Novel Strategies for Efficient Computational Electromagnetic (CEM) Simulation of Microstrip Circuits, Antennas, Arrays and Metamaterials

As mentioned in Part-I [1], rapid prototyping plays a critical role in the design of antennas and related planar circuits for wireless communications, especially as we embrace the 5G/6G protocols going forward into the future. Existing commercial software modules are often inadequate for this task in the millimeter-wave range since the memory requirements and runtimes are often too high for them to be acceptable as design tools. Using approximate equivalent circuit models for various components comprising the antenna and the feed system is not the answer either, because these models are not sufficiently accurate. Consequently, it becomes necessary to resort to the use of more sophisticated simulation techniques based on full-wave solvers that are numerically rigorous, albeit computer-intensive. Furthermore, optimizing the dimensions of antennas and circuits to enhance the performance of the system is frequently desired, and this often exacerbates the problem since the simulation must be run a large number of times to achieve the performance goal, namely an optimized design. Consequently, as pointed out earlier, it is highly desirable to develop accurate yet efficient techniques, both in terms of memory requirements and runtimes, to expedite the design process as much aspossible. In the first part of this paper [1], we presented three strategies to address these issues, mostly related to Green’s Functions of layered media. We have shown that the proposed techniques are not only useful for antennas and printed circuits on layered media but also for antennas embellished with metamaterials for the purpose of their performance enhancement. In this sequel to Part-I, we present several other Efficient Computational Electromagnetic (CEM) simulation strategies for expediting the runtime and improving the capability of handling large problems that are highly memory-intensive. These include a domain decomposition technique, which utilizes the Characteristic Basis Function Method (CBFM); the T-matrix approach which is also useful for hybridizing Finite Methods (FEM or FDTD) with the Method of Moments (MoM); Mesh truncation in Finite Method by using a conformal Perfectly Matched Layer (PML); and Graphics Processing Unit (GPU) acceleration of MoM and FDTD codes.

An important advance in the finite difference time domain (FDTD) algorithms is Berenger's perfect matched layer (PML), along with its derivatives. In recent years several new explicit and implicit FDTD algorithms have appeared on the scene, of which each requires a specific PML. To simplify programming, the authors derive a universal uniaxial PML formulation, which is universally applicable to the Yee FDTD, FDTD with higher-order stencils and implicit FDTD algorithms. Numerical results show the efficiency and versatility of the new method.

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. It was first proven by Chew and Liu that a fictitious elastic PML half-space also exists in solids, which completely absorbs elastic waves, in spite of the coupling between compressional and shear waves. The PML absorbing boundary condition provides much higher absorption than other previous ABCs in finite-difference methods. In this work, a method is presented to extend the perfectly matched layer to simulating acoustic wave propagation in absorptive media. This nonphysical material is used at the computational edge of a finite-difference time-domain (FDTD) algorithm as an ABC to truncate unbounded media. Two aspects of the acoustic PML are distinct: (a) For a perfectly matched layer in an intrinsically absorptive medium, an additional term involving the time-integrated pressure field has to be introduced to account for the coupling between the loss from the PML and the normal absorptive loss; (b) In contrast to the full elastodynamic problem, the acoustic PML requires a splitting only on the pressure field, but not on the particle velocity field. The FDTD algorithm is validated by analytical solutions and other numerical results for two- and three-dimensional problems. Unlike the previous ABCs, the PML ABC effectively absorbs outgoing waves at the computational edge even when a dipping interface intersects the outer boundary.

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.

A two-dimensional finite difference time domain (FDTD) algorithm is implemented to simulate wave propagation and scattering in a heterogeneous fluid-elastic environment. The FDTD algorithm is fourth-order accurate in space and second-order accurate in time. The perfectly matched layer (PML) absorbing boundary condition is adapted to eliminate artificial reflections caused by the boundaries of the finite computational domain. Computational accuracy is verified by considering radiation from a periodic array of pulsed line sources and from a fluid line source near a submerged elastic layer. The finite difference results are in excellent agreement with the numerically evaluated spectral integrals which can be derived for these problems. The finite difference algorithm is then applied to scattering from a rough fluid-solid interface, and to scattering from an elastic cylinder above or buried beneath a rough fluid-solid interface. Scattered signals are processed with the Gaussian windowed transform, which provides an initial image representation for signature identification and classification algorithms.

The application of finite-volume, time-domain techniques to EM scattering from cavities and inlets

This paper presents a design of a multiband microstrip circular patch antenna. The antenna of a single patch is designed for the operation at 2.45 GHz and 5.2 GHz ISM (industrial, scientific, and medical) band. This band is occupied by the bluetooth and high performance radio local area network (HIPERLAN) applications. In addition, with the aid of a circular array, the previous antenna can be designed to operate in a place of x band (8.4 GHZ) used by the spacecraft-to-ground communication link. The return loss, input impedance, and the radiation pattern are calculated. Under the condition of the return loss is less than 10dB, the bandwidth at 2.45, 5.2 and 8.4 GHz are 24 %, 7.7%, and 6.7%, respectively. The analysis and design of the antenna is carried out using of the finite difference time domain (FDTD) with the perfect matched layer (PML) in addition to a numerical package based on the method of moment (MOM). The obtained results are compared with the available published data and the results of the cavity resonance technique. Good agreements are found.

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.

Nowadays, complex electromagnetic scenarios carried out by numerical techniques can be solved easily by state-of-the-art technology computers. Thus, many numerical techniques have been emerged in order to solve the different problems. In this way, scientists can define and predict the various circumstances for any problem. In this study, a microstrip patch antenna has been analyzed by using finite difference time domain (FDTD) method which is the one of the most utilized technique in computational electromagnetics. Antenna has been fed through the Gaussian pulse from the microstrip line. Microstrip patch antenna has been designed as three layered structure which are ground, substrate and patch. Although the ground and patch layers have been selected as perfectly electric conductor (PEC), substrate layer has been selected as a dielectric material whose dielectric constant has been 4.4. Also, designed antenna has been surrounded by perfectly matched layer (PML). FDTD based investigations have been performed for 200, 400, 600 and 800 time steps, respectively. Results have showed that the electric field has radiated from the points of discontinuity of the investigated antenna and electric field radiation pattern of the antenna has been varied for each time step. As a part of this study, the antenna has been simulated through the commercial electromagnetic simulation software. In this way, both electric field radiation and reflection coefficient results have been obtained. Dimensions and electrical properties of antenna investigated through the FDTD method have also been defined for simulation studies. Simulation results have showed that the resonance frequency of the antenna has been observed at 5.077 GHz and 9.28 GHz.

In this study, we introduced multitransient electromagnetic (MTEM) method as an effective tool for shale gas exploration. We combined the uniaxial perfectly matched layer (UPML) equation with the first derivative diffusion equation to solve for a finite difference time domain (FDTD) UPML equation, which was discretized to form an algorithm for 3D modeling of earth impulse response and used in modeling MTEM response over 2D South China shale gas model. We started with stepwise demonstration of the UPML and the FDTD algorithm as an effective tool. Subsequently, quantitative study on the convergence of MTEM earth impulse response was performed using different grid setup over a uniform earth material. This illustrates that accurate results can be obtained for specified range of offset. Furthermore, synthetic responses were generated for a set of geological scenarios. Lastly, the FDTD algorithm was used to model the MTEM response over a 2D shale gas earth model from South China using a PRBS source. The obtained apparent resistivity section from the MTEM response showed a similar geological setup with the modeled 2D South China shale gas section. This study confirmed the competence of MTEM method as an effective tool for unconventional shale gas prospecting and exploitation.

In this paper an unsplit anisotropic perfectly matched layer (PML) medium, previously utilized in the context of finite element analysis, is implemented in the finite difference time domain (FDTD) algorithm. The FDTD anisotropic PML is easy to implement in the existing FDTD codes, and is well suited for truncating inhomogeneous and layered media without special treatment required in the conventional PML approach. A further advantage of the present approach is improved performance at lower frequencies. The applications of the unsplit anisotropic PML/FDTD method are illustrated by considering the problems of a plane wave propagation and an open microstrip line.

Ground penetrating radar (GPR) forward is one of the geophysical research directions.Through the forward of geological model,the database of radar model can be enriched and the characteristics of typical geological radar echo images can be understood,which in turn can guide the data interpretation of GPR measured profile,thereby improving the GPR data interpretation level.In this article,the interpolating wavelet scale function by using iterative interpolation method is presented,and the derivative of scale function is used in spatial differentiation of discrete Maxwell equations. The forward modeling formula of GPR based on the interpolation wavelet scale method is derived by using fourth-order Runge-Kutta method (RK4) for calculating the higher time derivative.Compared with the conventional finite difference time domain (FDTD) algorithm based on the central difference method,the interpolation wavelet scale algorithm improves the accuracy of GPR wave equation in both space and time discretization.Firstly,the FDTD algorithm and the interpolation wavelet scale method are applied to the forward modeling of a layered model with analytic solution. Single channel radar data and analytical solution fitting indicate that the interpolation wavelet scale method has higher accuracy than FDTD,with the same mesh generation used.Therefore,auxiliary differential equation perfectly matching layer (ADE-PML) boundary condition is used on an interpolation wavelet scale,and the comparisons between reflection errors obtained using CPML (FDTD),RK4ADE-PML (FDTD),and RK4ADE-PML (interpolating wavelet scales) in a homogeneous medium model show that the absorption effect of RK4ADE-PML (interpolating wavelet scales) is better than the other two absorbing boundaries.Finally,interpolation wavelet scale method,with both UPML,FDTD and RK4ADE-PML loaded,is used for two-dimensional GPR forward modeling,showing good absorption effect for evanescent wave.From all the experimental results,the following conclusions are obtained.1) Using the derivative of the interpolating wavelet scale function instead of central difference schemes for the spatial derivative discretization of Maxwell equations and time derivative calculated using the fourth-order Runge Kutta algorithm,the interpolating wavelet scale algorithm has higher accuracy than regular FDTD algorithm due to the improvement in the spatial and time accuracy of GPR wave equation.2) The best absorption layer parameters of interpolating wavelet scale RK4ADE-PML are selected, when the maximum value of the reflection error is the minimum.The maximum reflection error can reach-93 dB,which increases 20 dB compared with that of UMPL boundary in FDTD algorithm.And the higher simulation accuracy of interpolating wavelet scale algorithm than FDTD algorithm is confirmed after calculating single channel radar data.3) Comparing wave field snapshots of GPR forward modeling,radar pictures from wide-angle method and section method indicates that interpolating wavelet scale RK4ADE-PML reduces reflection error of absorption boundary,improves both spatial and time accuracy,is more effective than UPML boundary in eliminating false reflection of large angle incidence, and has better absorption effect for evanescent wave and low-frequency wave.

Finite-Difference Time-Domain (FDTD) is the most popular time-domain approach in computational electromagnetics. Due to the Courant-Friedrich-Levy (CFL) condition and the perfect match layer (PML) boundary precision, FDTD cannot simulate soil medium whose surface is connected by multiple straight lines or curves (multi-scale) accurately and efficiently, which greatly limits the application of FDTD method to simulate buried objects in soils. Firstly, this study proposed the absorption boundary and adopted two typical perfect matching layers (UPML and CPML) to compare their absorption effects, and then using the three forms of improved Yee-FDTD algorithm, alternating-direction implicit (ADI-FDTD), unconditionally stable (US-FDTD) and hybrid implicit explicit finite time-domain (HIE-FDTD) to divide and contrast the boundary model effects. It showed that the HIE-FDTD was suitable for inversion of multi-scale structure object modeling, while ADI-FDTD and US-FDTD were ideal for single-boundary objects in both uniaxial perfectly matched layer (UMPL) and convolution perfectly matched layer (CPML) finite element space. After that, all the models were tested by computer performance for their simulated efficiency. When simulating single boundary objects, UPML-US-FDTD and ADI-FDTD could achieve the ideal results, and in the boundary inversion of multi-scale objects, HIE-FDTD modeling results and efficiency were the best. Test modeling speeds of CPML-HIE-FDTD were compared with three kinds of waveform sources, Ricker, Blackman-Harris and Gaussian. Finally, under the computer condition in which the CPU was i5-8250, the HIE-FDTD model still had better performance than the traditional Yee-FDTD forward modeling algorithm. For modeling multi-scale objects in farmland soils, the methods used CPML combined with the HIE-FDTD were the most efficient and accurate ways. This study can solve the problem that the traditional FDTD algorithm cannot construct non-mesh objects by utilizing the diversity characteristics of Yee cell elements. Keywords: Yee-FDTD, multi-scale objects, modeling effectiveness, Ground Penetrating Radar, farmland soils DOI: 10.25165/j.ijabe.20201306.5443 Citation: Li Y H, Zhao Z X, Qiu Z, Luo Y F, Zhu Y C. Modeling effectiveness and identification of multi-scale objects in farmland soils with improved Yee-FDTD methods. Int J Agric & Biol Eng, 2020; 13(6): 150–158.

In the wave propagation simulation by finite difference time domain (FDTD), the perfectly matched layer (PML) is often applied to eliminate the reflection artifacts due to the truncation of the finite computational domain. In the acoustic Logging-While-Drilling (LWD) FDTD simulation, due to high impedance contrast between the drill collar and fluid in the borehole, the stability and efficiency of PML scheme is critical to simulate complicated wave modes accurately. In this paper, we compare four different PML implementations in FDTD in the acoustic LWD simulation, including splitting PML (SPML), Multi-axis PML (MPML), Non-splitting PML (NPML), and complex frequencyshifted PML (CFS-PML). The simulation indicates that NPML and CFS-PML can more efficiently absorb the guide wave reflection from the computational boundaries than SPML and MPML. For large simulation time, SPML, MPML and NPML are numerically instable. However, stability of MPML can be improved further to some extent. Among all, CFS-PML is the best choice for LWD modeling. The effects of CFS-PML parameters on the absorbing efficiency are investigated, including damping profile, frequency-shifted factor, scaling factor and PML thickness. For a typical LWD case, the best value for maximum of quadratic damping profile d0 is about 1. The optimal parameter space for the maximum value of linear frequency-shifted factor α0 and scaling factor β0 depends on the PML damping profile and thickness. If the PML thickness is 10 grids, the reflection residual can be reduced to less than 1%, using optimal CFS-PML parameters, while only about 0.5‰ reflection artifacts are observed for 20 grids PML buffer.

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems