The perfectly matched layer boundary condition for scalarfinite-difference time-domain method

The perfectly matched layer (PML) boundary condition for the scalar finite-difference time-domain (FDTD) method is developed in this letter. It is demonstrated that the PML is suitable and effective in computation of optical waveguides. The results also show how to optimize the parameters of PML     

Total-and scattered-field decomposition technique for the finite-element time-domain method

A new finite-element time-domain (FETD) volumetric plane-wave excitation method for use with a total- and scattered-field decomposition (TSFD) is rigorously described. This method provides an alternative to the traditional Huygens' surface approaches commonly used to impress the incident field into the total-field region. Although both the volumetric and Huygens' surface formulations theoretically provide for zero leakage of the impressed wave into the scattered-field region, the volumetric method provides a simple path to numerically realize this. In practice, the level of leakage for the volumetric scheme is determined by available computer precision, as well as the residual of the matrix solution. In addition, the volumetric method exhibits nearly zero dispersion error with regard to the discrete incident field.     

An effective algorithm for implementing perfectly matched layers in time-domain finite-element simulation of open-region EM problems

An algorithm is presented to implement perfectly matched layers (PMLs) for the time-domain finite-element (TDFE) simulation of two-dimensional open-region electromagnetic scattering and radiation problems. The proposed algorithm is based on the TDFE solution of a special vector wave equation similar to the one in an anisotropic and dispersive medium. The impact of the PML on the stability of the resultant TDFE solution is studied for a variety of temporal discretization schemes, and it is shown that the proposed algorithm for implementing PML can support unconditionally stable TDFE schemes. Both the total- and the scattered-field formulations are described, and numerical simulations of radiation and scattering problems are presented to validate the proposed PML algorithm for the mesh truncation of the TDFE solution.     

A finite-element time-domain method using prism elements formicrowave cavities

A finite-element time-domain (FETD) method for solving Maxwell's equations was developed by combining prism-based edge elements with central differencing in the time domain. This method solves for the electric field as a vector function of space and time in finite cylindrical cavity geometries of arbitrary geometry. Two stability analyses of this method are performed using the growth factor technique and the Z-transform. Furthermore, the computational complexity of the present approach is also investigated, This method has been implemented and its validity tested by studying the resonant frequencies of various microwave cavities     

Thin sheet modeling using shell elements in the finite-element time-domain method

The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this paper, the focus is on modeling of thin material sheets and coatings in the finite-element time-domain method. The proposed method is based on degenerated prism elements, so-called shell elements. For a dielectric sheet the thickness is assumed small compared to the wavelength for all frequencies of interest. An important characteristic of the method is that it takes the discontinuity of the normal electric field component at a dielectric interface into account. The accuracy of the method is demonstrated for three different scattering cases. Comparisons are made with analytical data and results obtained on grids for which the thickness of the sheets is resolved. Good agreement is observed in all cases.     

A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations

This paper presents a general approach for the stability analysis of the time-domain finite-element method (TDFEM) for electromagnetic simulations. Derived from the discrete system analysis, the approach determines the stability by analyzing the root-locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix. The approach is applicable to the TDFEM simulation involving dispersive media and to various temporal discretization schemes such as the central difference, forward difference, backward difference, and Newmark methods. It is shown that the stability of the TDFEM is determined by the material property and by the temporal and spatial discretization schemes. The proposed approach is applied to a variety of TDFEM schemes, which include: (1) time-domain finite-element modeling of dispersive media; (2) time-domain finite element-boundary integral method; (3) higher order TDFEM; and (4) orthogonal TDFEM. Numerical results demonstrate the validity of the proposed approach for stability analysis.     

Approximate scalar finite-element beam-propagation method withperfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Pade approximant operator is employed. To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide     

A three-dimensional time-domain finite-element formulation for periodic structures

A formulation is presented for a three-dimensional time-domain finite-element method that can be used to analyze the scattering of a plane wave obliquely incident on a (doubly) infinite periodic structure using one unit cell. A broadband frequency response can be obtained in a single execution. The specifics of the method are shown for scattering problems, but it should be straightforward to extend it to radiation problems. The method solves for a transformed field variable (instead of solving directly for the electric field) in order to easily enable periodic boundary conditions in the time domain. The accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions. Accurate results are obtained when the excitation (frequency range) and the geometry are such that no higher order propagating Floquet modes are present. The accuracy is degraded in the presence of higher order propagating modes due to the rather simple absorbing boundary condition that is used with the present formulation. The method is found to be stable even for angles of incidence close to grazing.     

Implementing a finite-element time-domain program in parallel

A number of issues relating to the implementation of a parallel finite-element program are discussed, including choice of programming language (principally FORTRAN90 versus C++), data-communication environment, matrix partitioner, and parallel preconditioner. Some results computed for an intricately shaped load in a microwave applicator are presented     

Complex finite-element method applied to the analysis of opticalwaveguide amplifiers

A complex finite-element method and a three-level model for erbium ions are applied to obtain gain and propagation constants for erbium-doped waveguide amplifiers (EDWA's). The complex refractive index profile includes the effect of the dopant polarization induced by the pump field. The method allows to consider arbitrary dopant density profile as well as the modal structure of the pump field. For different waveguide geometries we obtain gain curves as function of pump intensity as well as slight variations in the modal propagation constants. The threshold pump power is shown to be a function of the waveguide geometry, which agrees qualitatively with experimental results,     

Efficient time-domain and frequency-domain finite-element solutionof Maxwell's equations using spectral Lanczos decomposition method

An efficient three-dimensional solver for the solution of the electromagnetic fields in both time and frequency domains is described. The proposed method employs the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation after applying the mass-lumping procedure is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution. This technique is, therefore, an implicit unconditionally stable finite-element time and frequency-domain scheme, which requires the implementation of the Lanczos process only at the largest time or frequency of interest. Consequently, a multiple time- and frequency-domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time. The efficiency and effectiveness of this new technique are illustrated by using numerical examples of three-dimensional cavity resonators     

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.     

Perfectly matched layer for transmission line modelling (TLM)method

The authors present a development of Berenger's perfectly matched layer (PML) for direct application to the transmission line modelling (TLM) method of electromagnetic simulation     

Perfectly matched layer media with CFS for an unconditionallystable ADI-FDTD method

A perfectly matched layer (PML) medium with complex frequency shifted (CFS) constitutive parameters is introduced for the three-dimensional alternating direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method. The absorbing boundary is implemented using the convolutional PML (CPML) approach. It is demonstrated that the resulting ADI-CPML scheme is unconditionally stable. The effectiveness of the absorbing medium as a function of the time step is also demonstrated. The proposed method has the advantage that it allows the application of the ADI method to low-frequency analysis     

A new global time-domain electromagnetic simulator of microwavecircuits including lumped elements based on finite-element method

This paper proposes an extension of the finite-element time-domain method for the global electromagnetic analysis of complex inhomogeneous microwave distributed circuits, containing linear or nonlinear lumped elements. This technique combines Maxwell's equations and circuit equations, directly using SPICE software for the lumped part. Its validation is performed through the study of a strongly coupled two-element active antenna     

The perfectly matched layer (PML) boundary condition for the beam propagation method

The perfectly matched layer (PML) boundary condition for the Helmoltz equation is developed and applied to the finite-difference beam propagation method. Its effectiveness is verified by way of examples.     

Analysis of the frequency response of SAW filters using finite-difference time-domain method

The finite-difference time-domain (FDTD) technique was extended to analyze the frequency response of surface acoustic wave (SAW) filters. In this method, the partial derivatives of quasi-static Maxwell's equations and the equation of motion are discretized to centered finite differences. In addition, the perfectly matched layer boundary condition was applied to reduce spurious reflections. Two structures are considered in this paper. First, the model was applied to analyze the influence of the number of electrodes on the frequency response of a SAW filter fabricated on a zinc oxide (ZnO) substrate. Then, the proposed method was further extended to analyze the frequency response of a ZnO/diamond/Si-layered SAW filter. The simulated results are in a good agreement with the existing experimental data, indicating that the FDTD method was an appropriate approach for modeling SAW devices.     

CAD applying the finite-element method for dielectric-resonatorfilters

The progress of numerical techniques now permit us to analyze rigorously complex devices such as dual-mode cavity multipole filters or planar passive elements for coplanar monolithic microwave integrated circuits (MMICs). In this paper, we describe a rigorous design of dielectric resonator (DR) filters applying the finite-element method (FEM). We first present a dual mode coupling technique which replaces classical DRs, coupling, and tuning screws, which are commonly used in dual-mode filters, by slotted DRs. Next, a new theoretical analysis based on the contribution to the dual-mode filter response of the first DR hybrid mode and of higher order modes is described. This analysis can be applied to any type of microwave dual-mode filter. It allows us to define a procedure which explains the presence and controls the position of the two transmission zeros in the filter responses. In this paper, this procedure has been applied to improve filtering performances of a dual-mode DR filter. Finally, a synthesis method is developed to rigorously design for the first time, a four- and an eight-pole slotted DR elliptic filters. The experimental results were obtained with no tuning and the theoretical ones show good agreement     

Full-wave simulation of electromagnetic coupling effects in RF and mixed-signal ICs using a time-domain finite-element method

This paper describes the computer simulation and modeling of distributed electromagnetic coupling effects in analog and mixed-signal integrated circuits. Distributed electromagnetic coupling effects include magnetic coupling of adjacent interconnects and/or planar spiral inductors, substrate coupling due to stray electric currents in a conductive substrate, and full-wave electromagnetic radiation. These coupling mechanisms are inclusively simulated by solving the full-wave Maxwell's equations using a three-dimensional (3-D) time-domain finite-element method. This simulation approach is quite general and can be used for circuit layouts that include isolation wells, guard rings, and 3-D metallic structures. A state-variable behavioral modeling procedure is used to construct simple linear models that mimic the distributed electromagnetic effects. These state-variable models can easily be incorporated into a VHDL-AMS simulation providing a means to include distributed electromagnetic effects into a circuit simulation.     

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.