Generalized Alternating-Direction Implicit Finite-Difference Time-Domain Method in Curvilinear Coordinate System

Introduction: A number of techniques have been proposed to extend the classical Yee’s finite-difference time-domain (FDTD) algorithm to a grid that is conformal to curved objects. Such methods, including the nonorthogonal FDTD (NFDTD) [1, 2], can accurately represent the curved boundaries without resorting to inefficient staircase orthogonal meshes. However, their significant advantage is offset by the fact that they suffer from late time instabilities. In [3], it is demonstrated that the instability of NFDTD is inherent. Although a ‘time-subgriding’ approach is presented there to reduce the late time instability, an unconditionally stable NFDTD is still not obtained. In this Letter, we introduce a novel approach to discretise Maxwell’s equations using only the covariant components. It is demonstrated that the new NFDTD algorithm is stable over a very long period of numerical simulation. Moreover, the algorithm is less computationally intensive than other NFDTD methods [1, 2] where both of the covariant and contravariant components are needed. The proposed technique is validated by simulation results on a circular waveguide resonator.

This paper proposes a reconfigured horn antenna with reduced side-lobe radiation by using electromagnetic band gap (EBG) structure. A mushroom-like structure with a circular-shaped patch as unit cell is designed to achieve a complete EBG. The EBG structure is lined on the metal wall along the E-plane of the horn antenna. This causes the surface waves on the metal wall to be suppressed, resulting in lower side-lobe emission. A conducting wedge is inserted on the gap between the EBG structure and waveguide feed aperture to achieve impedance matching in the antenna. In addition, the proposed horn antenna is suitable for high power systems due to a purely metallic construction of the EBG structure.

In this paper, we present an equivalent circuit (EC) based technique which combined with the numerical method to optimize the EBG structures with simple square-loop frequency selective surfaces (FSSs), they can take on in-phase reflection characteristic in some broad-band electromagnetic band gap (EBG) structures. By using the multilayered FSSs in this type of EBG structure, the surface waves and current could stopped effectively. The geometry and working of the antenna with this EBG structure are detailed and the design method is proposed.

This paper presents a circularly polarized printed circuit board (PCB) patch antenna using mushroom-like electromagnetic band gap (EBG) structure for gain enhancement. Unlike the popular method of using artificial magnetic conductor (AMC) or EBG structure as the ground of the antenna, we place the mushroom-like EBG structure around the patch antenna to avoid increasing the number of PCB layers. The EBG structure works in-phase reflection around 24.25 GHz by optimizing design. Limited by the size of the antenna, only twelve EBG units can be distributed around the corner-cut square circularly polarized patch antenna. Simulation results show that gain of the antenna enhances 0.8 dB and cross polarized gain reduces about 15 dB, moreover, the axial ratio is also improved.

Electromagnetic Bandgap (EBG) structures are increasingly utilized by a variety of microwave and optical devices as filters for unwanted signals. One such application is their incorporation in power distribution network (PDN) of electronic circuits where the EBG structure replaces one of the reference voltage planes thus forming a shielded EBG structure. The EBG induces a wide (on the order of few GHz) omni-directional stopband in the operating frequency range of the PDN which mitigates the so called simultaneous switching noise (SSN) on the power plane. The challenging aspect in designing an EBG for such applications is to achieve a wide stopband centered at low GHz frequencies while maintaining a reasonably small unit cell size and a low profile. Indeed, the dimensions of the unit cell of the EBG structure for low frequency designs can become relatively large with respect to the size of the host dielectric substrate. Therefore, availability of a systematic design approach that can provide a fast and accurate means of performance prediction to enable geometry tweaking and design optimization will be of critical importance in utilizing EBG structures in such applications.

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is a promising unconditionally stable scheme that may improve the computational efficiency. However, no general dispersive media were considered in the ADI-FDTD community. The dispersive property, in fact, is important for semiconductor device design at radio-frequency. In this paper, the ADI-FDTD method is applied to complex structures such as on-chip spiral inductor with honeycomb oxide trench, buried layer removal, and radial patterned ground shield. The proposed formula is applicable to linearly dispersive and lossy media. Using this approach, the overall accuracy has been obtained with little computational overhead

The current source implementation for the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is examined in this letter. By regarding the ADI-FDTD method as an approximate factorization of the Crank-Nicolson scheme, current source is naturally coupled into simulations. As a result, field distribution is much more improved and free of asymmetry.

A rigorous yet computationally efficient three-dimensional numerical method has been proposed based on modified alternating-direction-implicit (ADI) finite difference time domain methods (FDTD) and it has the capability of modeling the eccentric property of magnetic material being anisotropic, dispersive or nonlinear. The proposed algorithm solves Maxwell's equations and LLG equations simultaneously, requiring only tridiagonal matrix inversion as in ADI FDTD. The accuracy of the modeling has been validated by the simulated dispersive permeability of a continuous ferrite film with a 1.5 μm-thickness, using a time-step size 104 times larger than the Courant limit. The permeability agrees with the theoretical prediction and magneto-static spin wave modes are observed. Moreover, electric current sheet radiators close to perfect electrical conductors loaded with 2 μm-thick ferrite films are simulated, which exhibit a radiation efficiency 20dB higher than conventional dipole antennas on the same scale.

Band notched circular monopole antennas for ultra-wide band applications are proposed in this paper. The proposed antennas in this paper can reject worldwide interoperability for microwave access WiMAX band (3.3–3.8 GHz) and wireless local area network WLAN band (5–6 GHz). Antennas utilises mushroom-type electromagnetic band gap (EBG) structures and I-slot embedded edge located via (ELV) EBG structures to achieve band-notched designs. The advantages of band notched designs using EBG structures like notch-frequency tuning, dual-notch antenna designs and stable radiation pattern are also verified. Various antenna designs with slot in EBG structures, variations in placement of EBG structures, number of EBG structures and ELV type EBG structures are simulated. About 30% reduction in size of EBG structures is obtained if conventional mushroom type EBG is replaced by proposed I-slot embedded ELV-EBG structure. Fabricated and measured results are in good agreement with simulated ones.

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.

This paper presents a design of a dielectric resonator antenna (DRA) for millimeter-wave applications. An electromagnetic band gap (EBG) structure is used in the antenna design to enhance the antenna characteristics. The simulated with and without EBG results of the designed antenna is calculated to show the parameters such as impedance bandwidth, reflection coefficient, and gain. The parameters of the proposed antenna have improved after the periodic unit cell structure (EBG) introduction. The obtained reflection coefficients of the proposed antenna with and without EBG structure are −30.5 dB and −20.8 dB, respectively. In the presence of an EBG structure antenna shows a peak gain of 25 dBi, which is higher than the without EBG (8 dBi) structure. The designed antenna resonates at 33 GHz with an impedance bandwidth of 700 MHz. The Ansys HFSS software is used to design and simulate the proposed antenna.

In this paper a novel microstrip antenna is proposed using electromagnetic band gap (EBG) structure for mobile and wireless applications. It covers two mobile bands ranging from (2.20–2.29) GHz and (2.29–2.30) GHz. An extremely compact size EBG structure is applied in a square shape. After applying EBG structure to the proposed design, performance characteristics such as percentage bandwidth and return loss enhance by 5.1% and 5% respectively. Also by changing the feed and shorting pole (via) position, the same structure is used for ISM (2.45 ± 0.05) GHz band with resonant frequency 2.45 GHz. The measured and simulated results show very good agreement. The design structure is fabricated using FR4 substrate with dielectric constant 4.4, loss tangent 0.02 and thickness 1.6 mm.

Electromagnetic Bandgap (EBG) structures have been successfully applied for suppressing the Simultaneous Switching Noise (SSN) between the power and ground planes. Aimed at the relative narrow bandwidth and the poor performance in low frequency of the conventional Uniplanar-Compact EBG (UC-EBG) structure, a novel EBG structure formed by adding spiral-shaped metal strips on the conventional UC-EBG is proposed. This new EBG structure significantly enhance the equivalent inductance between the neighboring nuit cells, as well as change the character of the stop-band. Simulation results show that the new EBG structure can achieve a bandwidth reach 4.35GHz.This stop-band is 47.5% wider than the conventional UC-EBG structure, and 17.5% wider than the reference EBG structure in literature. The excellent SSN suppression is achieved between 0.18-4.53GHz in the depth of -40dB.

Patch antenna arrays are used extensively due to their low profile structure, light weight and low cost. Patch antenna arrays have been widely used for a variety of wireless applications. However, a major drawback of this type of antenna arrays is mutual coupling and bandwidth. Mutual Coupling losses can be reduced effectively by placing Electromagnetic band gap (EBG) structures, also called photonic band gap (PBG) structures. In this paper, different types of Electromagnetic Band Gap (EBG) structures are proposed to be placed in between the patch antenna arrays to reduce the mutual coupling loss. These EBG structures are designed as small as possible because of system compactness. Hence the design of novel compact hybrid EBG structures are more challenging for wireless applications. In this paper various hybrid EBG structures showed with and without vias are compared with the defined antenna parameters.KeywordsEBG structurespatch antenna arraysmutual coupling lossstructure realizationband passstop bandcompact sizebandwidthvias

Graphene, which is considered to be an infinitely thin two-dimension material, is a very promising optoelectronic material and has received much attention due to its outstanding electrical and optical properties. This paper describes an efficient message-passing interface (MPI) parallel implementation of the finite difference time domain (FDTD) algorithm for modeling infinite Graphene sheet simulations. The algorithm, which is based on the domain decomposition approach, reduces the number of field components to be exchanged between the neighboring processors as compared with the conventional parallel MPI FDTD implementation. Numerical simulations are included to show the effectiveness of the proposed parallel algorithm.