共查询到20条相似文献,搜索用时 0 毫秒
1.
We design a perfectly matched layer for the advection–diffusion equation. We show that the reflection coefficient is exponentially small with respect to the damping parameter and the width of the PML and this independently of the advection and of the viscosity. Numerical tests assess the efficiency of the approach. 相似文献
2.
Tomáš Dohnal 《Journal of computational physics》2009,228(23):8752-8765
This paper constructs perfectly matched layers (PML) for a system of 2D coupled nonlinear Schrödinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable linear part. The PML construction is performed in Laplace–Fourier space via a modal analysis and can be viewed as a complex change of variables. The mixed derivatives cause the presence of waves with opposite phase and group velocities, which has previously been shown to cause instability of layer equations in certain types of hyperbolic problems. Nevertheless, here the PML is stable if the absorption function σ lies below a specified threshold. The PML construction and analysis are carried out for the linear part of the system. Numerical tests are then performed in both the linear and nonlinear regimes checking convergence of the error with respect to the layer width and showing that the PML performs well even in many nonlinear simulations. 相似文献
3.
4.
Murthy N. Guddati Senganal Thirunavukkarasu 《Journal of computational physics》2009,228(21):8112-8134
With the goal of minimizing the domain size for molecular dynamics (MD) simulations, we develop a new class of absorbing boundary conditions (ABCs) that mimic the phonon absorption properties of an unbounded exterior. The proposed MD-ABCs are extensions of perfectly matched discrete layers (PMDLs), originally developed as an absorbing boundary condition for continuous wave propagation problems. Called MD-PMDL, this extension carefully targets the absorption of phonons, the high frequency waves, whose propagation properties are completely different from continuous waves. This paper presents the derivation of MD-PMDL for general lattice systems, followed by explicit application to one-dimensional and two-dimensional square lattice systems. The accuracy of MD-PMDL for phonon absorption is proven by analyzing reflection coefficients, and demonstrated through numerical experiments. Unlike existing MD-ABCs, MD-PMDL is local in both space and time and thus more efficient. Based on their favorable properties, it is concluded that MD-PMDL could provide a more effective alternative to existing MD-ABCs. 相似文献
5.
With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the accuracy aspects of local ABCs designed for the scalar anisotropic wave equation in the frequency domain (time harmonic case). The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL). PMDL is a simple variant of perfectly matched layers (PML) and is equivalent to rational approximation-based local ABCs. Specifically, we derive a sufficient condition for PMDL to accurately absorb wave modes with outgoing group velocities and this condition turns out to be a simple bound on the PMDL parameters. The reflection coefficient derived in this paper clearly reveals that the PMDL absorption is based on group velocities, and not phase velocities, and hence a PMDL can be designed to correctly identify and accurately absorb all outgoing wave modes (even those with opposing signs of phase and group velocities). The validity of the sufficient condition is demonstrated through a series of frequency domain simulations. In part 2 of this paper [S. Savadatti, M.N. Guddati, Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling, J. Comput. Phys. (2010), http://dx.doi.org/10.1016/j.jcp.2010.05.017], the accuracy condition presented here is shown to govern both the well-posedness and accuracy aspects of PMDL designed for transient (time-dependent) modeling of scalar waves in anisotropic media. 相似文献
6.
Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling
With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the well-posedness and accuracy aspects of local ABCs designed for the transient modeling of the scalar anisotropic wave equation. The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL), a simple variant of perfectly matched layers (PML) that is also equivalent to rational approximation based ABCs. Specifically, we derive the necessary and sufficient condition for the well-posedness of the initial boundary value problem (IBVP) obtained by coupling an interior and a PMDL ABC. The derivation of the reflection coefficient presented in a companion paper (S. Savadatti, M.N. Guddati, J. Comput. Phys., 2010, doi:10.1016/j.jcp.2010.05.018) has shown that PMDL can correctly identify and accurately absorb outgoing waves with opposing signs of group and phase velocities provided the PMDL layer lengths satisfy a certain bound. Utilizing the well-posedness theory developed by Kreiss for general hyperbolic IBVPs, and the well-posedness conditions for ABCs derived by Trefethen and Halpern for isotropic acoustics, we show that this bound on layer lengths also ensures well-posedness. The time discretized form of PMDL is also shown to be theoretically stable and some instability related to finite precision arithmetic is discussed. 相似文献
7.
8.
Effects of shaded facets on the performance of metal-coated etched diffraction grating demultiplexer
A finite-difference time-domain (FDTD) method combined with a periodic boundary condition is used to analyze the diffraction efficiency of an etched diffraction grating (EDG) demultiplexer coated with a metallic film at the backside. The numerical results show that the diffraction loss is mainly due to the scattering effect of shaded facets of a metal-coated grating at both the polarizations. However, the same shaded facets can produce a higher loss for a TM polarization than that for a TE polarization, which induces a higher polarization dependent loss (PDL) of the demultiplexer. 相似文献
9.
全矢量有限元模型及其在光波导中的应用 总被引:2,自引:0,他引:2
为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明:光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗(confinement loss)随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低. 相似文献
10.
采用本征模展开法(EME)结合完全匹配层(PML)边界条件,研究了由TiO2和SiO2复合膜结构组成的平面光子晶体Bragg微腔的模式特性,分析了介质厚度无序对微腔模式的调制以及入射角对局域长度的影响.结果表明,若光束正入射,带边局域长度要大于禁带局域长度,随着无序度的增加光子通带的透过率逐渐降低,而禁带的透过率逐渐上升.当无序度较小时,局域长度随随机度的变化在带边和禁带内表现出相反的规律.当无序度较大时,局域长度不仅和随机度、带隙有关,还受到材料的影响;若光束斜入射,TE模的局域长度要远小于TM模对应的值,且其最小值向短波方向移动。此外,入射角和膜层数的变化都会导致局域长度的起伏. 相似文献
11.
In this study a discontinuous Galerkin method (DG) for solving the three-dimensional time-dependent dissipative wave equation is investigated. In the case of unbounded problems, the perfectly matching layer (PML) is used to truncate the computational domain. The aim of this work is to investigate a simple selection method for choosing the basis order for elements in the computational mesh in order to obtain a predetermined error level. The selection method studied here relies on the error estimates provided by Ainsworth [M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, Journal of Computational Physics 198(1) (2004) 106–130]. The performance of the non-uniform basis is examined using numerical experiments. In the simulated model problems, a feasible method choosing the basis order for arbitrary sized elements is achieved. In simulations, the effect of dissipation and the choices of the PML parameters on the performance of the DG method are also investigated. 相似文献
12.
Licheng Cui Hongsheng Yang 《International Journal of Infrared and Millimeter Waves》2003,24(9):1567-1576
Finite-difference time-domain (FDTD) method is used to calculate the driving-point impedance of the circular groove guide diode mount. A simple way is proposed to approximate the curvilinear metal boundary of circular groove guide. Discrete equations are obtained from the Ampere's law and Faraday's law. Perfectly matched layer (PML) is applied on the open boundary of circular groove guide. At last program is made to obtain the field components. The driving-point impedance can be achieved from the ratio of the Fourier transform of the voltage and the Fourier transform of the current. The cutoff frequency and field pattern of the dominant mode are also obtained with well agreement with the theoretical results, this verifies the validity of the FDTD program. 相似文献
13.
The time-dependent behavior of a simply-supported functionally graded beam bonded with piezoelectric sensors and actuators
is studied using the state-space method. The creep behavior of bonding adhesives between piezoelectric layers and beam is
characterized by a Kelvin-Voigt viscoelastic model, which is practical in a high temperature circumstance. Both the host elastic
functionally graded beam and the piezoelectric layers are orthotropic and in a state of plane stress, with the former being
inhomogeneous along the thickness direction. A laminate model is employed to approximate the host beam. Moreover, the coupling
effect between the elastic deformation and electric field in piezoelectric layers is considered. Results indicate that the
viscoelastic property of interfacial adhesives has a significant effect on the function of bonded actuators and sensors with
time elapsing. 相似文献
14.
15.
This paper presents a new numerical model to investigate the vibro-acoustic behaviour of two laminated glass plates enclosing a thin viscothermal fluid cavity. The aim of this work is to develop an original five layer (two skins plies, two adhesive films and a core ply) laminated plate finite element by mixing Kirchhoff and Mindlin plate’s theory. The formulation is based on the theory that accounts for the transverse shear in the adhesive films and in the core. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of fluid and by taking into account the fluid-structure interaction. The discretization of the energy functional by finite element method gives after minimisation a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. Therefore, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system’s response. Then, the validation of the new laminate finite element model is achieved by comparing the sandwich plate results against data obtained from literature. Subsequently, predicted responses, such as the vibration transmissibility and the transmission loss of the coupled system, for a given laminated double glazing under an imposed homogeneous pressure are presented and discussed. Numerical results show the importance of both lamination and viscothermal fluid effects on double glazing vibro-acoustic behaviour. 相似文献
16.
17.
Dan Zhang Hongting Jia Kiyotoshi Yasumoto 《International Journal of Infrared and Millimeter Waves》2007,28(11):1003-1010
We analyzed the frequency and quality factor of microcavities on a two-dimensional photonic crystal, using a Fourier series
expansion method combined with perfectly matched layers (PMLs). Numerical examples are demonstrated and discussed to show
that the resonant frequency and the quality factor Q values can be calculated by the present method using PMLs. 相似文献
18.
19.
A full-wave modal analysis of two-dimensional, lossy and anisotropic optical waveguides using the finite element method (FEM) is presented. In order to describe the behavior of radiating fields, anisotropic perfectly matched layer boundary conditions are applied for the first time in modal solvers. The approach has been implemented using high order edge elements. The resulting sparse eigenvalue algebraic problem is solved through the Arnoldi method. Application to an antiresonant reflecting optical waveguide is reported. 相似文献
20.
Rafał Kotyński Maciej Dems Krassimir Panajotov 《Optical and Quantum Electronics》2007,39(4-6):469-479
We present a numerical method for the analysis of translationally invariant systems with anisotropic and dispersive electric
and magnetic properties. This material model enables us to calculate the mode structure of photonic devices such as photonic
crystal fibres (PCF) containing inclusions with anisotropic, conducting, magnetic, or negative index materials. The method
is based on the popular plane wave (PWM) discretisation scheme applied to the generalised vectorial transmission line equations.
The analysis is focused on the calculation of radiation losses. For this purpose we consider a uniaxial perfectly matched
layer (UPML) termination of the otherwise periodic system. We asses the accuracy of the method and the properties of spurious
modes created inside the UPML. 相似文献