Modal MRTD approaches for the efficient analysis of waveguidediscontinuities

This paper, the multi-resolution time-domain (MRTD) technique is applied to the waveguide discontinuity problem for fast-scattering parameter computation. To improve the computational efficiency, both three-dimensional (3-D) waveguide regions, including discontinuities, and one dimensional (1-D) homogeneous waveguide region, terminated with the modal absorbing boundary condition (ABC), are simulated in the wavelet domain with the mode composition/expansion algorithm from the modal analysis. A WG-90 rectangular waveguide with a thick asymmetric iris is analyzed and the numerical results are compared with conventional finite-difference time-domain (FDTD) results and mode-matching results     

Application of Haar-wavelet-based multiresolution time-domainschemes to electromagnetic scattering problems

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite-difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation, which, in our case, consists of a pulsed plane wave. Also, we consider scattering in a half-space environment, with application to subsurface sensing. The results illustrate the advantage of the Haar MRTD method as compared with the classic FDTD, which consists of reduced memory and execution time requirements, without sacrificing accuracy     

Multiresolution time-domain analysis of plane-wave scattering fromgeneral three-dimensional surface and subsurface dielectric targets

The multiresolution time domain (MRTD) is used to analyze wide-band plane-wave scattering from general dielectric targets embedded in a lossy half-space, with free-space scattering as a special case. A Haar wavelet expansion is used for simplicity, this constituting a generalization of the widely used finite-difference time-domain (FDTD) method. In addition to developing the mathematical formulation, example results are presented for several targets, with the MRTD results validated through comparison with an independent frequency-domain method-of-moments solution and an FDTD model     

MRTD: new time-domain schemes based on multiresolution analysis

The application of multiresolution analysis to Maxwell's equations results in new multiresolution time-domain (MRTD) schemes with unparalleled inherent properties. In particular, the approach allows the development of MRTD schemes which are based on scaling functions only or on a combination of scaling functions and wavelets leading to a variable mesh grading. The dispersion of the MRTD schemes compared to the conventional Yee finite-difference time-domain (FDTD) scheme shows an excellent capability to approximate the exact solution with negligible error for sampling rates approaching the Nyquist limit. Simple microwave structures including dielectric materials are analyzed in order to illustrate the application of the MRTD schemes and to demonstrate the advantages over Yee's FDTD scheme with respect to memory requirements and execution time     

Dispersion properties and applications of the Coifman scaling function based S-MRTD

We illustrate some salient dispersion properties of the Coifman scaling function based multiresolution time domain (MRTD) technique (Coifman S-MRTD) and discuss its applicability to modeling problems of interest in microwave and wireless communication engineering. Having been recently introduced, this method presents advantages similar to those of the Daubechies-based MRTD, namely highly linear numerical dispersion and finite support of the basis functions involved. It is additionally shown that inherent accuracy-computational complexity trade-offs related to with its dispersion properties can be utilized to accelerate its execution, without compromising its accuracy. Since the Coifman basis function is non-symmetric, the modeling of perfect electric conducting boundaries cannot be pursued via the image theory approach presented in the past. Therefore, a modified approach, along with its computationally efficient implementation, is proposed and validated. Several case studies and comparisons with the conventional finite-difference time-domain method demonstrate the usefulness of Coifman S-MRTD as a time-domain analysis and design tool.     

Three-dimensional simulation of eccentric LWD tool response in boreholes through dipping formations

We simulate the response of logging-while-drilling (LWD) tools in complex thee-dimensional (3-D) borehole environments using a finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Several techniques are applied to the FDTD algorithm to improve the computational efficiency and the modeling accuracy of more arbitrary geometries/media in well-logging problems: (1) a 3-D FDTD cylindrical grid to avoid staircasing discretization errors in the transmitter, receiver, and mandrel geometries; (2) an anisotropic-medium (unsplit) perfectly matched layer (PML) absorbing boundary condition in cylindrical coordinates is applied to the FDTD algorithm, leading to more compact grids and reduced memory requirements; (3) a simple and efficient algorithm is employed to extract frequency-domain data (phase and amplitude) from early-time FDTD data; (4) permittivity scaling is applied to overcome the Courant limit of FDTD and allow faster simulations of lower frequency tool; and (5) two locally conformal FDTD (LC-FDTD) techniques are applied to better simulate the response of logging tools in eccentric boreholes. We validate the FDTD results against the numerical mode matching method for problems where the latter is applicable, and against pseudoanalytical results for eccentric borehole problems. The comparisons show very good agreement. Results from 3-D borehole problems involving eccentric tools and dipping beds simultaneously are also included to demonstrate the robustness of the method.     

Multiresolution time-domain algorithm using CDF biorthogonalwavelets

A new approach to the multiresolution time-domain (MRTD) algorithm is presented in this paper by introducing a field expansion in terms of biorthogonal scaling and wavelet functions. Particular focus is placed on the Cohen-Daubechies-Feauveau (CDF) biorthogonal-wavelet class, although the methodology is appropriate for general biorthogonal wavelets. The computational efficiency and numerical dispersion of the MRTD algorithm are addressed, considering several CDF biorthogonal wavelets, as well as other wavelet families. The advantages of the biorthogonal MRTD method are presented, with emphasis on numerical issues     

Numerical calculation of diffraction coefficients of genericconducting and dielectric wedges using FDTD

Classical theories such as the uniform geometrical theory of diffraction (UTD) utilize analytical expressions for diffraction coefficient for canonical problems such as the infinite perfectly conducting wedge. We present a numerical approach to this problem using the finite-difference time-domain (FDTD) method. We present results for the diffraction coefficient of the two-dimensional (2-D) infinite perfect electrical conductor (PEC) wedge, the 2-D infinite lossless dielectric wedge, and the 2-D infinite lossy dielectric wedge for incident TM and TE polarization and a 90° wedge angle. We compare our FDTD results in the far-field region for the infinite PEC wedge to the well-known analytical solutions obtained using the UTD. There is very good agreement between the FDTD and UTD results. The power of this approach using FDTD goes well beyond the simple problems dealt with in this paper. It can, in principle, be extended to calculate the diffraction coefficients for a variety of shape and material discontinuities, even in three dimensions     

基于FDTD的薄膜体声波谐振器的数值分析

提出了基于时域有限差分方法对薄膜体声波谐振器进行数值分析的新方法.利用时域有限差分法理论对压电材料的控制方程和牛顿方程在空间和时间上进行了离散化,通过得到的差分方程直接得出了声场传播的时域数值解.使用该数值方法对薄膜体声波谐振器的电学特性阻抗进行了分析,并将结果与一维Mason模型的解析解进行了比较验证.     

Innovative absorbing-boundary conditions for the efficient FDTDanalysis of lightning-interaction problems

Absorbing boundary conditions are developed for the efficient truncation of three-dimensional finite-difference time-domain (3-D FDTD) meshes, used for the analysis of low-frequency transient problems, such as the lightning interaction with an aircraft. The proposed boundary conditions are combined with an innovative time-marching scheme in order to assure numerical stability of the FDTD procedure for millions of time-iterations. The main advantage of the developed approach consists in the great computer saving allowed in the analysis of FDTD problems in which the space discretization step is several thousands of times smaller than the minimum wavelength excited by the transient source. Numerical applications are included in order to demonstrate the accuracy and efficiency of the proposed method     

A FDTD-based modal PML

The finite-difference time-domain (FDTD) method is one of the most popular numerical methods for solving electromagnetic problems because of its algorithmic simplicity and flexibility. For an open waveguide structure, modal perfectly matched layer (PML) schemes have been developed as efficient absorbing terminations. However, since these PML schemes are not derived directly from the FDTD algorithm, they do not perform as well as the original three-dimensional (3-D) PMLs. In this letter, a FDTD-based one-dimensional modal PML is proposed. Because it is derived directly from the FDTD formulation, its numerical dispersion characteristics are very close to the original FDTD method. Relative differences between results obtained with the proposed method and the original 3-D PML are found to be less than -220dB, and the proposed modal PML is shown to perform at least the same as the original PML if not better.     

Finite-difference approach to the solution of time-domain integralequations for layered structures

A numerical algorithm for the analysis of transient electromagnetic fields in planar structures is proposed based on the time-domain magnetic-field integral equation (MFIE), electric-field integral equation (EFIE), and the marching-on-in-time approach. The field vectors are represented in terms of vector potential functions which are calculated either by integration or by the three-dimensional (3-D) wave equation according to the geometry of the structure. Thus, the algorithm combines the advantages of integral equation techniques and finite-difference schemes. While this approach is applicable to any geometries, it is especially suitable for multilayered planar structures and is competitive to the finite-difference time-domain (FDTD) method in the case of open and radiating problems. Theoretical results are verified by the analysis of a pulse propagation in a homogeneous open-end microstrip line     

A Three-Dimensional Semi-Implicit FDTD Scheme for Calculation of Shielding Effectiveness of Enclosure With Thin Slots

The hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) scheme for a 2-D transverse electric (TE) wave is extended to a full 3-D electromagnetic wave in this paper. With the weakly conditional stability, this approach simulates shielding effectiveness of an enclosure with high computation efficiency. Numerical formulations of the 3-D HIE-FDTD scheme are presented, and simulation results are compared to those obtained by using the conventional 3-D FDTD and alternating-direction implicit (ADI) FDTD methods. The accuracy and efficiency of the 3-D HIE-FDTD for prediction of shielding effectiveness are validated by numerical simulation results.     

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.     

Theoretical and experimental characterization of theEMP-interaction with composite-metallic enclosures

A numerical procedure is developed for the prediction of the electric and magnetic field distribution inside an enclosure having aluminum and carbon-fiber reinforced composite (CFRC) walls, illuminated by a transient electromagnetic plane wave. The composite panel is simulated by an effective layer model; time-domain surface impedance boundary conditions are enforced on the external faces of the composite slab, to express the relations among the tangential electric and magnetic field components. A coupling model for the calculation of the current induced along thin wires inside the enclosure is presented. The proposed models are implemented in a three-dimensional (3-D) finite-difference time-domain (FDTD) procedure, which is applied to the analysis of the shielding performances of an aluminum box with one CFRC face, illuminated by a transient electromagnetic wave. The computed results are compared with measured data obtained by using a full scale EMP generator     

Unexpected physical phenomena indicated by FDTD modeling of theSigma-60 deep hyperthermia applicator

We investigate the numerical convergence properties of two-dimensional (2-D) and three-dimensional (3-D) finite-difference time-domain (FDTD) models of the BSD-2000 Sigma-60 annular phased array used for deep hyperthermia. The FDTD modeling data indicate unexpected physical phenomena for the case of Sigma-60 excitation of an elliptical tissue phantom embedded in a circular water bolus. These phenomena include: (1) high-Q energy storage; (2) electromagnetic (EM) mode flipping within the water bolus/phantom; and (3) whispering-gallery transmission of energy to the opposite side of the phantom relative to the exciting dipole pair. We conclude that these phenomena substantially impact the FDTD numerical modeling of this system, and further conclude that the whispering-gallery effect can impact clinical applications of the Sigma-60     

Scattering analysis by the multiresolution time-domain method usingcompactly supported wavelet systems

We present a formulation of the multiresolution time-domain (MRTD) algorithm using scaling and one-level wavelet basis functions, for orthonormal Daubechies and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelet families. We address the issue of the analytic calculation of the MRTD coefficients. This allows us to point out the similarities and the differences between the MRTD schemes based on the aforementioned wavelet systems and to compare their performances in terms of dispersion error and computational efficiency. The remainder of the paper is dedicated to the implementation of the CDF-MRTD method for scattering problems. We discuss the approximations made in implementing material inhomogeneities and validate the method by numerical examples     

Rigorous analysis of the influence of the aspect ratio of Yee's unit cell on the numerical dispersion property of the 2-D and 3-D FDTD methods

In this paper, the influence of the aspect ratio of Yee's unit cell on the numerical dispersion errors [in terms of the physical phase-velocity error (PVE) and the velocity-anisotropy error (VAE)] of two-dimensional (2-D) finite-difference time-domain (FDTD) and three-dimensional (3-D) FDTD methods is comprehensively investigated. Numerical results reveal that, for a fixed mesh resolution, the physical PVE and the VAE of both the 2-D and 3-D FDTD methods converge to certain limits for higher aspect ratio. Most importantly, it is found for the first time that for the 2-D and 3-D cases the converged dispersion errors (i.e., the limits) are, respectively, about 2.0 and 1.5 times of the corresponding square and cubic unit cells; and the validity of the above theoretical prediction is verified through numerical tests. The investigation carried out in this paper certainly confirms, from the numerical dispersion point of view, that very accurate numerical results can still be obtained even when the aspect ratio of the cells is higher. Consequently, it gives design engineers more freedom and confidence to use the FDTD methods, especially when the aspect ratio of the cells has to be greatly adjusted due to the special requirement of structures under study.     

Application of the biorthogonal multiresolution time-domain method to the analysis of elastic-wave interactions with buried targets

The biorthogonal multiresolution time-domain (Bi-MRTD) method is introduced for the analysis of elastic-wave interaction with buried targets. We provide a detailed discussion on implementation of the perfectly matched layer and on treatment of the interface between two different materials. The algorithm has also been parallelized by the use of the message-passing interface. The numerical results show that numerical dispersion can be significantly improved by using biorthogonal wavelets as bases, as compared to the conventional pulse expansion employed in the finite-difference time-domain (FDTD) method. We demonstrate that with comparison to the second-order FDTD, the Bi-MRTD yields significant CPU time and memory savings for large problems, for a fixed level of accuracy.     

Finite-difference time-domain algorithm for solving Maxwell'sequations in rotationally symmetric geometries

In this paper, an efficient finite-difference time-domain algorithm (FDTD) is presented for solving Maxwell's equations with rotationally symmetric geometries. The azimuthal symmetry enables us to employ a two-dimensional (2-D) difference lattice by projecting the three-dimensional (3-D) Yee-cell in cylindrical coordinates (r, φ, z) onto the r-z plane. Extensive numerical results have been derived for various cavity structures and these results have been compared with those available in the literature. Excellent agreement has been observed for all of the cases investigated