基于FDTD算法的新型亚网格技术

提出了一种基于空间滤波（Spatial Filtering-Finite-Difference Time-Domain,SF-FDTD）算法的亚网格技术,使得FDTD算法的Courant-Friedrich-Levy（CFL）稳定性条件可通过空间频域滤波操作得以提高,从而获得高稳定度FDTD算法.进一步将SF-FDTD算法应用到亚网格技术中,可使亚网格区域时间步长的选取取与粗网格一致,从而极大地提高了计算效率.数值计算结果表明,在求解带有精细结构的电磁问题上,所提算法具有较高的准确性和有效性.     

A novel subgridding scheme based on a combination of thefinite-element and finite-difference time-domain methods

A simple and versatile local mesh refinement scheme, based on the hybridization of the finite-element (FE) and the finite-difference time-domain (FDTD) algorithms, is presented. The scheme achieves considerable flexibility in subgridding by using a transition region between the coarse and fine FDTD grids, meshed according to an unstructured grid, and solved by means of the FE method in the TD. An interpolation scheme in the time domain, which allows the use of different time steps in the coarse and fine mesh regions, is included in the paper     

Conservative and Provably Stable FDTD Subgridding

The finite difference time domain (FDTD) method is a common, robust simulation technique for transient electromagnetic interactions with complicated structures. However, the standard FDTD method is limited to cartesian grids everywhere in the computational grid. Many practitioners have extended FDTD to handle multiresolution problems by using finer grids near structures with small geometrical features abutted to coarse grids in regions of empty space. Unfortunately, subgridding implementations based on interpolation or extrapolation of neighboring field values can exhibit late time instabilities. Herein, a subgridding method based on multigrid finite element principles will be developed and its stability proven. Numerical results will assess its performance in 2-D and 3-D.     

Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) technique is an unconditionally stable time-domain numerical scheme, allowing the /spl Delta/t time step to be increased beyond the Courant-Friedrichs-Lewy limit. Execution time of a simulation is inversely proportional to /spl Delta/t, and as such, increasing /spl Delta/t results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for electromagnetic compatibility problems. Once the basics of the ADI-FDTD technique are presented and the differences of the relative accuracy of ADI-FDTD and standard FDTD are discussed, the problems that benefit greatly from ADI-FDTD are described. A discussion is given on the true time savings of applying the ADI-FDTD technique. The feasibility of using higher order spatial and temporal techniques with ADI-FDTD is presented. The incorporation of frequency dependent material properties (material dispersion) into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one-dimensional and three-dimensional problem space. The scheme is shown to be both accurate and unconditionally stable.     

一种非条件稳定的隐式时域有限差分法

介绍一种基于交替方向隐式(ADI)技术的时域有限差分法(FDTD).该方法是非条件稳定的,时间步长不再受到Courant稳定条件的限制,而是由数值色散误差来确定.与传统的FDTD相比,ADI-FDTD增大了时间步长,从而缩短了总的计算时间,特别是当空间网格远小于波长时,优点更加突出.首次把完全匹配层(PML)边界条件应用到ADI-FDTD计算中,采用幂指数形式的时间步进算法,推导了相应的迭代公式.进行了实例计算,并与传统FDTD的结果对比,验证了ADI-FDTD的有效性与优越性.     

An efficient analysis of planar microwave circuits using aDWT-based Haar MRTD scheme

A new wavelet-based technique to generate multiresolution time-domain schemes is presented in this paper. By using symbolic calculus, a rigorous and general formulation of subgridding at every level of multiresolution is obtained. As it is rigorously equivalent to a finer finite-difference time-domain (FDTD) scheme, it does not require any particular treatments for boundary conditions. This technique has been successfully applied to the study of microstrip structures. The near- and the far-field computation can be both improved in terms of CPU time and memory storage, while maintaining the same accuracy as the classical FDTD computation     

Conformal method to eliminate the ADI-FDTD staircasing errors

The alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable method and allows the time step to be increased beyond the Courant-Friedrich-Levy (CFL) stability condition. This method is potentially very useful for modeling electrically small but complex features often encountered in applications. As the regular FDTD method, however, the spatial discretization in the ADI-FDTD method is only first-order accurate for discontinuous media; several researchers have shown that the errors can be very high when the regular ADI-FDTD method is applied to such discontinuous media. On the other hand, the conformal FDTD method has recently emerged as an efficient FDTD method with higher order accuracy. In this work, a second-order accurate ADI-FDTD method using the conformal approximation of spatial derivatives is proposed. This new scheme, called the ADI-CFDTD method, retains the second-order accuracy in both temporal and spatial discretizations even for discontinuous media with metallic structures, and is unconditionally stable. 2D and 3D examples demonstrate the efficacy of this method and its application in EMC problems.     

Passive equivalent circuit of FDTD: an application to subgridding

The finite difference time domain (FDTD) method gives accurate results for many problems but uses a large amount of computer memory and time. This can be reduced by using subgrids (fine grids) only around critical areas in the problem domain. The fields within the coarse and fine grids are found using standard FDTD equations, while at the boundary of the subgrid, interpolation of coarse grid fields is utilised. However, a simple interpolation as reported in literature exhibits late time instability. The authors present a stable scheme of updating the subgrid boundary fields by replacing the grid discontinuity with an equivalent circuit. The stability and accuracy of this new scheme is demonstrated through calculation of the cutoff wavelength of a dielectric slab loaded waveguide for various slab thickness     

3-D FDTD method with weakly conditional stability

A novel 3-D FDTD method with weakly conditional stability is presented. The time step in this method is only determined by one space discretisation. Compared with the ADI-FDTD method, this method has better accuracy and higher computation efficiency. CPU time for this weakly conditionally stable FDTD method can be reduced to about 3/4 of that for the ADI-FDTD scheme     

Optimization of subgridding schemes for FDTD

A procedure to optimize the coupling coefficients between fine and coarse mesh regions for two-dimensional (2-D) finite-difference time-domain (FDTD) subgridding algorithms is introduced. The coefficients are optimized with respect to different angles and expanded in a form suitable for FDTD computation     

一种适用于ADI-FDTD法的非分裂式完全匹配层

基于FDTD法中场量D-H(电位移矢量-磁场强度)迭代公式,导出了适用于AD I-FDTD法的场量非分裂式完全匹配层(PML)的实现方案,与现有的其它AD I-FDTD法的PML技术相比,具有物理概念清晰、易于操作并节省计算机资源的优点。数值结果证明:该PML技术能有效地解决吸收边界的问题,为AD I-FDTD法的发展与推广应用提供了条件。     

An iterative ADI-FDTD with reduced splitting error

We present a new iterative alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. By recognizing the ADI-FDTD method as a special case of a more general iterative approach to solve the Crank-Nicolson (CN) FDTD scheme, the splitting error in ADI-FDTD can be reduced systematically. Numerical examples are used to illustrate the improved accuracy of this method.     

A higher order (2,4) scheme for reducing dispersion in FDTDalgorithm

A finite-difference time-domain (FDTD) scheme with second-order accuracy in time and fourth-order in space is discussed for the solution of Maxwell's equations in the time domain. Compared with the standard Yee (1966) FDTD algorithm, the higher order scheme reduces the numerical dispersion and anisotropy and has improved stability. Dispersion analysis indicates that the frequency band in which the higher order scheme yields an accurate solution is widened on the same grid, this means a larger space increment can be chosen for the same excitation. Numerical results show the applications of the scheme in modeling wide-band electromagnetic phenomena on a coarse grid     

A subgridding method for the time-domain finite-difference methodto solve Maxwell's equations

A modification to the time-domain finite-difference method (TDFDM) that uses a variable step size is investigated. The entire computational volume is divided into a coarse grid with a large step size. A fine grid with a small step size is introduced only around discontinuities. The corresponding time increments are related to the spatial increments with the same ratio in order to minimize the numerical dispersion. The fields within the coarse and fine grids are found using the TDFDM, while an interpolation in space and time is utilized to calculate the tangential electric field on the coarse-fine grid boundary. This subgridding decreases the required computer memory and therefore expands the capability of the TDFDM. The technique is shown to be numerically stable and does not entail any extra numerical error. The method is applied to the calculation of waveguides and microstrips     

Investigation on the characteristics of the envelope FDTD based on the alternating direction implicit scheme

This letter presents numerical characteristics of recently developed the envelope FDTD based on the alternating direction implicit scheme (envelope ADI-FDTD). Through numerical simulations, it is shown that the envelope ADI-FDTD is unconditionally stable and we can get better dispersion accuracy than the traditional ADI-FDTD by analyzing the envelope of the signal. This fact gives the opportunity to extend the temporal step size to the Nyquist limit in certain cases. Numerical results show that the envelope ADI-FDTD can be used as an efficient electromagnetic analysis tool especially in the single frequency or band limited systems.     

Low-reflection subgridding

The paper presents a novel three-dimensional subgridding scheme applicable to the finite-difference technique in the time and frequency domains. Transfer of fields between a main grid and a refined volume is performed using a simple linear interpolation. Very low-reflection levels from the main to local grid interface are obtained by co-location of fields used in the interpolation process. The technique allows material traverse without any special boundary treatment. The accuracy of the scheme is verified in numerical tests showing excellent performance even for high refinement factors.     

色散媒质中ADI-FDTD的PML

基于交替方向隐式(ADI)技术的时域有限差分法(FDTD)是一种非条件稳定的计算方法,该方法的时间步长不受Courant稳定条件限制,而是由数值色散误差决定。与传统的FDTD相比, ADI-FDTD增大了时间步长, 从而缩短了总的计算时间。该文采用递归卷积(RC)方法导出了二维情况下色散媒质中ADI-FDTD的完全匹配层(PML)公式。应用推导公式计算了色散土壤中目标的散射,并与色散媒质中FDTD结果对比,在大量减少计算时间的情况下,两者结果符合较好。     

用于电磁波多尺度问题求解的高效FDTD-PITD混合算法北大核心CSCD

针对电磁波多尺度问题的高效仿真需求,提出了基于亚网格技术的时域有限差分(FDTD)方法与时域精细积分(PITD)方法的混合数值算法。该混合算法的基本思想是采用局部亚网格技术分别对精细结构区域以及其他区域进行剖分,并应用FDTD方法和PITD方法分别对粗网格区域与细网格区域进行求解,同时构建信息交互策略交换细网格区域与粗网格区域的计算信息。一方面该方法减少了电磁波多尺度问题的网格剖分数目,显著降低了内存需求;另一方面由于应用于细网格区域的PITD方法不受Courant-Friedrich-Levy(CFL)数值稳定性条件的限制,该混合方法能够采用较大的时间步长进行仿真,减少了迭代步数以及CPU执行时间。数值计算结果验证了混合算法的稳定性、可行性以及高效性。     

ADI-FDTD方法在乳腺癌检测正向计算中的应用

传统的时域有限差分(Finite-Difference Time-Domain, FDTD)算法受到稳定性条件的制约, 时间步长受限于空间网格的尺寸.医学应用讲究即时性, 为提高成像的速度, 文中采用无条件稳定的交替隐式时域有限差分(Alternating-Direction Implicit Finite-Difference Time-Domain, ADI-FDTD)算法替代传统的FDTD算法进行正向计算, 通过实验得出采用ADI-FDTD算法在保证精度的前提下, 计算时间可缩短为FDTD算法的四分之一, 为乳腺癌微波即时成像提供了可能.     

ADI-FDTD algorithm in curvilinear co-ordinates

The alternating direction implicit (ADI) scheme has been successfully applied to the finite-difference time-domain (FDTD) method to achieve an unconditionally stable algorithm. The ADI-FDTD method is extended to the curvilinear co-ordinate system to form an alternating direction implicit nonorthogonal FDTD (ADI-NFDTD) method. The numerical results show that the proposed ADI-NFDTD algorithm demonstrates better late time stability compared to the conventional NFDTD scheme.