Finite-difference Time-domain Computational Domain Research Articles

Efficient FDTD Simulation for the EM Analysis of Faraday Rotation in the Ionosphere

In this work, we propose an efficient finite-difference time-domain (FDTD) simulation technique for the electromagnetic (EM) wave analysis of the Faraday rotation angle in the ionosphere. For this purpose, we first model the physical ionosphere as a scaled-down FDTD computational domain by a space-compression factor. Next, the Faraday rotation angle calculated from the FDTD simulation is calibrated by multiplying the space-compression factor. Numerical examples demonstrate that this novel space-compression-and-calibration technique can lead to a computationally efficient FDTD simulation for the EM analysis of the Faraday rotation angle without accuracy degradation.

Numerical Investigation of Light Extraction Efficiency of GaN-based Vertical Blue Micron-Scale Light-Emitting Diode Structures.

The light extraction efficiency (LEE) of GaN-based vertical blue micron-scale light-emitting diode (μ-LED) structures was investigated numerically using three-dimensional finite-difference timedomain (FDTD) methods. The entire μ-LED chip was included in the FDTD computational domain to determine the LEE accurately. As the lateral dimensions of μ-LEDs increased from 5 to 30 μm, the LEE decreased gradually because of the increased portion of light trapped inside the LED chip and the increased light absorption in the GaN layers with increasing chip size. The LEE varied strongly with the p-GaN thickness for the μ-LED with a flattop surface, which could be explained by the strong dependence of the spatial distribution of the emission patterns on the p-GaN thickness. This dependence on the p-GaN thickness decreased when the surface of the μ-LED chip was patterned. A high LEE of >80% could be achieved in LEDs with properly chosen parameters. The FDTD simulation results presented in this study are expected to be employed advantageously in designing μ-LED structures with a high LEE.

A Corner-Free Truncation Strategy in Three-Dimensional FDTD Computation

The corner-free truncation (CFT) strategy is proposed to improve the efficiency of numerical simulation in computational electrodynamics. The spherical boundary, namely the CFT strategy, is built up in the Cartesian coordinate system, which has been implemented via making use of the impedance-matched layer. The proposed CFT strategy is used for terminating computational domain of the conventional finite-difference time-domain (FDTD) to absorb the outward electromagnetic waves. Moreover, based on the proposed boundary, the computation becomes simpler. The original FDTD computational domain is reduced to be nearly a half, and the computational resource is saved significantly, both of which are due to the fact that no curvilinear model is applied in truncating the boundary. The numerical simulations of target scattering problems have been achieved to validate the proposed algorithm.

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.

Efficient FDTD Implementations of the Higher-Order PML Using DSP Techniques for Arbitrary Media

Efficient and unsplit-field implementations of the higher-order PML based on the digital signal processing (DSP) techniques and the complex frequency shifted perfectly matched layer (CFS-PML) formulations are proposed to truncate the finite-difference time-domain (FDTD) computational domains. The CFS-PML implementation is introduced based on the stretched coordinate PML (SC-PML) and the uniaxial anisotropic PML (UPML), respectively. These formulations are completely independent of the material properties of the FDTD computational domain and hence can be applied to truncate arbitrary media without any modification. Moreover, the higher-order PML has the advantages of both the conventional PML and the CFS-PML in terms of absorbing performances. Three numerical simulations have been carried out in three dimensional (3-D) FDTD computational domains to validate these formulations. It is shown in the numerical simulations that the proposed PML formulations with the higher-order scheme are effective in terms of attenuating both the low-frequency propagating waves and evanescent waves and reducing late-time reflections, and also hold comparatively good absorbing performances as compared with the conventional SC-PML and the convolution PML (CPML) with the CFS scheme.

An absorbing boundary condition for general dispersive medium and general FDTD spatial scheme

Based on the stretched coordinate perfectly matched layer (SC-PML) formulation and the auxiliary differential equation method, an absorbing boundary condition for general dispersive medium is presented, and applied to both the standard finite difference time domain (FDTD) method and the high-order FDTD method. The proposed D-H formulations are completely independent of the material properties of the FDTD computational domain. Thus they can be directly applied to the simulations involving arbitrary dielectrics. Numerical results show that compared with the CPML, the proposed method is versatile, has an improved absorbing performance and low computational complexity, and can substantially reduce the computational time.

Simulation of corona at lightning-triggering wire: Current, charge transfer, and the field-reduction effect

[1] We have examined, using the finite difference time domain (FDTD) method for solving discretized Maxwell's equations, the effect of upward extending wire, used for artificial lightning initiation from natural thunderclouds, and corona space charge emanated from this wire on the close ground-level electric field (prior to lightning initiation). The wire current and charge transfer are also estimated. The lightning-triggering wire is assumed to be perfectly conducting and extending vertically upward with a constant speed of v = 150 m/s. Owing to the limitations of the FDTD method, the wire radius is set to r = 0.27 m, larger than the actual radius (0.1 mm), but the results are not expected to be much influenced by this assumption. The corona space charge that emanated from the wire surface is represented by a conducting cylindrical sheath of outer radius r = 2, 4, 8, and 16 m, coaxial with the wire (the dynamics of corona discharge are not considered here). Other geometries of the corona space charge sheath are considered as well. It has been found that the results presented here are insensitive to the value of corona sheath conductivity ranging from 10−8 S/m to infinity. The corona space charge layer at the ground is simulated by perfectly conducting cylindrical tubes placed on the ground surface, coaxial with the upward extending conductor. The quasi-static electric field between the thundercloud charge source and the ground is simulated by creating a quasi-uniform, upward directed electric field of 43 kV/m between two parallel conducting plates limiting the FDTD computational domain. The simulated corona space charge at the ground reduced the electric field at the ground surface to 5.5 kV/m, a typical value at the time of rocket launch. The upward directed electric field Ez on the ground surface in the vicinity of triggering wire decreases with increasing the altitude of the wire top. When the wire-top altitude is 200 m, the reduction of Ez at horizontal distance d = 60 m is about 17, 26, 31, 40, and 52% relative to the background value of 5.5 kV/m for r = 0.27, 2, 4, 8, and 16 m, respectively, while the corresponding reduction of Ez at d = 360 m in all cases is only 1% or less. The calculated results for r ≈ 4 to 16 m agree reasonably well with Ez variations measured at d = 60 and 350 m from the triggering wire by Biagi et al. (2011). This indicates that the electric field reduction in the vicinity of triggering wire, prior to lightning initiation, is primarily caused by the presence of corona space charge emanated from the wire to a radius of about 4 m or more, as opposed to the presence of wire alone. The total charge transfer from the ground to the wire (whose top is at an altitude of 200 m) is 1.2, 4.5, 6.6, 9.5, and 14 mC for r = 0.27, 2, 4, 8, and 16 m, respectively. The corresponding currents flowing in the wire are 2.1, 7.9, 11, 15, and 22 mA. The model-predicted charges and currents for r = 2 to 4 m are consistent with limited measurements available in the literature, smaller than the values based on the field-reduction calculations, but still of the order of meters. The radial electric field near the top of 200 m high cylindrical conductor can exceed 400 kV/m (which is sufficient for positive streamer propagation) when its radius is up to 8 m, confirming corona sheath radii of the order of meters inferred from the field-reduction and wire charge/current analyses.

Modified Z‐transform‐based FDTD algorithm for the anisotropic perfectly matched layer

AbstractA modified Z‐transform‐based algorithm for implementing the D‐H anisotropic perfectly matched layer (APML) is presented for truncating the finite‐difference time‐domain (FDTD) lattices. The main advantage is that, as compared with the previous Z‐transform‐based implementation for the D‐H APML, the proposed algorithm requires less auxiliary variables in the PML regions, and thus the memory requirement and the computational time are saved. These formulations are simple and independent of the material properties of the FDTD computational domain. Two numerical tests have been carried out to validate these formulations. Copyright © 2007 John Wiley & Sons, Ltd.

Efficient parallel PML algorithms for truncating finite difference time domain simulations

In this paper, the parallel implementation of the stretched coordinate perfectly matched layer (SC-PML) and the wave equation PML (WE-PML) formulations is presented for truncating three-dimensional (3-D) finite difference time domain (FDTD) grids. In the proposed parallel algorithms, the FDTD computational domain is divided into contiguous non-overlapping subdomains using two-dimensional topology and the interprocessor communications between the neighboring subdomains are carried out by using the message passing interface (MPI) system. The performance of the proposed parallel algorithms has been studied by using a point source radiating in 3-D domains and performed on a network of PCs interconnected with Ethernet. It has been observed that the WE-PML parallel algorithm is approximately 2.3 faster than the SC-PML parallel algorithm.

Three dimensional MPI parallel implementation of the PML algorithm for truncating finite-difference time-domain Grids

Three dimensional parallel implementation of the perfectly matched layer (PML) formulations are presented for truncating finite-difference time-domain (FDTD) Grids. The FDTD computational domain is divided into subdomains using one-dimensional topology and the interprocessor communication operations between the subdomains are carried out by using the message-passing interface (MPI) library. The validity of the proposed algorithm is shown through numerical simulations carried out for a point source radiating in three-dimensional domains of different sizes and performed on a network of PCs interconnected with Ethernet.

$Z$-Transform Implementation of the CFS-PML for Arbitrary Media

An efficient implementation of the complex frequency-shifted perfectly matched layer (CFS–PML) based on stretched coordinate PML (SC–PML) formulations and the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> -transform method is presented for truncating the finite-difference time domain (FDTD). This method is completely independent of the material properties of the FDTD computational domain and hence can be applied to the modeling of arbitrary media without any modification. A numerical test has been carried out in three dimensions to validate these formulations. It is shown that the proposed formulations with a CFS scheme are efficient in attenuating evanescent waves and reducing late-time reflections.

Z-Transform Implementations of the CFS-PML

Four implementations of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the uniaxial anisotropic PML (UPML) formulations and Z-transform methods are presented for truncating the finite-difference time-domain (FDTD) lattices. These formulations are independent of the material properties of the FDTD computational domain and hence can be applied to the modeling of general media. Particularly, a new algorithm to minimize memory requirement is introduced. Two numerical simulations of the dispersive media have been carried out in three dimensions to validate these formulations. It is shown that the proposed formulations with the CFS scheme are efficient in attenuating of evanescent waves and reducing late-time reflections.

Efficient implementation of stretched co-ordinate perfectly matched layer using DSP techniques

An efficient and unsplit-field algorithm for implementing the stretched co-ordinate perfectly matched layer (SC-PML) based on digital signal processing (DSP) techniques is presented for truncating the finite-difference time-domain (FDTD) lattices. The advantage of the proposed algorithm is that only one additional auxiliary variable is required in all corners and at all edges of the PML regions by means of a new memory-minimised algorithm for a high-order difference equation and thus memory requirement is saved significantly compared with that in published papers about the SC-PML. These formulations are independent of the material properties of the FDTD computational domain.

Z-transform implementation of the perfectly matched layer for truncating FDTD domains

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.

Digital filtering technique for the FDTD implementation of the anisotropic perfectly matched layer

A new algorithm is presented for the finite difference time domain (FDTD) implementation of the anisotropic perfectly matched layer (PML) using the digital signal processing. The algorithm is based on modeling the anisotropic PML region as a set of infinite-impulse response (IIR) digital filters. The advantage of the proposed method is that it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are implemented using D and B fields rather than E and H, and this allows the PML to be independent from the material properties of the FDTD computational domains. Numerical tests have been carried out in two dimensions to validate the formulations.

A full-wave analysis of interdigital capacitors for planar integrated circuits

A finite-difference time-domain (FDTD) model has been developed to determine the circuital and electromagnetic compatibility performances of a large class of interdigital capacitors (IDCs). The model, based on a new conformal FDTD scheme, employs the free-space dyadic Green's functions to analyze the field behavior near and far from the FDTD computational domain. Using the proposed model, various IDC structures have been analyzed and a frequency-independent equivalent circuit, which include surface and volume wave effects, has been introduced. A good agreement with numerical results already available in literature has been found.

State-space FDTD implementation of anisotropic perfectly matched layer

New formulations based on the state-space approach are presented for implementing the anisotropic perfectly matched layer into the finite difference time domain (FDTD) algorithm. The formulations are simple and independent from the material properties of the FDTD computational domain. Numerical tests are included to validate the proposed formulations.

Transmitter‐receiver‐transmitter configurations of ground‐penetrating radar

Three‐dimensional ground‐penetrating radar (GPR) geometries are simulated using the finite difference time domain (FDTD) method. The GPR is modeled with a receiver and two transmitters with arbitrary polarizations in order to cancel the direct signals emitted by the two transmitters at the receiver. This GPR configuration is used to simulate scenarios involving single or multiple targets with arbitrary sizes. The buried objects are modeled as cylindrical disks. Perfectly matched layer absorbing boundary conditions are used to terminate the layered FDTD computational domain.

Application of Signal-Processing Techniques To Dipole Excitations in the Finite-Difference Time-Domain Method

The applications of discrete-time signal-processing techniques, such as windowing and filtering for the purpose of implementing accurate excitation schemes in the finite-difference time-domain (FDTD) method are demonstrated. The effects of smoothing windows of various lengths and digital lowpass filters of various bandwidths and characteristics are investigated on finite-source excitations of the FDTD computational domain. Both single-frequency sinusoidal signals and multifrequency arbitrary signals are considered.

Simulations of ground-penetrating radars over lossy and heterogeneous grounds

The versatility of the three-dimensional (3D) finite-difference time-domain (FDTD) method to model arbitrarily inhomogeneous geometries is exploited to simulate realistic ground-penetrating radar (GPR) scenarios for the purpose of assisting the subsequent designs of high-performance GPR hardware and software. The buried targets are modeled by conducting and dielectric prisms and disks. The ground model is implemented as lossy with surface roughness, and containing numerous inhomogeneities of arbitrary permittivities, conductivities, sizes, and locations. The impact of such an inhomogeneous ground model on the GPR signal is demonstrated. A simple detection algorithm is introduced and used to process these GPR signals. In addition to the transmitting and receiving antennas, the GPR unit is modeled with conducting and absorbing shield walls, which are employed to reduce the direct coupling to the receiver. Perfectly matched layer absorbing boundary condition is used for both simulating the physical absorbers inside the FDTD computational domain and terminating the lossy and layered background medium at the borders.