Recursively Convolutional CFS-PML in 3-D Laguerre-FDTD Scheme for Arbitrary Media

In the simulation of airborne transient electromagnetic method (ATEM) in time-domain, the truncated boundary reflection can bring a big error to the results. The complex frequency shifted perfectly matched layer (CFS-PML) absorbing boundary condition has been proved to have a better absorption of low frequency incident wave and can reduce the late reflection greatly. In this paper, we apply the CFS-PML to three-dimensional numerical simulation of ATEM in time-domain to achieve a high precision .The expression of divergence equation in CFS-PML is confirmed and its explicit iteration format based on the finite difference method and the recursive convolution technique is deduced. Finally, we use the uniformity half space model and the anomalous model to test the validity of this method. Results show that the CFS-PML can reduce the average relative error to 2.87% and increase the accuracy of the anomaly recognition.

In this letter, the convolutional implementation of the complex frequency shifted perfectly matched layer (CFS-PML) absorbing boundary condition (ABC) is proposed for the finite-difference time-domain (FDTD) method of solving wave equation. The FDTD solution time-marching formulations of the developed wave-equation convolutional CFS-PML (CPML) ABC are derived. Several numerical experiments are used to verify the capacity of the proposed algorithm. Solution results confirm that the proposed CPML ABC can obtain excellent absorption for both traveling waves and evanescent waves.

A new numerical discretization of the complex frequency shifted‐perfectly matched layer (CFS‐PML) is presented for truncation of open domains. This discretization is based on the theory of discrete differential forms applied to electromagnetism, which guarantees both the simplification of the algorithms and a more elegant formulation of expression. The curl Maxwell's equations are solved in time domain in terms of electric e magnetic fields. The Ampere‐Maxwell law with, the constitutive relations included through the Hodge operator, is discretized in space by applying the Galerkin method. Conversely, the Faraday law is represented by topological relations via incidence matrix. The time domain discretization uses the leap‐frog scheme with a recursive convolution inside PML region. Two examples are shown, the first one to validate the CFS‐PML procedure and the second one to solve a typical ground penetrating radar scenario which include a lossy media. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:351–357, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27298

In order to study the reflection of electromagnetic wave in Lorentz media, A novel piecewise linear recursive convolution(PLRC) method based on the auxiliary differential equation (ADE) of finite-difference time-domain(FDTD) technique is used to obtain the formulation of 2-D TM wave propagation in lossy Lorentz media.In 1-D case, the reflected coefficients calculated by the PLRC ADE-FDTD method and exact theoretical result are excellent agreement.This expresses that the 2-D formulas of electromagnetic wave propagation in lossy Lorentz media are right.Furthermore, Plane wave reflected by Lorentz media layer is calculated and simulated.Results display that reflected effect is evident.

Discontinuous-Galerkin Time-Domain (DGTD) methods are highly efficient solution methods for solving the time-dependent Maxwell's equations [1]. DGTD methods are high-order accurate and highly parallel. Recently, a Discontinuous Galerkin Finite Element Time-Domain (DGFETD) method has been introduced [2]. Both the electric and magnetic fields are expanded via hierarchical Nedelec curl-conforming mixed-order basis functions [3]. Similar to the DGTD method, tangential field continuity is weakly constrained across shared boundaries. The use of curl-conforming basis functions that satisfy Nedelec's criterion avoids the concern of spurious solutions [4]. Hence, the formulation avoids the need for penalty methods [1]. Furthermore, the method does not require upwind flux terms for stability. The focus of this paper is the simulation of electromagnetic waves propagating in complex dispersive media via the DGFETD method. The difficulty of simulating dispersive media in the time domain is that the constitutive relations require a convolution. Performing a direct convolution is far too expensive, so more efficient schemes must be introduced. Dispersive materials have been modeled with FDTD and FETD methods [5] as well as within DGTD methods [6–8]. To preserve high-order accuracy in the DGTD algorithm, auxiliary differential equation (ADE) based-methods have been proposed to represent the constitutive relations. In this paper, a high-order DGFETD algorithm is proposed for simulating the fields in dispersive media based on an ADE formulation. The method is applied to a Drude and multiple pole Debye and Lorentz dispersive media models. The proposed algorithm is validated through the simulation of a number of canonical problems demonstrating that the algorithm preserves the high-order accuracy of the DGFETD method.

In this letter, the composite scattering of a plasma-coated target above a randomly rough sea surface is investigated by the finite-difference time-domain (FDTD) method with pulsed wave excitation. Both sea water and plasma layer are regarded as isotropic and dispersive media, and they satisfy the Debye model and the Drude model, respectively. The auxiliary differential equation (ADE) technique is incorporated into the FDTD scheme to deal with the dispersive media. To ensure the feasibility of our present method, the scattering of a perfect electrically conducting target without coating above dispersive sea surface by the ADE-FDTD method is compared with the result obtained by the parallel method of moments, which requires an individual run for every frequency of interest. Finally, the normalized radar cross section of a plasma-coated target above rough sea surface is calculated and analyzed for different parameters in detail.

A novel finite-difference time-domain (FDTD) formulation for dispersive media called the JE convolution (JEC) method is derived using the convolution relationship between the current density J and the electric field E. The high accuracy of the JEC method is confirmed by computing the reflection and transmission coefficients for a nonmagnetized plasma slab in one dimension. It is found that the new method has an accuracy comparable to the auxiliary differential equation (ADE) while having the same computational efficiency as the less accurate recursive convolution (RC) method. Numerical simulations also show that the JEC method exhibits significantly higher accuracy than the RC method in modeling wave attenuation inside the plasma.

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.

The numerical dispersion is one of the main factors to affect the accuracy of the finite-difference time-domain (FDTD) method. It can be easy to be taken for granted that a smaller time step leads to smaller simulation errors. This paper reveals that smaller time steps do not always make more accurate results in FDTD simulations. We analytically investigated how time steps affect the numerical dispersion of two FDTD methods: the leapfrog FDTD(2,2) method and the FDTD(2,4) method. The investigations in this paper show that in the FDTD(2,2) method, a larger time step limited by the Courant-Friedrichs-Lewy (CFL) condition is more helpful to reduce the numerical dispersion error. However, in the FDTD(2,4) method, as the time step grows, the numerical dispersion error decreases at the beginning and then increases. Several numerical examples are carried out to verify our analysis.

An finite-difference time-domain (FDTD) scheme for simulating wave propagation inside Cole-Cole (CC), Havriliak-Negami (HN), or Raicu (R) dispersive media is proposed. The main difficulty in FDTD implementations for such media is the fact that the time-domain polarization relations are fractional integro-differential equations. To circumvent this difficulty, the dispersive susceptibility of the medium is modeled by Padé approximants. It is proven that under certain conditions the Padé approximant is equal to a weighted sum of Debye terms, while the physical restrictions for positive weights and relaxation times are fulfilled with certainty. Hence, a set of first-order auxiliary differential equations (ADEs), which approximate the original fractional polarization relation, is derived and directly embedded in the FDTD scheme. In contrast to previous works, the derivation of the Debye expansion of the original dispersive permittivity is carried out in a straightforward manner without involving nonlinear optimization techniques. Comparisons between analytical and FDTD results of the reflection and transmission coefficients as well as of the transfer functions inside the dispersive media illustrate the efficiency of the proposed scheme, over wideband frequency domains.

A simple but efficient finite-difference time-domain (FDTD) method integrated with auxiliary differential equation (ADE) for modelling periodic graphene-based structures is proposed. Based on the integral form of Ampere's circuital law, the derived equations are simpler than those of subcell method proposed by the others. Numerical experiments are carried out to validate our method in comparison with the results of analytical and commercial software CST. It is further applied to study some periodic graphene-based Split-Ring Resonators (GSRR) structures, and their tunable transmission properties are investigated.

Finite-difference time-domain method for three-dimensional grid of hexagonal prisms

The Lorentz–Drude model incorporated Maxwell equations are simulated by using the three-dimensional finite difference time domain (FDTD) method and the method is parallelized on multiple graphics processing units (GPUs) for plasmonics applications. The compute unified device architecture (CUDA) is used for GPU parallelization. The Lorentz–Drude (LD) model is used to simulate the dispersive nature of materials in plasmonics domain and the auxiliary differential equation (ADE) approach is used to make it consistent with time domain Maxwell equations. Different aspects of multiple GPUs for the FDTD method are presented such as comparison of different numbers of GPUs, transfer time in between them, synchronous, and asynchronous passing. It is shown that by using multiple GPUs in parallel fashion, significant reduction in the simulation time can be achieved as compared to the single GPU.

This paper presents the modelling of wire medium using a finite-difference time-domain (FDTD) method. The flat subwavelength lenses formed by the wire medium (lattices of parallel metallic wires) have been modelled in FDTD through the effect medium approach. The auxiliary differential equation (ADE) method has been applied in FDTD model in order to take into account both the frequency dispersion effect and the spatial dispersion effect which was found recently. The developed formulas have been implemented in a two-dimensional (2-D) FDTD model and validated by comparing transmission coefficient calculated from analytical solutions. The simulation results demonstrate the subwavelength imaging capability of the wire medium lenses.

On basis of the auxiliary differential equation, an improved convolutional perfectly matched layer (CPML) scheme has been proposed and applied to the three-dimensional weakly conditionally stable (WCS) finite-difference time-domain (FDTD) method. With this method, the maximum error is reduced effectively, and the absorption effect is more obvious. The simulation results show the proposed improvement scheme with more calculation accuracy than initial CPML under various Courant-Friedrich-Levy number (CFLN) conditions while ensuring similar calculation time and memory cost. Moreover, when CFLN is increased to eight, the calculation time is <30% of the traditional method, which proved the proposed method with more calculation efficiency.