Finite-difference Time-domain Domain Research Articles

Compact BZT-ME-PML for modeling FDTD subsurface sensing and imaging

Depending on the matrix exponential (ME) method, a compact and highly-accurate implementation of the perfectly matched layer (PML) with the complex-frequency-shifted (CFS) scheme based upon the bilinear Z-transform (BZT) technique is developed for modeling the finite-difference time-domain (FDTD) problems on the very low frequency (VLF) subsurface sensing and the very high frequency (VHF) imaging. By using ME method, the proposal becomes a compact first-order differential matrix form so that it can completely circumvent convolution operations, formula rearrangements, or variable replacements during mathematical derivations. Furthermore, the BZT-ME-PML can not only flexibly terminate arbitrary media because of adding the DB constitutive relation, but efficiently attenuate evanescent waves and decrease late-time reflections due to incorporating the CFS scheme. Besides, the BZT-ME-PML can maintain higher absorption performances when it comes closer to truncate the FDTD domain with targets so that smaller computational regions can be adopted for modeling 3D open-domain subsurface sensing and imaging cases, resulting in palpable improvements in memory requirement and CPU time. The numerical simulations on the subsurface sensing and imaging have been carried out to illustrate the validity and accuracy of the approach.

Electromagnetic and Semiconductor Modeling of Scanning Microwave Microscopy Setups

This article presents finite difference time domain (FDTD) and finite element method (FEM) based electromagnetic modeling and simulation of an industrial scanning microwave microscopy (SMM) material measurement setup. These two methods have been employed to cross verify each other for classical electromagnetic simulations of the homogeneous conductive materials under SMM. For the SMM simulations involving semiconductor materials, however, a coupled multiphysics solver is required in addition to the pure electromagnetic analysis. As a solution to this problem, an FEM-based semiconductor Poisson-Drift-Diffusion (PDD) solver and its coupling to transient electromagnetic solver is presented in this article. The considered SMM setup consists of a conductive fine tip suspended at a certain height above the sample. For the validation purposes of electromagnetic solvers, the numerical modeling was based on both the time domain FEM (TD-FEM) and FDTD. Both numerical methods extract the scattering parameters from the computed field of the conductive or dielectric samples. At the second stage of the analysis, the TD-FEM solver is coupled with the time domain PDD semiconductor solver in order to simulate charge transport and explain behavior of the charges in semiconducting domains under electromagnetic illumination similar to SMM setups.

An Efficient 3-D FDTD-PE Hybrid Model for Radio Wave Propagation With Near-Source Obstacles

A novel 3-D hybrid model is presented for the prediction of propagation of radio waves in the presence of complex obstacles located on regular perfectly conducting terrain. The finite-difference time-domain (FDTD) method is implemented to model the source and obstacle regions, and the wave is then propagated by using the parabolic equation (PE) method-based algorithm. The source region contains all the complex obstacles and takes into consideration all the possible wave interactions in that region. The transition region between the FDTD domain and the PE domain is carefully treated in order to avoid numerical incompatibilities and to realize the time-/frequency-domain transition. The method is applied for different scenarios, starting with relatively simple obstacles like knife-edges for the verification and validation of the approach and then including more complex obstacles to the propagation medium. The results are compared to those obtained from full FDTD implementations of the same scenarios.

The implementation of unconditionally stable higher order PML based on the implicit CNAD-FDTD algorithm

ABSTRACTAn unconditionally stable implementation of the higher order complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank–Nicolson-approximate-decoupling (CNAD) algorithm and the bilinear transform (BT) method is proposed to terminate the finite-difference time-domain (FDTD) lattice. The proposed scheme not only takes advantage of the CNAD algorithm in terms of reducing computational time but also has the advantage of the conventional FDTD algorithm in terms of absorbing performance. Two numerical examples are provided to validate the proposed implementation in the homogenous free space and lossy FDTD domains. The results show that the proposed scheme can overcome the Courant–Friedrich–Levy condition compared with the conventional FDTD method and further enhance the absorbing performance compared with the first order PML implementation.

Lightning-Induced Voltages on a Distribution Line With Surge Arresters Using a Hybrid FDTD–SPICE Method

Installing lightning arresters is an effective way to protect distribution lines from lightning-induced voltages. Spacing effectiveness of lightning arresters is one of the main concerns in the industry. Different separation distances of arresters have been proposed in the literature. In these studies, the simulations are made with simplified circuit models, which are not sufficient to support their conclusions. This paper presents a hybrid finite-difference time-domain (FDTD) SPICE method for analyzing lightning-induced overvoltages on a distribution line with arresters being installed. The FDTD method gives a full-wave solution of the induced voltages. To handle nonlinear lightning arresters, this FDTD method is integrated with a circuit solver SPICE. A diode-based model for the arrester is proposed using a SPICE subcircuit and is coupled to the FDTD domain as a connecting port. For the verification purpose, the method is compared with the results obtained in the rocket-triggered lightning experiment, in which no arresters were installed. Lightning-induced overvoltages on the distribution line with different arrester spacing arrangements are analyzed finally. Efficient arrester spacing under both first and subsequent strokes is investigated.

New version of FDTD with GFM program in Schwarzschild space–time

Finite difference time domain (FDTD) method in curved space–time is developed by filling the flat space–time with an equivalent medium. Green function Method (GFM) in curved space–time is solving transport equations. This is a new version of FDTD and GFM program in Schwarzschild space–time. The code for connection boundary and output boundary are included into the new version, so that electromagnetic scattering problem (not by black holes) in Schwarzschild space–time can be solved by this new version. New version program summaryProgram Title: FDTD with GFM in Schwarzschild space–timeProgram Files doi:http://dx.doi.org/10.17632/8fxbp578ys.2Licensing provisions: GPLv3Programming language: MATLABJournal reference of previous version: Comput. Phys. Comm. 225 (2018) 166–173Does the new version supersede the previous version?: YesReasons for the new version: Electromagnetic scattering problems cannot be solved by the old version. The code for connection boundary and output boundary are included into the new version, so that scattering problems (not by black holes) can be solved by the new version.Summary of revisions: The code for connection boundary and output boundary are included into the new version.Nature of problem: Simulating electromagnetic propagation and scattering in Schwarzschild space–time.Solution method: The electric field and the magnetic field are [1] (1)E=c(A0;1−A1;0,A0;2−A2;0,A0;3−A3;0)−−gϵ0(Ã3;2−Ã2;3,Ã1;3−Ã3;1,Ã2;1−Ã1;2)(2)Z0H=c−g(A3;2−A2;3,A1;3−A3;1,A2;1−A1;2)+1ϵ0(Ã0;1−Ã1;0,Ã0;2−Ã2;0,Ã0;3−Ã3;0)where c is the vacuum light speed, ϵ0 is vacuum permittivity, Z0 is the vacuum wave impedance, g is the determinant of metric matrix. Aα and Ãα are electric and magnetic potential respectively. The potentials can be expressed in integral form: (3)Aα(x)=μ04π∫Gαβ′(x,x′)Jβ′(x′)−g(x′)d4x′(4)Ãα(x)=ϵ04π∫Gαβ′(x,x′)J̃β′(x′)−g(x′)d4x′where μ0 is vacuum permeability, Gαβ′ is Green function, Jα and J̃α are electric and magnetic current respectively. Equation (57) in [2] has shown the expression of Aα;γ used in Eq. (1) and (2). By comparing Eq. (3) and (4) it can be seen that the expression of Ãα;γ can be obtained by replacing μ0 with ϵ0, J with J̃.The connection boundary and output boundary should be included when solving scattering problems by FDTD method [3]. The zone within the connection boundary is the total field zone, and the zone outside the connection boundary is the scatter field zone (Fig. 1). The incident wave is incorporated into FDTD simulation through connection boundary [3]. Usually the observer is very far away from the scatterer. It is impossible to simulate the whole field distribution between scatterer and observer by FDTD method. To obtain far field outside the FDTD domain, the electromagnetic current on output boundary should be integrated using Green function method which has been introduced in [2].Electric dipole is adopted as the excitation source. To reduce leakage, the distance between the positive charge and the negative charge is set to the mesh size of FDTD. At the positions of the two charges, the differential elements of electric current are (5)Jα−gd3x=(±cq,0,0,0)where q is the charge. At the midpoint of the two charges, the differential element of electric current is (6)Jα−gd3x=(0,dqdtl)where l is the vector directing from −q to q. The incident electromagnetic field on connection boundary can be calculated by Green function method which has been introduced in [2].The effective electromagnetic current ( Jα, J̃α) and their time derivatives (Jα,0, J̃α,0) on output boundary are calculated in the following way:The 3-D effective electric current J=(J1,J2,J3) and magnetic current J̃=(J̃1,J̃2,J̃3) on output boundary are: (7)J(k+1∕2)=n×H(k+1∕2)J̃(k)=−n×E(k)where n is the outer normal vector on output boundary, and k is time step. The time derivatives of 3-D current can be obtained by difference formulas (8)J,0(k)=J(k+1∕2)−J(k−1∕2)Δx0J̃,0(k−1∕2)=J̃(k)−J̃(k−1)Δx0where Δx0=cΔt is the size of time step. The time derivatives of J0 and J̃0 can be obtained by the law of charge conservation: (9)J0,0(k+1∕2)=−∇⋅J(k+1∕2)J̃0,0(k)=−∇⋅J̃(k)where the divergence of J and J̃ can be written as the difference of H and E respectively. J0 and J̃0 can be obtained by difference formulas: (10)J0(k+1)=J0(k)+Δx0J0,0(k+1∕2)J̃0(k+1∕2)=J̃0(k−1∕2)+Δx0J̃0,0(k)[1]J. L. Synge, Relativity: The General Theory, North-Holland, 1960.[2]Shouqing Jia, Dongsheng La and Xuelian Ma, Comput. Phys. Comm. 225 (2018) 166–173.[3]Atef Z. Elsherbeni and Veysel. Demir, The Finite-Difference Time-Domain Method For Electromagnetics with MATLAB Simulations, 2nd Ed, SciTech Publishing, 2015.

A Stable FDTD Method With Embedded Reduced-Order Models

The computational efficiency of the Finite-Difference Time-Domain (FDTD) method can be significantly reduced by the presence of complex objects with fine features. Small geometrical details impose a fine mesh and a reduced time step, significantly increasing computational cost. Model order reduction has been proposed as a systematic way to generate compact models for complex objects, that one can then instantiate into a main FDTD mesh. However, the stability of FDTD with embedded reduced models remains an open problem. We propose a systematic method to generate reduced models for FDTD domains, and embed them into a main FDTD mesh with guaranteed stability up to the Courant-Friedrichs-Lewy (CFL) limit of the fine mesh. With a simple perturbation technique, the CFL of the whole scheme can be further extended beyond the fine grid's CFL limit. Reduced models can be created for arbitrary domains containing inhomogeneous and lossy materials. Numerical tests confirm the stability of the proposed method, and its potential to accelerate multiscale FDTD simulations.

An optimized hybrid Convolutional Perfectly Matched Layer for efficient absorption of electromagnetic waves

A hybrid technique is studied in order to improve the performance of Convolutional Perfectly Matched Layer (CPML) in the Finite Difference Time Domain (FDTD) medium. This technique combines the first order of Higdon's annihilation equation as Absorbing Boundary Condition (ABC) with CPML to vanish the Perfect Electric Conductor (PEC) effects at the end of the CPML region. An optimization algorithm is required to find optimum parameters of the proposed absorber. In this investigation, the Particle Swarm Optimization (PSO) is utilized with two separate objective functions in order to minimize the average and peak value of relative error. Using a standard test, the overall performance of the proposed absorber is compared to the original CPML. The results clearly illustrate this method provides approximately 10 dB enhancements in CPML absorption error. The performance, memory and time requirement of the novel absorber, hybrid CPML (H-CPML), was analyzed during 2D and 3D tests and compared to most reported PMLs. The H-CPML requirement of computer resources is similar to CPML and can simply be implemented to truncate FDTD domains. Furthermore, an optimized set of parameters are provided to generalize the hybrid method.

Second-order PML: Optimal choice of [formula omitted]-order PML for truncating FDTD domains

The nth-order PMLs based on the unsplit-field formulations and the Z-transform methods are proposed to truncate the finite-difference time-domain (FDTD) domains, which will be validated through numerical simulations whether the higher-order PML with more than two poles, such as n=3, will hold better absorption performance as compared with the conventional, complex frequency shifted (CFS), second-order perfectly matched layer (PMLs). The advantages and disadvantages of different PMLs are demonstrated. It has shown that the higher-order PMLs have the advantages of both the conventional and the CFS PMLs in terms of absorption performance, since the conventional PML is ineffective at absorbing the evanescent waves and the CFS-PML is incapable of absorbing low-frequency propagating waves. It is clearly shown that the second-order PML is overall the optimal choice for truncating arbitrary FDTD domains, since it not only requires less computational time and memory, but holds almost the same absorption performance as compared with the third-order PML. Three numerical simulations have been carried out in three-dimensional (3D) problems to confirm the analysis.

Effective CNAD- and ADE-Based CFS-PML Formulations for Truncating the Dispersive FDTD Domains

An effective and unsplit-field implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank-Nicolson-approximate-decoupling (CNAD) and the auxiliary differential equation (ADE) method is proposed to truncate the dispersive finite-difference time-domain (FDTD) domains. The proposed formulations take full advantage of the capacity of the CFS-PML for attenuating evanescent waves and reducing late-time reflections. Furthermore, the proposed formulations have an advantage of the unconditional stability of the original CN-FDTD method. Two numerical tests have been carried out to validate the proposed formulations in the two-dimensional FDTD domains composed of the linear Debye and the Lorentz dispersive media, respectively. It is shown in the numerical tests that the proposed formulations can not only increase the time step size over the Courant–Friedrichs–Lewy (CFL) limit as compared with the conventional FDTD, but also hold good absorbing performance.

Efficient implementation of multi-pole UPML using trapezoidal approximation for general media

Based on the uniaxial anisotropic perfectly matched layer (UPML) with multi-poles, unsplit-field implementation of the higher-order PML using the trapezoidal approximation (TA) method is proposed to terminate the finite-difference time-domain (FDTD) computational domains. From the point of view of the Courant–Friedrichs–Levy (CFL) condition, to the best of our knowledge, time step based on the TA only needs to meet CFL condition, whereas time step based on the matched Z-transform (MZT) method has to make it smaller for retaining stability and desirable accuracy. Moreover, these formulations are completely independent of the material properties of the FDTD domains and hence can be applied to truncate arbitrary media without any modification because of the D–B constitutive relations used in Maxwell's equations. Four numerical examples have been carried out in three dimensional (3D) FDTD computational domains to validate these formulations. It is shown that the proposed UPML formulations with two poles are effective in terms of attenuating both the low-frequency propagating waves and evanescent waves and reducing late-time reflections, and also can produce results as accurate as the published MZT-UPML but with fewer number of steps and less CPU time.

Optimized Programs for Shaped Conductive Backfill Material of Grounding Systems Based on the FDTD Simulations

A new transient grounding resistance calculation model is proposed for the finite-difference time-domain (FDTD) method. In FDTD, the perfectly matched layer is backed by the perfect electric conductor (PEC) wall. By stretching the grounding system lifting line to the PEC wall, the grounding system performance is simulated. With this model, a 2-D cylindrical coordinate domain FDTD simulation was carried out to study cylindrically shaped conductive backfill material (SCBM) performance with fine grids. From experimental results, some optimal programs have been derived for SCBM in grounding systems. It is found that a large metal rod size can reduce the SCBM resistance only when the main body conductivity is low, and the reduction effect declines as the conductivity increases. Second, the SCBM resistance is as low as the resistance of a conductor of the same size when the main body conductivity reaches 0.5 S/m. Third, enlarging the SCBM radius can reduce the grounding resistance, and resistance can also be reduced by enlarging the SCBM length when it is less than its effective length. Fourth, the grounding resistance of an SCBM, whose conductivity is linear or parabolic type varied, can be as low as that of a totally high conductivity SCBM.

<i>Z</i>-Transform Implementation of the CFS-PML for Truncating 3D Meta-Material FDTD Domains

Efficient Z-transform implementa-tion of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the stretched coordinate PML (SC-PML) formulations and the D-B formulations is proposed for truncating meta-material finite-difference time-domain (FDTD) lattices. In the proposed PML formulations, the Z-transform method is incorporated into the CFS-PML FDTD implementation. The main advantage of the proposed formulations can allow direct FDTD implementation of the Maxwell’s equations in the PML regions. A numerical test has been carried out in a three dimensions (3-D) FDTD domain to validate the proposed formulations. It is shown that the proposed formulations with CFS scheme are efficient in holding good absorbing performances.

A locally conformal FDTD analysis of a thin printed antenna for wideband wireless applications

A compact wideband planar-printed antenna for wireless communications is presented. A suitable shape of the antenna arms and a proper tapering of the feeding line are employed to achieve an impedance bandwidth of more than 10 GHz useful to meet the requirements of several wireless communication standards. An enhanced locally conformal finite-difference time-domain (FDTD) numerical procedure, based on a suitable normalization of the electromagnetic field-related quantities together with a near-to-far-field transformation, is developed to perform the full-wave analysis of the radiating structure. The proposed numerical procedure allows the accurate evaluation of the electromagnetic field distribution from the FDTD domain up to the far-field region, achieving a reduced computational burden compared with conventional FDTD formulations. Using the proposed technique, the electromagnetic and circuital behaviour of the antenna is then derived and analyzed in detail. Numerical results concerning the antenna parameters are in good agreement with experimental measurements. Copyright © 2010 John Wiley & Sons, Ltd.

FDTD-PLRC Technique for Modeling of Anisotropic-Dispersive Media and Metamaterial Devices

The goal of this paper is to develop a versatile computational engine based on the finite-difference time-domain (FDTD) technique to comprehensively demonstrate the broadband behaviors of devices designed utilizing anisotropic-dispersive metamaterials. In this regard, the frequency-dependent behavior of dispersive materials is incorporated into the FDTD equations with the use of a piecewise linear recursive convolution (PLRC) approach. The FDTD domain is effectively terminated utilizing convolutional perfectly matched layered (CPML) absorbing walls, which are derived from the complex frequency-shifted (CFS) formulation. The CPML has the advantage that it operates only on the filed intensities and has nothing to do with the and constitutive relationships. The CPML is also highly absorptive to both propagating and evanescent waves. Therefore, it would be of great interest for terminating metamaterials having complex constitutive parameters. The developed method is also capable of characterizing periodic configurations illuminated by normal incident plane waves. The FDTD engine is successfully validated through the analyses of several complex metamaterials. The design and characterization of novel devices such as a patch antenna printed on metasubstrate with anisotropic epsiv (omega) - mu (omega)parameters, an electrically small antenna embedded in negative permittivity resonator, and an anisotropic-dispersive self-biased hexagonal ferrite-coupled line (FCL) circulator are highlighted.

Complex Envelope Crank-Nicolson Nearly PML Algorithm for the Left-handed Material FDTD Simulations

Unconditionally stable complex envelope (CE) absorbing boundary conditions (ABCs) are presented for truncating left handed material (LHM) domains. The proposed algorithm is based on incorporating the Crank Nicolson (CN) scheme into the CE finite difference time domain (FDTD) implementations of the nearly perfectly matched layer (NPML) formulations. The validity of the formulations is shown through numerical example carried out in one dimensional Lorentzian type LHM FDTD domain.

Unconditionally stable Crank-Nicolson nearly PML algorithm for truncating linear Lorentz dispersive FDTD domains

In this paper, unconditionally stable formulations of the nearly perfectly matched layer are presented for truncating linear dispersive finite-difference time-domain (FDTD) grids. In the proposed formulations, the Crank-Nicolson and bilinear frequency-approximation techniques are used to obtain the update equations for the field components in linear dispersive media. A numerical example carried out in a one-dimensional Lorentz dispersive FDTD domain is included and it has been observed that the proposed formulations not only give accurate results, but also completely remove the stability limit of the conventional FDTD algorithm

On the accuracy of the nearly PMLfor nonlinear FDTD domains

In this letter, the first implementation of the nearly perfectly matched layer (NPML) for truncating nonlinear dispersive finite-difference time-domain (FDTD) grids is presented. In the proposed method, the Z-transform theory is employed in the FDTD implementations of the NPML formulations. The performance of the NPML was investigated through a numerical example carried out in two-dimensional Kerr-Raman nonlinear and Lorentz-dispersive domain, and it has been observed that the NPML is capable of absorbing nonlinear electromagnetic waves.

ZT‐ADIPML: Unconditionally stable PML algorithm for FDTD simulations

AbstractUnconditionally stable formulations of the perfectly matched layer (PML) are presented for truncating linear dispersive finite‐difference time‐domain (FDTD) grids. In the proposed formulations, the 𝒵‐transform theory is employed in the alternating‐direction implicit FDTD (ADI‐FDTD) algorithm to obtain update equations for the field components in dispersive media. The validity of the proposed formulations is shown through a numerical example carried out in 1D linear Lorentz dispersive FDTD domain. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 393–396, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21360

Generalized 3-D DSP-based FDTD algorithm for modelling the APML

A generalized method for implementing the diagonal anisotropic perfectly matched layer (APML) in the finite difference time domain (FDTD) algorithm is presented for truncating three-dimensional (3-D) open region domains. The method is based on incorporating the digital signal processing algorithms developed for digital filters into the APML formulations. In this method, the permittivity and the permeability tensors of the APML are modelled as a set of infinite impulse response digital filters by using the Bilinear transformation technique. The proposed method has the advantage of the simplicity as it allows direct FDTD implementation of Maxwell’s equations in the APML region and also can be used for modelling general FDTD domains such as lossy, dispersive, anisotropic, or nonlinear without any modifications. The new formulations are validated by analyzing 3-D radiation and guided-wave problems.