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
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
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
To efficiently simulate and calculate the radar cross section(RCS) related electromagnetic problems by employing the finite-difference time-domain(FDTD) algorithm, an efficient stretched coordinate perfectly matched l...To efficiently simulate and calculate the radar cross section(RCS) related electromagnetic problems by employing the finite-difference time-domain(FDTD) algorithm, an efficient stretched coordinate perfectly matched layer(ESC-PML) based upon the exponential time differencing(ETD) method is proposed.The proposed implementation can not only reduce the number of auxiliary variables in the SC-PML regions but also maintain the ability of the original SC-PML in terms of the absorbing performance. Compared with the other existed algorithms, the ETDFDTD method shows the least memory consumption resulting in the computational efficiency. The effectiveness and efficiency of the proposed ESC-PML scheme is verified through the RCS relevant problems including the perfect E conductor(PEC) sphere model and the patch antenna model. The results indicate that the proposed scheme has the advantages of the ETD-FDTD method and ESC-PML scheme in terms of high computational efficiency and considerable computational accuracy.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.
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.
基金supported by the National Natural Science Foundation of China(61571022611971022)。
文摘To efficiently simulate and calculate the radar cross section(RCS) related electromagnetic problems by employing the finite-difference time-domain(FDTD) algorithm, an efficient stretched coordinate perfectly matched layer(ESC-PML) based upon the exponential time differencing(ETD) method is proposed.The proposed implementation can not only reduce the number of auxiliary variables in the SC-PML regions but also maintain the ability of the original SC-PML in terms of the absorbing performance. Compared with the other existed algorithms, the ETDFDTD method shows the least memory consumption resulting in the computational efficiency. The effectiveness and efficiency of the proposed ESC-PML scheme is verified through the RCS relevant problems including the perfect E conductor(PEC) sphere model and the patch antenna model. The results indicate that the proposed scheme has the advantages of the ETD-FDTD method and ESC-PML scheme in terms of high computational efficiency and considerable computational accuracy.
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.
