计算电大尺寸建筑物内电波场强的PSTD方法

本文采用一种新的时域数值方法－伪谱时域（ＰＳＴＤ）法来计算电大尺寸建筑物内电波场强。提出了由初始条件技术和一维ＰＳＴＤ方程对入射平面波脉冲进行模拟,并利用纯散射场法和线性插值把平面波引入求解问题空间,有效地解决了ＰＳＴＤ方法中入射波设置问题。数值结果表明这种新方法用于模拟电大尺寸建筑物内电波场强的精度和有效性。     

An unconditionally stable scheme for the finite-difference time-domain method

In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.     

Analyses of bounces on power distribution networks using an unconditionally stable finite-difference time-domain method

An unconditionally stable finite-difference time-domain (US-FDTD) method is utilized for analyzing the bounces on structures of power distribution networks (PDNs), which is a critical issue in the electromagnetic compatibility analysis of mobile devices. The US-FDTD method does not utilize the explicit leapfrog time scheme of conventional FDTD method and can solve problems with fine structures well, such as via, thin material and so on. By using this full-wave method, electromagnetic fields between power/ground plane pairs are analyzed and discontinuities of through-hole vias are taken into account in the modeling of PDNs.     

二维无条件稳定时域有限差分方法

基于半隐式的Crank-Nicolson差分格式给出了一种无条件稳定时城有限差分方法。和传统FDTD法中采用的显式差分格式不同,对Maxwell方程组采用半隐式差分格式,在时间和空间上仍然是二阶精确的。但时间步长不再受稳定性条件的限制,只需考虑数值色散误差对其取值的制约。利用分裂场完全匹配层吸收边界截断计算空间,为保证PML空间的无条件稳定性,其方程也采用半隐式差分格式。数值结果表明相同条件下US-FDTD方法与传统FDTD方法的计算精度是相同的,而且在增大时间步长时US-FDTD方法是稳定的和收敛的。可以预见US-FDTD方法在模拟具有电小结构问题时具有实际意义。     

The 3-D multidomain pseudospectral time-domain method for wideband simulation

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a well-posed PML is developed as an accurate and efficient solver for Maxwell's equations in conductive and inhomogeneous media. The curved object is accurately treated by curvilinear coordinate transformation. Spatial derivatives are obtained by the Chebyshev collocation method to achieve a high-order accuracy. Numerical results show an excellent agreement with solutions obtained by the FDTD method under fine sampling.     

An unconditionally stable extended (USE) finite-element time-domain solution of active nonlinear microwave circuits using perfectly matched layers

This paper proposes an extension of the unconditionally stable finite-element time-domain (FETD) method for the global electromagnetic analysis of active microwave circuits. This formulation has two advantages. First, the time-step size is no longer governed by the spatial discretization of the mesh, but rather by the Nyquist sampling criterion. Second, the implementation of the truncation by the perfectly matched layers (PML) is straightforward. An anisotropic PML absorbing material is presented for the truncation of FETD lattices. Reflection less than -50 dB is obtained numerically over the entire propagation bandwidth in waveguide and microstrip line. A benchmark test on a microwave amplifier indicates that this extended FETD algorithm is not only superior to finite-difference time-domain-based algorithm in mesh flexibility and simulation accuracy, but also reduces computation time dramatically.     

More accurate and efficient unconditionally stable FDTD method

A more accurate and efficient unconditionally stable finite-difference time-domain (US-FDTD) method is proposed. The two key points of the proposed US-FDTD method are: defining the field components at only n and (n + 1) time steps; and arranging the left and right hands of the original updating equations to be as accurate (in respect of time) as possible. It is demonstrated that the US-FDTD method is more efficient (in both computer memory and CUP time) and more accurate than the recently developed ADI-FDTD method     

Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method

In order to deal with the stability problem restricted by the finite-difference time-domain (FDTD) and conventional pseudospectral time domain (PSTD), the multidomain PSTD algorithm based on alternating-direction implicit (ADI) technique is proposed in this paper. This algorithm improves the stability and efficiency of conventional PSTD, while it maintains the accuracy and flexibility of conventional PSTD for an accurate treatment of arbitrarily curved objects. A compact matrix form is derived to effectively describe two-dimensional ADI multidomain pseudospectral time domain (ADI-MPSTD) algorithm. Numerical results show an excellent agreement with analytical solutions as well as results obtained by the FDTD algorithm, and fully demonstrate a remarkable improvement in stability and efficiency.     

Split-field PML implementations for the unconditionally stable LOD-FDTD method

We introduce and compare two split-field implementations of the perfectly matched layer (PML) for the unconditionally stable locally one-dimensional (LOD) finite-difference time-domain (FDTD) method. The LOD-FDTD formalism is expanded in terms of a symmetric source implementation. It is verified that the relative performance of both PML implementations is superior to the split PML performance in the alternating direction implicit (ADI) FDTD method.     

Error between unconditionally stable FDTD methods and conventional FDTD method

Both the ADI-FDTD method and the CN-FDTD method can be viewed as approximate factorisation of the conventional FDTD scheme, so the error between these methods and the conventional FDTD method is obtained. It is shown that the error is associated with the time step size, the permittivity and the permeability of the medium, and the spatial variation rate of field. The space discretisation has no relation with the error, which is demonstrated by numerical examples     

A pseudospectral method for time-domain computation ofelectromagnetic scattering by bodies of revolution

We present a multidomain pseudospectral method for the accurate and efficient time-domain computation of scattering by body-of-revolution (BOR) perfectly electrically conducting objects. In the BOR formulation of the Maxwell equations, the azimuthal dependence of the fields is accounted for analytically through a Fourier series. The numerical scheme in the (r,z) plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution. A modified matched-layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time-domain boundary conditions along edges. Numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis-symmetric objects, including spheres, cone-spheres, and finite cylinders, is compared with results from the literature, illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods. To emphasize the versatility of the presented framework, we compute plane wave scattering by a missile and find satisfactory agreement with method-of-moment (MoM) computations     

An unconditionally stable two-stage CMOS amplifier

This paper describes a two-stage CMOS amplifier that is stable for any capacitive load. This is achieved through the use of an optimized cascoded compensation topology. A new level shifting technique allows independent optimization of drive capability, noise and systematic offset voltage. The circuit is 0.1 mm² in a 2 μm technology and has a quiescent current consumption of 110 μA     

A three-dimensional unconditionally stable ADI-FDTD method in the cylindrical coordinate system

An unconditionally stable finite-difference time-domain (FDTD) method in a cylindrical coordinate system is presented in this paper. The alternating-direction-implicit (ADI) method is applied, leading to a cylindrical ADI-FDTD scheme where the time step is no longer restricted by the stability condition, but by the modeling accuracy. In contrast to the conventional ADI method, in which the alternation is applied in each coordinate direction, the ADI scheme here performs alternations in mixed coordinates so that only two alternations in solution matching are required at each time step in the three-dimensional formulation. Different from its counterpart in the Cartesian coordinate system, the cylindrical ADI-FDTD includes an additional special treatment along the vertical axis of the cylindrical coordinates to overcome singularity. A theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness of the cylindrical algorithm in solving electromagnetic-field problems.     

The 3-D multidomain pseudospectral time-domain algorithm for inhomogeneous conductive media

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a strongly well-posed perfectly matched layer (PML) is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in inhomogeneous and conductive media. This approach allows for an accurate treatment of curved geometries by multidomain decomposition and curvilinear coordinate transformation. Numerical experiments show the results agree excellently with analytical solutions and results of other well-known algorithms, and demonstrate a remarkable improvement in accuracy and efficiency over the FDTD method. The 3-D multidomain PSTD algorithm is then applied to calculate radar cross sections (RCS).     

On the modeling of conducting media with the unconditionally stable ADI-FDTD method

The Courant-Friedrich-Levy stability condition has prevented the conventional finite-difference time-domain (FDTD) method from being effectively applied to conductive materials because of the fine mesh required for the conducting regions. In this paper, the recently developed unconditionally stable alternating-direction-implicit (ADI) FDTD is employed because of its capability in handling a fine mesh with a relatively large time step. The results show that the unconditionally alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method can be used as an effective universal tool in modeling a medium regardless of its conductivity. In addition, the unsplit perfectly matched layer combined with the ADI-FDTD method is implemented in the cylindrical coordinates and is proven to be very effective even with the cylindrical structures that contain open conducting media.     

Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials

Backward-wave (BW) materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions. These materials were predicted to have many unusual electromagnetic properties, among them amplification of the near-field of a point source, which could lead to the perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev. Lett. vol. 85, pp. 3966, 2000]. Often systems containing BW materials are simulated using the finite-difference time-domain technique. We show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving BW materials problematic. The pseudospectral time-domain technique, on the other hand, uses a collocated grid and is free of this artifact. It is also shown that when modeling the dispersive BW material, the linear frequency approximation method introduces error that affects the frequency of vanishing reflection, while the auxiliary differential equation, the Z-transform, and the bilinear frequency approximation method produce vanishing reflection at the correct frequency. The case of vanishing reflection is of particular interest for field reconstruction in imaging applications.     

An unconditionally stable 3-D ADI-MRTD method free of the CFLstability condition

In this paper, an alternating direction implicit (ADI) technique is applied to the recently developed multiresolution time-domain (MRTD) method, resulting in an unconditionally stable ADI-MRTD scheme free of the Courant-Friedich-Lecy (CFL) stability condition. The unconditional stability is theoretically proved, and preliminary numerical results are presented to validate the scheme. Because the scheme is now free of the stability condition, its time step is determined only by modeling accuracy. The price for having the unconditional stability is, however, that the required computation memory becomes almost twice of that for the original MRTD     

无条件稳定的交替方向隐式FDTD算法

介绍了一种新的FDTD算法-交替方向隐式时域有限差分法（ADI-FDTD）,该方法采用求解微分方程的交替方向隐格式改造了FTD算法,使其能无条件稳定,从而极大地节约计算时间,成为一种计算时域电磁场分布的高效算法,同时,首次尝试利用ADI-FDTD方法结合时域近远场变换技术计算天线方向图,数值实验的结果和传统FDTD方法及理论值进行了对比,数值结果一致性较好,并节约了运算所占用的资源,提高了计算效率。     

Uniaxial perfectly matched layer media for an unconditionally stable 3-D ADI-FD-TD method

An unsplit-field perfectly matched layer (PML) medium based on Gedney's uniaxial PML (UPML) scheme is proposed for an unconditionally stable three-dimensional alternating direction implicit finite-difference time-domain (ADI-FD-TD) method. The effectiveness of the proposed ADI-UPML absorber is demonstrated through a numerical example. In addition, to have a better understanding on the ADI-FD-TD method, the actual performance (i.e., while both the reflection and dispersion errors are considered) of the ADI-UPML as a function of the time step is also illustrated.     

The transfinite-element time-domain method

This paper presents an efficient time-domain method for computing the propagation of electromagnetic waves in microwave structures. The procedure uses high-order vector bases to achieve high-order accuracy in space, Newmark's method to provide unconditional stability in time, and the transfinite-element method to truncate the waveguide ports. The resulting system matrix is real, symmetric, positive-definite, and can be solved by using the highly efficient multilevel preconditioned conjugate gradient algorithm. Since the method allows large time steps and nonuniform grids, the computational complexity for problems with irregular geometries is superior to that of the finite-difference time-domain method.