Finite-difference Time-domain Program Research Articles

Study on the propagation properties of TM electromagnetic wave in Lossy left‐handed material based on CUDA‐implemented parallel

By using the method of Finite Difference Time Domain (FDTD) and the technology of Compute Unified Device Architecture (CUDA), the propagation characteristics of electromagnetic waves in Left-Handed Materials (LHM) have been studied in this paper. The LHM slab was matched with the free space and the secondary focusing phenomenon of LHM was simulated. Compared with the serial FDTD program, our work showed that this method had a high accuracy. The phase compensation effect and the inverse Snell effect of LHM were also discussed by using the parallel FDTD method based on CUDA, which further proved that our results were consistent with the theoretical study. By comparing the calculation time of traditional FDTD program with that of the CUDA based parallel FDTD program, we conclude that the latter is more efficient than the former. This parallel method can be used as a more efficient way to study LHM.

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.

Design of multiband PIFA with low SAR value for all commercial mobile communication bands

A low profile planar inverted-F antenna is proposed for mobile handset applications. Thus, our target is to introduce a new antenna that supports both services, the proposed antenna have broadband characteristic which includes all commercial service bands, GSM850/GSM900/GPS/GSM1800/GSM1900/WCDMA2100/802.11b/g/LTE2600 (824–2690 MHz) as well as 802.11a/n (5150–5825 MHz). Overall size of the antenna is 21 × 45 × 8 mm3 is well suited for mobile handsets due to its low profile, small size, wide bandwidth, the radiation patterns are satisfactorily omnidirectional across the antenna's operation bands, and good gain (the gain in some frequency bands is higher than 4 dBi). The antenna not only has a compact size, but also it supports a low specific absorption rate (SAR) radiation at all the operating frequencies. In addition, the proposed antenna is assessed using the finite difference time domain (FDTD) program written with MATLAB to validate the results. The antenna meets three challenging parameters: the compact size, the multiband operation including the low frequency bands, and the low SAR radiation. The measured results exhibit good agreement with the simulation results from CST and the FDTD program written with MATLAB. As a result, the designed antenna is suitable for small mobile devices and slim wireless applications. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:194–201, 2015.

Modeling Human Head at Microwave Frequencies Using Optimized Debye Models and FDTD Method

Debye models for tissues found in the human head are presented. The parameters of the Debye models are optimized to measured data of different head tissues. Excellent consistency over the frequency band from 0.1 GHz to 5 GHz is shown with improved accuracy compared to current models using the Cole-Cole approximation. The auxiliary differential-equation based method is used to incorporate the derived models into a finite-difference time-domain program. The validity of the derived models are verified by comparing the fields produced in a realistic 2-D phantom head using a finite-difference time-domain program with the proposed Debye models, and a method of moments solver.

Enhanced Modulation Bandwidth in Complex Cavity Injection Grating Lasers

Enhanced modulation bandwidth in complex cavity lasers can be obtained by exploiting the coupling between two adjacent cavity modes having proper spectral separation. We investigate the conditions that a complex cavity injection laser device must satisfy in order to take advantage of this effect to significantly increase its modulation bandwidth and we present a general design rule. According to the proposed guidelines, a structure is designed and then dynamically analyzed using a finite-difference time-domain program to show the validity of the proposed method. As an example the proposed guidelines have been adapted also to the design of a distributed Bragg reflector laser and extended modulation was found.

Performance analysis and optimization of three-dimensional FDTD on GPU using roofline model

The Finite-Difference Time-Domain (FDTD) method is commonly used for electromagnetic field simulations. Recently, successful hardware-accelerations using Graphics Processing Unit (GPU) have been reported for the large-scale FDTD simulations. In this paper, we present a performance analysis of the three-dimensional (3D) FDTD on GPU using the roofline model. We find that theoretical predictions on maximum performance agrees well with the experimental results. We also suggest the suitable optimization methods for the best performance of FDTD on GPU. In particular, the optimized 3D FDTD program on GPU (NVIDIA Geforce GTX 480) is shown to be 64 times faster than the naively implemented program on CPU (Intel Core i7 2600).

MICROWAVE HEAD IMAGING FOR STROKE DETECTION

This paper proposes an algorithm for wide-band microwave imaging for the detection of a hemorrhagic stroke. A realistic head phantom and finite-difference time-domain program are used to estimate back-scattered signals which are subsequently used in the image reconstruction process. The proposed imaging approach can lead to a portable and cost effective system; particularly suitable for rural medical clinics that lack the necessary resources in effective stroke diagnosing.

Design of temperature-independent arrayed waveguide gratings based on the combination of multiple types of waveguide

We develop a design theory for a temperature-independent arrayed waveguide grating (TI-AWG) based on the combination of multiple types of waveguide. Each type of waveguide has a path-length difference between adjacent arrayed waveguides, and the path-length difference ratio is introduced as tuning parameter. A TI-AWG with Si wire and slot waveguides is given as an example. The thermal spectra shift of the TI-AWG can be tuned from redshift to blueshift in an ultralarge range, and the modified interference order can be reduced or enhanced. The device size is about one-fifth that of the narrow-wide-wire design that uses a combination of narrow and wide Si wire waveguides. The results are verified by the simulation of prototype devices via a two-dimensional finite-difference time-domain program.

Finite-difference Time-domain Study on Birefringence Changes of the Axon During Neural Activation

Recently, there has been a growing interest in optical imaging of neural activity because the optical neuroimaging has considerable advantages over conventional imaging. Birefringence of the axon has been reported to change during neural activation, but the neurophysiological origin of the change is still unresolved. This study hypothesizes that the birefringence signal is at least partially attributed to the transient cellular volume change associated with nerve excitation. To examine this hypothesis, we investigated how the intensity of cross-polarized light transmitting through the axon would change as the size of the axon changes. For this purpose, a two-dimensional finite-difference time-domain program was developed with the improvement of the total-field/scattered-field method which reduces numerical noise. The results support our hypothesis in that the computed cross-polarized signals exhibit some agreement with previously-reported birefringence signals.

Propagation of surface acoustic waves through sharply bent two-dimensional phononic crystal waveguides using a finite-difference time-domain method

In this paper, we adopt the finite-difference time-domain (FDTD) method to analyze surface acoustic waves propagating in two-dimensional phononic waveguides. To implement the FDTD program for dealing with surface acoustic waves, the Bloch theorem and absorbing boundary conditions are employed to deal with the periodic boundary condition and reflection from a numerical boundary. A phononic crystal consisting of circular steel cylinders that form a square lattice in an epoxy matrix is considered as an example to study phononic crystal waveguides. The dispersion relation and displacement fields are calculated to identify the band gaps and eigenmodes. The result shows the existence of a complete band gap of surface waves and thus an acoustic waveguide is created accordingly. Eigenmodes of surface waves inside the waveguide are indicated and pseudo surface acoustic waves propagating inside the straight waveguide are demonstrated. Further, waveguides with a sharp bend are reported and an improved design is suggested to enhance energy transmission.

Parallel numerical simulation of the ultrasonic waves in a prestressed formation

Formation stress prediction plays an important role in petroleum production. Understanding ultrasonic wave propagation in a stress-induced anisotropic formation will help us to find an efficient method to correctly predict formation stress or formation pore pressure. In this work, a parallel 3D finite-difference time domain (FDTD) method is developed to simulate elastic wave propagation in pre-stressed formations. A perfectly matched layer (PML) is used as an absorbing boundary condition. The acceleration ration of total CPU computation time and the lasting time of the program run in the super computer-ShenTeng 6800 in the Super Computation Center of Chinese Academy of Science (CAS) are tested. It shows that the acceleration factor of the parallel FDTD program is considerably high even if the domain is only divided in one direction. When the total computation model size fixed, the acceleration factor of 8 CPU and 64 CPU is 3.0 and 13.8, respectively. The velocities under various static stresses are obtained by processing the array data calculated with the FDTD using Prony’s method. The linear relation between velocity and the applied pre-stress is in agreement with that predicted by the acoustoelasticity theory. Results from the numerical simulation confirm the reciprocity principle and the superposition principle.

Three-dimensional phononic band gap calculations using the FDTD method and a PC cluster system

This paper aims at studying the band gap phenomena of three-dimensional phononic crystals using the finite difference time domain (FDTD) method and a PC cluster system. In the paper, Bloch's theorem is applied to the wave equation and to the boundary conditions of the periodic structure. We calculate the variations of displacements and take discrete Fourier transform to acquire the resonances of the structures. Then, the dispersion relations of the bulk acoustic wave can be obtained and the band gaps are predicted accordingly. On the other hand, because of larger data calculation in three-dimensional phononic crystals, we introduce the PC cluster system and parallel FDTD programs written with respect to the architecture of a PC cluster system. Finally, we discuss the numerical calculation of two-dimensional and three-dimensional phononic crystals consisting of steel/epoxy and draw conclusions regarding the band gap phenomena between these phononic crystals.

Source location in an urban setting using time reversal with small sensor arrays

The finite-difference, time-domain (FDTD) method was used with time reversal to explore acoustic pulse source location in an urban setting with the source outside the array of sensors. The FDTD program simulates two-dimensional sound propagation from an omnidirectional point source, including reflection and diffraction from buildings. Pressure versus time is recorded at various hypothetical sensor locations. During time-reversal playback, each sensor becomes an omnidirectional point source generating a time-reversed version of the pressure it received. A number of sensor arrays were modeled in various urban settings to identify the limitations of using time reversal to locate a non-line-of-sight source outside the array. In general, as the number of sensors and spatial extent of the array increases, the ability to locate the source increases as well. A 19-sensor hexagonal array 8 m across, for example, is capable of locating a source on the opposite side of a building. Two small four-sensor arrays 10 m from each other are adequate for around-the-corner source location. A single small array of three or four sensors spaced 1 to 2 m apart was generally insufficient to locate the source.

FDTD ANALYSIS OF A DUAL-FREQUENCY MICROSTRIP PATCH ANTENNA

Characteristics of a single-layer, dual-frequency microstrip patch antenna, which uses a T-strip loaded rectangular microstrip patch, are studied. This antenna is easy to achieve good impedance matching at both frequencies by tuning the feed position and other design parameters. Another advantageous aspect is that it has high polarization purity. A detailed parameter study is performed and the theoretical analysis is based on the finite-difference time-domain (FDTD) method. The FDTD programs are developed and validated by measurement results. The effects of various antenna parameters on two resonant frequencies, frequency ratio, and radiation pattern characteristics of the antenna are analyzed and discussed. It is shown that various frequency ratios (1.5–2.49) can be obtained by varying the design parameters of this antenna. Similar radiation patterns with same polarization are obtained at two resonant frequencies. Several design curves are presented. 156 Gao, Li, and Sambell

A Hybrid Computational Electromagnetics Formulation for Simulation of Antennas Coupled to Lossy and Dielectric Volumes

A heterogeneous hybrid computational electromagnetics method is presented, which enables different parts of an antenna simulation problem to be treated by different methods, thus enabling the most appropriate method to be used for each part. The method uses a standard frequency-domain moment-method program and a finite-difference time-domain program to compute the fields in two regions. The two regions are interfaced by surfaces on which effective sources are defined by application of the Equivalence Principle. An extension to this permits conduction currents to cross the boundary between the different computational domains. Several validation cases are examined and the results compared with available data. The method is particularly suitable for simulation of the behavior of an antenna that is partially buried, or closely coupled with lossy dielectric volumes such as soil, building structures or the human body.

A class of analytical absorbing boundary conditions originating from the exact surface impedance boundary condition

A new class of analytical absorbing boundary conditions (ABCs) for the truncation of the finite-difference time-domain (FDTD) lattice is introduced. These ABC originate from the exact impedance boundary operator and contain both electric and magnetic fields. The performance of the proposed second-order ABCs is studied with a two-dimensional FDTD program. The results indicate that the proposed ABCs work approximately as well as the third-order analytical ABCs, even if they are essentially as easy to implement as the second-order Mur ABC. Also, in this paper, the relation between the so-called Engquist-Majda operator for the absorption of plane waves and the exact surface impedance boundary condition is discussed.

The Analysis of Post-Mount in W-Band Circular Groove Guide

Finite-difference time-domain (FDTD) method is used to calculate the driving-point impedance of the circular groove guide diode mount. A simple way is proposed to approximate the curvilinear metal boundary of circular groove guide. Discrete equations are obtained from the Ampere's law and Faraday's law. Perfectly matched layer (PML) is applied on the open boundary of circular groove guide. At last program is made to obtain the field components. The driving-point impedance can be achieved from the ratio of the Fourier transform of the voltage and the Fourier transform of the current. The cutoff frequency and field pattern of the dominant mode are also obtained with well agreement with the theoretical results, this verifies the validity of the FDTD program.

FDTD Simulation of Photonic-Crystal Lasers and Their Relaxation Oscillation

We have developed an finite-difference time-domain program that can analyze photonic devices with gain and/or dispersion. As an example, a two-dimensional photonic-crystal laser is simulated. The simulation can show the relaxation oscillation behavior at extremely high current injection.

Modeling microwave and hybrid heating processes including heat radiation effects

This paper presents an efficient simulation tool for conventional, microwave, and combined heating. Two heat-transfer mechanisms are included: conductive and radiant heat transfer. The conductive heat transfer is modeled by a finite-difference algorithm. A modeling technique for radiant heat transfer in nonuniform grids has been developed and is here presented for the first time. For the radiant heat transfer a finite-difference scheme is not applicable, as radiation from a material surface; is not bounded to the immediate vicinity, as is conductive heat transfer. Therefore, ray optical methods are used. Rays connecting mutually visible surfaces are obtained by a new fast method. Necessary, but acceptable simplifications allow fast computations. The algorithms are integrated conveniently together with an electromagnetic finite-difference time-domain program to one simulation tool. Representative simulations are presented for an oven heated conventionally, by microwaves, and by a combination of both.

A dual‐frequency compact microstrip patch antenna

In this paper, a new dual‐frequency, compact antenna, which uses an H‐shaped microstrip patch with a shorting pin, is described. Compared with the conventional rectangular patch antenna, this antenna can achieve both a significant reduction of antenna size and a dual‐frequency operation with a single feed. More freedoms for tuning the resonant frequencies, the frequency ratio, and the input impedance are available because of more design parameters. A detailed parameter study is performed, and the theoretical analysis is based on the finite difference time domain (FDTD) method. The FDTD programs are developed and validated by measurement results. The effects of several antenna parameters on two resonant frequencies, frequency ratio, and radiation pattern characteristics of the antenna are analyzed and compared. It is shown that various frequency ratios (1.91–4.23) can be obtained by varying the design parameters of this antenna. Several design curves are presented.