proved to be s...In this paper,we are concerned about the stability analysis for a Perfectly Matched Layer(PML)recently developed by Becache et al.[5]for simulating wave propagation in the Drude metamaterial.This PML is proved to be stable originally in[6]through a modal analysis.Here we establish its stability by the energy method.A FDTD scheme is developed and analyzed.Numerical simulations illustrate the stability of the PML model and its effectiveness in absorbing outgoing waves in the Drude medium.展开更多
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(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In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer （PML） is introduced to enclose the cavity, and the PML formulations for both TM and TE polarizations are presented. Existence, uniqueness and convergence of the PML solutions are considered. Numerical experiments demonstrate that the PML method is efficient and accurate for solving cavity scattering problems.
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 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.
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.
文摘In this paper,we are concerned about the stability analysis for a Perfectly Matched Layer(PML)recently developed by Becache et al.[5]for simulating wave propagation in the Drude metamaterial.This PML is proved to be stable originally in[6]through a modal analysis.Here we establish its stability by the energy method.A FDTD scheme is developed and analyzed.Numerical simulations illustrate the stability of the PML model and its effectiveness in absorbing outgoing waves in the Drude medium.
