采用FDTD/FVTD混合算法分析蝶形微带天线

用FDTD和FVTD混合算法分析了蝶形微带天线的反射损失.在适于矩形网格的区域采用常规的非均匀FDTD算法,在微带贴片天线的斜边或PEC弯曲表面处采用FVTD算法,重叠区域的场通过邻近场的线性插值得到.程序仿真和实际测量结果的比较表明在较宽的频带内,该算法在不损失精度,不显著增加CPU时间和内存的情况下,极大地降低了常规FDTD所要求的网格密度.     

Hybrid finite-volume finite-difference time-domain modelling ofcurved surfaces

A computationally efficient hybrid finite-volume finite-difference time-domain (FV-FDTD) method is proposed to model the scattering from curved objects. The hybrid FV-FDTD method uses a local conforming mesh consisting of only two FVTD cells, one either side of the scatterer's contour, giving a better approximation to the surface. The improved definition of the scatterer using the hybrid FV-FDTD method is shown to improve the solution in comparison to the FDTD method     

Three-dimensional CAD-based mesh Generator for the Dey-Mittra conformal FDTD algorithm

It is well-known that the finite-difference time-domain (FDTD) method is subject to significant errors due to the staircasing of surfaces that are not precisely aligned with major grid planes. Dey and Mittra introduced a locally conformal method (D-FDTD) that has shown substantial gains in the accuracy of modeling arbitrary surfaces in the FDTD grid. A mesh generator for this purpose was reported by Yu and Mittra. In this paper, we present the formulation and validation of an alternative CAD-based mesh generator for D-FDTD that has improved capabilities for arbitrary three-dimensional (3-D) perfect electric conductor (PEC) geometries. This mesh generator is capable of importing AutoCad and ProE files of 3-D PEC scatterers and resonators. It can reduce the required FDTD grid resolution by up to 4:1 in each Cartesian direction in 3-D relative to conventional staircased FDTD models when modeling cavity resonances of complex PEC structures such as twisted waveguides.     

Conformal hybrid finite difference time domain and finite volumetime domain

A hybrid method that combines the finite difference time domain (FDTD) and the finite volume time domain (FVTD) methods is presented. The FVTD, based on a conformal and unstructured grid is used in the near vicinity of the surface of a scatterer, and the FDTD is used to model the fields in the surrounding area. The two are coupled together through interpolation. The vertex-based FVTD allows for more convenient and accurate interpolations than a conformal FDTD method. The hybrid method is validated through two examples-the scattering by a PEC cube and sphere-by comparison with the direct FDTD solution, and with an exact Mei series solution for the spherical case     

Analysis of curved and angled surfaces on a Cartesian mesh using anovel finite-difference time-domain algorithm

The widely accepted finite-difference time-domain algorithm, based on a Cartesian mesh, is unable to rigorously model the curved surfaces which arise in many engineering applications, while more rigorous solution algorithms are inevitably considerably more computationally intensive. A nonintensive, but still rigorous, alternative to this approach has been to incorporate a priori knowledge of the behavior of the fields (their asymptotic static field solutions) into the FDTD algorithm. Unfortunately, until now, this method has often resulted in instability. In this contribution an algorithm (denoted `SFDTD' for second-order finite difference time domain) is presented which uses the static field solution technique to accurately characterize curved and angled metallic boundaries. A hitherto unpublished stability theory for this algorithm, relying on principles of energy conservation, is described and it is found that for the first time a priori knowledge of the field distribution can be incorporated into the algorithm with no possibility of instability. The accuracy of the SFDTD algorithm is compared to that of the standard FDTD method by means of two test structures for which analytic results are available     

Hybrid finite-difference time-domain modeling of curved surfacesusing tetrahedral edge elements

A hybrid finite-difference time-domain (FDTD) method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces. The method employs the conventional FDTD method for most of the regular region but introduces the tetrahedral edge-based finite-element scheme to model the region near the curved surfaces. Without any interpolation for the fields on the curved surface, nor any additional stability constraint due to the finer division near the curved surfaces, the novel finite-element scheme is found to have second-order accuracy, unconditional stability, programming ease, and computational efficiency. The hybrid method is applied to solve the electromagnetic scattering of three-dimensional (3-D) arbitrarily shaped dielectric objects to demonstrate its superior performance     

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.     

Impedance boundary condition simulation in the FDTD/FVTD hybrid

The simulation of the impedance boundary condition (IBC) for the finite-difference time-domain (FDTD) and the finite-volume time domain (FVTD) hybrid algorithm with overlapping grids is explained in detail. This paper does not discuss the validity of the IBC model, and our model assumes the surface impedance or surface admittance has a constant resistive part and a nonnegative imaginary part, which is a linear function of frequency. This model is restrictive. But, with this assumption, the use of a convolution integral is avoided and for many applications this is sufficient. Comparisons of the calculations, based on our time-domain algorithm with the Mie series solutions and the method of moment (MoM) solutions, are given. The agreement between our solutions and the referenced solutions shows that our IBC simulation gives credible numerical results     

A technique for improving the accuracy of the nonuniformfinite-difference time-domain algorithm

This paper deals with the problem of improving the accuracy of the nonuniform finite-difference time-domain (NUFDTD) algorithm, which is known to contain higher discretization errors than the conventional uniform FDTD. The improvement is achieved by effectively canceling out the numerical reflections that typically occur due to dispersion in the nonuniform mesh. The modified nonuniform algorithm is applied to a generic coaxial discontinuity problem and to that of near-to-far-field transformation. The proposed method is simple, does not require any interpolations or extrapolations, provides higher accuracy than the conventional NUFDTD algorithm, and is stable     

A Locally Conformal Algorithm for Handling Curved Metallic Surfaces and Its Application

This paper describes a modified locally conformal algorithm for finite-difference time-domain (FDTD) method. Fields in the entire computational domain are computed by a regular FDTD algorithm except those near curved metallic surfaces, where special techniques proposed in this paper are applied. The computation efficiency of a regular FDTD method is maintained while a high space-resolution is obtained by this new algorithm. To validate the reliability of the algorithm, coaxial continuous transverse stub arrays at millimeter wave Ka-band and microwave X-band are tested, and the simulated results show good agreement with the experimental results from an HP-8510B Network Analyzer and the simulation results from software package HFSS.     

A hybrid Yee algorithm/scalar-wave equation approach

In this paper, two alternate formulations of the Yee algorithm, namely, the finite-difference time-domain (FDTD) vector-wave algorithm and the FDTD scalar-wave algorithm are examined and compared to determine their relative merits and computational efficiency. By using the central-difference divergence relation the conventional Yee algorithm is rewritten as a hybrid Yee/FDTD scalar-wave algorithm. It is found that this can reduce the computation time for many 3-D open geometries, in particular planar structures, by approximately two times as well as reduce the computer-memory requirements by approximately one-third. Moreover, it is demonstrated both mathematically and verified by numerical simulation of a coplanar strip transmission line that this hybrid algorithm is entirely equivalent to the Yee algorithm. In addition, an alternate but mathematically equivalent reformulation of the Enquist-Majda absorbing boundary condition based on the normal field component (relative to the absorbing boundary wall) is given to increase the efficiency of the hybrid algorithm in the modeling of open region problems. Numerical results generated by the hybrid Yee/scalar-wave algorithm for the Vivaldi antenna are given and compared with published experimental work     

A modified FDTD (2, 4) scheme for modeling electrically largestructures with high-phase accuracy

A new fourth-order finite-difference time-domain (FDTD) scheme has been developed that exhibits extremely low-phase errors at low-grid resolutions compared to the conventional FDTD scheme. Moreover, this new scheme is capable of combining with the standard Yee (1966) scheme to produce a stable hybrid algorithm. The problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford. With this new development, the FDTD method can now be used to successfully model structures that are thousands of wavelengths large, using the present day computer technology     

Analysis of the CDF biorthogonal MRTD method with application to PEC targets

We consider the biorthogonal Cohen-Daubechies- Feauveau (CDF) wavelet family in the context of a biorthogonal multiresolution time-domain (bi-MRTD) analysis. A disadvantage of previous bi-MRTD analyses is an inability to handle abrupt changes in material properties, particularly for a perfect electric conductor (PEC). A multiregion method is proposed to address PEC targets. The proposed method is based on the fact that the CDF bi-MRTD may be viewed as a linear combination of several conventional finite-difference time-domain (FDTD) solutions. The implementation of the connecting surface is also simplified. Several numerical results are presented, with comparison to analytic and FDTD results.     

Analyzing electromagnetic structures with curved boundaries onCartesian FDTD meshes

In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by traditional FDTD formulas. Therefore, this new algorithm is more efficient than general nonorthogonal FDTD schemes in terms of computer resources such as memory and central processing unit (CPU) time. Simulation results are presented and compared to those using other methods     

A hybrid 2-D ADI-FDTD subgridding scheme for modeling on-chipinterconnects

This paper presents a novel technique for extracting the propagation characteristics of on-chip interconnects. A hybrid two-dimensional subgridding scheme, based on a combination of the finite-difference time-domain (FDTD) method and the alternating-direction implicit (ADI-)FDTD technique, is utilized. The ADI-FDTD scheme is used for fine grid in the vicinity of the metallic etch, while the coarse FDTD grid is used outside this region. The advantage of the ADI-FDTD scheme is that it can be synchronized with the time marching step employed in the coarse FDTD scheme, obviating the need for the temporal interpolation of the fields in the process. This helps to render the hybrid ADI-FDTD subgridding scheme to be more efficient than the conventional FDTD subgridding algorithm in terms of the run time. The phase and attenuation constants of the dominant mode of a lossy stripline are computed by the proposed scheme to validate the technique     

Hybrid thin-slot algorithm for the analysis of narrow apertures infinite-difference time-domain calculations

A technique to incorporate a half-space aperture integral equation into a finite-difference time-domain (FDTD) code based on the offset Yee mesh (see K.S. Yee, ibid., vol. AP-14, p.302-7, 1966) is presented. To introduce the technique, linear apertures that are electrically narrow in both width and depth are discussed. The method incorporates an independent time-marching solution for the aperture problem into the FDTD code so that the aperture formally does not exist within the main FDTD mesh. A feedback scheme is introduced so that full exterior and interior coupling is included in the aperture solution. The technique is particularly useful for the analysis of apertures that are narrow both in width and depth with regard to the FDTD spatial cell. Previous thin-slot methods are shown to significantly underestimate the transverse gap electric field for this case, and an explanation for this is provided with the aid of the hybrid algorithm     

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.     

FDTD Schemes With Minimal Numerical Dispersion

A novel formulation of hybrid finite-difference time-domain (FDTD) methods is presented. Significant reduction of numerical dispersion is achieved by the proposed FDTD methods that combine the second-order and higher-order finite-differences. Also, the proposed FDTD methods exhibit significantly higher solution accuracy than the accuracy of standard FDTD schemes as a result of partial mutual cancellation of numerical errors provided by the developed FDTD update procedure. The residual numerical error of the phase velocity remains low even for sampling of a few points per wavelength. Also, the FDTD schemes based on the proposed approach are faster and more accurate than the corresponding purely higher-order FDTD schemes with the same mesh. Test examples are provided for validation purposes.      

On the solution of a class of large body problems with full orpartial circular symmetry by using the finite-difference time-domain(FDTD) method

This paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry. The method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem. It does so by dividing the problem into two parts: a larger 3-D region with circular symmetry, and a smaller 2-D region without circular symmetry. An finite-difference time-domain (FDTD) algorithm is used to analyze the circularly symmetric 3-D case, while a method of moments (MoM) code is employed for the nonsymmetric part of the structure. The results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system. The advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2-D as opposed to a full 3-D FDTD simulation. In addition to enhancing computational efficiency, the FDTD algorithm used in this paper also features one improvement over conventional FDTD methods: a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces. The accuracy of the method is validated via a comparison of simulated and measured results     

Efficient compact 2-D time-domain method with weighted Laguerre polynomials

An efficient time-domain method based on a compact two-dimensional (2-D) finite-difference time-domain (FDTD) method combined with weighted Laguerre polynomials has been proposed to analyze the propagation properties of uniform transmission lines. Starting from Maxwell's differential equations corresponding to the compact 2-D FDTD method, we use the orthonormality of weighted Laguerre polynomials and Galerkin's testing procedure to eliminate the time variable. Thus, an implicit relation, which results in a marching-on-in-degree scheme, can be obtained. To verify the accuracy and efficiency of the hybrid method, we compare the results with those from the conventional compact 2-D FDTD and compact 2-D alternating-direction-implicit (ADI) FDTD methods. The hybrid method improves the computational efficiency notably, especially for complex problems with fine structure details that are restricted by stability constrains in the FDTD method.