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1.
提出了一种新的算法——高阶辛时域有限差分法(SFDTD(3, 4): symplectic finite-difference time-domain)求解含时薛定谔方程.在时间上采用三阶辛积分格式离散, 空间上采用四阶精度的同位差分格式离散, 建立了求解含时薛定谔方程的高阶离散辛框架;探讨了高阶辛算法的稳定性及数值色散性.通过理论上的分析及数值算例表明:当空间采用高阶同位差分格式时, 辛积分可提高算法的稳定度;SFDTD(3, 4)法和FDTD(2, 4)法较传统的FDTD(2, 2)法数值色散性明显改善.对二维量子阱和谐振子的仿真结果表明: SFDTD(3, 4)法较传统的FDTD(2, 2)法及高阶FDTD(2, 4)法有着更好的计算精度和收敛性, 且SFDTD(3, 4)法能够保持量子系统的能量守恒, 适用于长时间仿真. 相似文献
2.
辛时域有限差分算法研究等离子体光子晶体透射系数 总被引:1,自引:0,他引:1
相较于传统的时域有限差分算法,辛时域有限差分算法具有高准确度性和低色散性.传统的时域有限差分算法的计算准确度较低,数值色散误差较大,并且破坏了麦克斯韦方程的辛结构,从而导致其稳定性较差.然而辛时域有限差分算法可以克服这些缺点,从而保证了整个仿真计算的准确性和稳定性.本文基于辛时域有限差分算法,对等离子体光子晶体的带隙特性,透射系数等进行了研究,并与传统的时域有限差分算法进行了对比,验证了辛时域有限差分算法的优势和可行性. 相似文献
3.
Huajun Zhu Songhe Song & Yaming Chen 《advances in applied mathematics and mechanics.》2011,3(6):663-688
In this paper, we develop a multi-symplectic wavelet collocation method for
three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation
of the equations, wavelet collocation method based on autocorrelation functions
is applied for spatial discretization and appropriate symplectic scheme is employed
for time integration. Theoretical analysis shows that the proposed method is
multi-symplectic, unconditionally stable and energy-preserving under periodic
boundary conditions. The numerical dispersion relation is investigated. Combined
with splitting scheme, an explicit splitting symplectic wavelet collocation method
is also constructed. Numerical experiments illustrate that the proposed methods are
efficient, have high spatial accuracy and can preserve energy conservation laws exactly. 相似文献
4.
Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme
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The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite-difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB. 相似文献
5.
A High-Order Discontinuous Galerkin Method for the Two-Dimensional Time-Domain Maxwell's Equations on Curved Mesh
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Hongqiang Lu Yida Xu Yukun Gao Wanglong Qin & Qiang Sun 《advances in applied mathematics and mechanics.》2016,8(1):104-116
In this paper, a DG (Discontinuous Galerkin) method which has been widely
employed in CFD (Computational Fluid Dynamics) is used to solve the two-dimensional
time-domain Maxwell's equations for complex geometries on unstructured
mesh. The element interfaces on solid boundary are treated in both curved way
and straight way. Numerical tests are performed for both benchmark problems and
complex cases with varying orders on a series of grids, where the high-order convergence
in accuracy can be observed. Both the curved and the straight solid boundary
implementation can give accurate RCS (Radar Cross-Section) results with sufficiently
small mesh size, but the curved solid boundary implementation can significantly
improve the accuracy when using relatively large mesh size. More importantly, this
CFD-based high-order DG method for the Maxwell's equations is very suitable for
complex geometries. 相似文献
6.
7.
We compare microwave tunneling experiments using three types of potentials with calculations describing these systems, using only Maxwell's equations. The values obtained are identical within a very narrow error limit. Thus, microwave tunneling through evanescent waveguide regions, including superluminal tunneling velocities, is described by Maxwell's equations. The dispersion relation yields purely imaginary, complex, or real k-values. As an analogy, microwave tunneling presents an ideal tool for studying quantum mechanical tunneling. 相似文献
8.
结合有耗的Drude-Lorentz色散模型,提出了处理双色散模型的辛时域有限差分算法.基于矩阵分裂,辛传播算子和辅助差分方程技术,结合严格而巧妙的公式推导,构建了算法框架,并给出了详细的公式推导过程.为了验证本文算法的有效性和精确性,首先计算了一维空间双色散平板的透射系数,并与解析解对比,结果较好地符合,证明了该算法是有效而精确的.然后计算了三维空间中有实际意义的银分裂环,金属银的介电参数由Drude模型拟合.计算了该结构的透射系数,反射系数和吸收系数,得到了银分裂环的谐振频率和吸收频率,为实际实验结果提供了可供参考的计算结果. 相似文献
9.
Posteriori Error Estimation for an Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma
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Jichun Li 《advances in applied mathematics and mechanics.》2009,1(1):107-124
In this paper, we develop a residual-based a posteriori error
estimator for the time-dependent Maxwell's equations in the cold
plasma. Here we consider a semi-discrete interior penalty
discontinuous Galerkin (DG) method for solving the governing
equations. We provide both the upper bound and lower bound analysis
for the error estimator. This is the first posteriori error analysis
carried out for the Maxwell's equations in dispersive media. 相似文献
10.
11.
James V. Lambers 《advances in applied mathematics and mechanics.》2009,1(6):781-798
Ever since its introduction by Kane Yee over forty years
ago, the finite-difference time-domain (FDTD) method has been a
widely-used technique for solving the time-dependent Maxwell's
equations that has also inspired many other methods. This paper
presents an alternative approach to these equations in the case of
spatially-varying electric permittivity and/or magnetic
permeability, based on Krylov subspace spectral (KSS) methods. These
methods have previously been applied to the variable-coefficient
heat equation and wave equation, and have demonstrated high-order
accuracy, as well as stability characteristic of implicit
time-stepping schemes, even though KSS methods are explicit. KSS
methods for scalar equations compute each Fourier coefficient of the
solution using techniques developed by Golub and Meurant for
approximating elements of functions of matrices by Gaussian
quadrature in the spectral, rather than physical, domain. We show
how they can be generalized to coupled systems of equations, such as
Maxwell's equations, by choosing appropriate basis functions that,
while induced by this coupling, still allow efficient and robust
computation of the Fourier coefficients of each spatial component of
the electric and magnetic fields. We also discuss the application
of block KSS methods to problems involving non-self-adjoint spatial
differential operators, which requires a generalization of the block
Lanczos algorithm of Golub and Underwood to unsymmetric matrices. 相似文献
12.
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14.
M. Ludvigsen 《General Relativity and Gravitation》1975,6(2):165-173
A twisting shear free solution of Maxwell's equations is obtained by transforming to a complex coordinate system in which the corresponding solution is complex but twist free. The equations in this system are easily solved, and, by transforming back to the original coordinates, a twisting shear free solution of Maxwell's equations is obtained. 相似文献
15.
Jiangxing Wang Ziqing Xie & Chuanmiao Chen 《advances in applied mathematics and mechanics.》2015,7(6):796-817
An implicit discontinuous Galerkin method is introduced to solve the time-domain
Maxwell's equations in metamaterials. The Maxwell's equations in metamaterials
are represented by integral-differential equations. Our scheme is based on discontinuous
Galerkin method in spatial domain and Crank-Nicolson method in temporal
domain. The fully discrete numerical scheme is proved to be unconditionally stable.
When polynomial of degree at most $p$ is used for spatial approximation, our scheme is
verified to converge at a rate of $\mathcal{O}(τ^2+h^{p+1/2})$. Numerical results in both 2D and 3D
are provided to validate our theoretical prediction. 相似文献
16.
R. M. Gupta 《等离子体物理论文集》1972,12(3):179-183
The well-known linearization technique has been used to derive the dielectric tensor for a multicomponent plasma in the presence of a static magnetic field. The equation of motion for various species of particles has been considered with Maxwell's field equations and the dispersion relation for different specific cases have been obtained. 相似文献
17.
Sameer Ismail Farahat 《Fortschritte der Physik》1994,42(8):707-724
In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics. 相似文献
18.
A. Wünsche 《Annalen der Physik》1980,492(2):121-142
Boundary Conditions of Electrodynamics for Media with Spatial Dispersion and for Transition Layers Starting from Maxwell's equations of macroscopic electrodynamics for spatially inhomogeneous anisotropic media with spatial dispersion the boundary conditions are derived with an essentially new method using generalized functions and expansions of the fields in terms of moments. We find a complete infinite system of boundary conditions, which can be reduced to finite systems by approximations. For the special cases of first order spatial dispersion and for transition layers we obtain boundary conditions in the first approximation, which improve and generalize the usual ones. 相似文献
19.
《Physica B: Condensed Matter》2005,355(1-4):37-43
By considering that the implanted ions in a group-IV semiconductor agglomerate to form nanoclusters (NCs) and some of them acquire negative charge, we present an analytical study on excitation and propagation of Alfven wave (AW). Using multi-fluid analysis and Maxwell's equations, a linear dispersion relation for the AW in a semiconductor plasma has been derived. The presence of charged NCs is shown to split the waves into two components and significantly modifying their dispersion and absorption characteristics by creating a charge imbalance in the semiconductor plasma. The NCs, on account of their heavy masses, are assumed to be stationary in the background. 相似文献