Time-domain Implementation Research Articles

Optimal Design of Dispersion Filter for Time-Domain Split-Step Simulation of Pulse Propagation in Optical Fiber

The nonlinear Schrodinger equation can be solved by split-step methods, where in each step, linear dispersion and nonlinear effects are treated separately. This paper considers the optimal design of an FIR filter as the time-domain implementation for the linear part. The objective is to minimize the integral of the squared error between the FIR frequency response and the desired dispersion characteristics over the band of interest. This least square (LS) problem is solved in two approaches: the normal equation approach gives the explicit solution, whereas the singular value decomposition approach, which is based on the theory of discrete prolate spheroidal sequences, provides geometrical insights and reveals that the normal equation could be ill-conditioned. In addition, the frequency response might exhibit singular behaviors such as overshoot. We propose two filters that both can mitigate these shortcomings: the regularized LS filter achieves this by adding a regularization term to the objective function; the quadratically constrained quadratic programming-based filter addresses overshooting more efficiently by imposing a maximum magnitude constraint on the frequency response. Numerical results show that these filters can suppress the overshoots, control the squared error, reduce the filter length and lower the computational complexity. For both single channel and wavelength-division multiplexing channels, the proposed methods generate similar outputs as the standard split-step Fourier method.

Power Components Estimation According to IEEE Standard 1459–2010 Under Wide-Range Frequency Deviations

This paper proposes an accurate and computationally efficient time-domain implementation of the IEEE Standard 1459-2010 for power measurements. The most important parts are adaptive low- and bandpass finite-impulse-response (FIR) filters that extract dc and fundamental components, respectively. In addition, coefficient sensitivity problems of the large-order FIR comb cascade structure are overridden by using a multirate (decimation) digital signal processing technique. Even more, by using decimation antialiasing filters, the parameter estimation accuracy is improved. The symmetrical components are estimated through adaptive transformation matrix of phase shifters. The algorithm convergence provided a fast response and adaptability. The effectiveness of the proposed technique is demonstrated by simulation results. The algorithm shows a very high level of robustness and high measurement accuracy over a wide range of frequency changes.

Fast Implementation of FDTD-Compatible Green's Function on Multicore Processor

In this letter, numerically efficient implementation of the finite-difference time domain (FDTD)-compatible Green's function on a multicore processor is presented. Recently, closed-form expression of this discrete Green's function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations may cause long runtimes and numerical problems. The proposed fast implementation of the DGF is based on the multiple precision arithmetic and employs a common programming language extended with the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained, thus applicability of the DGF in FDTD simulations was significantly improved.

Implementation of FDTD-Compatible Green's Function on Graphics Processing Unit

In this letter, implementation of the finite-difference time domain (FDTD)-compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision arithmetic and may cause long runtimes. Therefore, we propose an acceleration of the DGF computations on a GPU employing the multiple precision arithmetic and the CUDA technology. We have achieved sixfold speedup relative to the reference DGF code executed on a multicore central processing unit. Results indicate that GPUs also represent an inexpensive source of computational power for accelerated DGF computations requiring the multiple precision arithmetic.

On the Validity of Approximate Formulas for the Evaluation of the Lightning Electromagnetic Fields in the Presence of a Lossy Ground

The accuracy of approximate formulas for the evaluation of lightning electromagnetic fields above and inside a lossy ground is investigated taking as reference full-wave numerical results obtained using a parallel implementation of the finite-difference time-domain (FDTD) technique. The return stroke channel is modeled using the antenna theory model with fixed inductive loading which is appropriately incorporated into the FDTD algorithm. First, the validity of the Cooray-Rubinstein (CR) formula for the evaluation of above-ground horizontal electric field is evaluated. The obtained results confirm the recent findings of Cooray according to which it is important to include propagation effects over a lossy ground in the magnetic field used in the CR formula, except at very close distance ranges for which propagation effects can be neglected. Second, we test the validity of the Cooray formula for the evaluation of underground horizontal electric fields. The Cooray formula allows for the evaluation of the underground horizontal electric field starting from the horizontal electric field at the air-soil interface. This latter can be calculated using either 1) the original CR formula in which the magnetic field at ground level is evaluated assuming the ground as a perfect conductor or 2) taking into account propagation effects in the computation of the magnetic field. We show that the assumption of a perfectly conducting ground for the evaluation of the magnetic field at ground level might lead to inaccuracies in the Cooray formula. However, the use of the Cooray formula taking into account propagation effects in the computation of the magnetic field results in acceptable predictions of the underground horizontal electric fields.

An Accurate and Efficient Two-Stage Channel Estimation Method Utilizing Training Sequences with Closed Form Expressions

A novel two-stage frequency domain channel estimation method especially suitable for the estimation of long channels such as ultra wide band channels is proposed. The proposed method can efficiently use the sequences with closed form analytical expressions such as the Legendre sequences. (The suggested method does not require a computationally intense search for good training sequences which is infeasible for long training sequences.) The method is shown to present a minor improvement in the total estimation error variance when compared with the conventional single stage frequency domain channel estimation. In addition, the proposed method has a very efficient time domain implementation requiring at most 2N multiplications, where N is the training sequence length, in comparison to O(N log N) multiplications required for the conventional method.

Modeling Propagation in Multifloor Buildings Using the FDTD Method

A three-dimensional parallel implementation of the finite-difference time-domain (FDTD) method has been used to identify and isolate the dominant propagation mechanisms in a multistorey building at 1.0 GHz. A novel method to visualize energy flow by computing streamlines of the Poynting vector has been developed and used to determine the dominant propagation mechanisms within the building. It is found that the propagation mechanisms depend on the level of internal clutter modeled. Including metallic and lossy dielectric clutter in the environment increases attenuation on some propagation paths, thereby altering the dominant mechanisms observed. This causes increases in the sector-averaged path loss and changes the distance-dependency exponents across a floor from 2.2 to 2.7. The clutter also reduces Rician K-factors across the floor. Directly comparing sector-averaged path loss from the FDTD simulations with experimental measurements shows an RMS error of 14.4 dB when clutter is ignored. However, this is reduced to 10.5 dB when the clutter is included, suggesting that the effects of clutter should not be neglected when modeling propagation indoors.

Source-independent time-domain waveform inversion using convolved wavefields: Application to the encoded multisource waveform inversion

Full waveform inversion requires a good estimation of the source wavelet to improve our chances of a successful inversion. This is especially true for an encoded multisource time-domain implementation, which, conventionally, requires separate-source modeling, as well as the Fourier transform of wavefields. As an alternative, we have developed the source-independent time-domain waveform inversion using convolved wavefields. Specifically, the misfit function consists of the convolution of the observed wavefields with a reference trace from the modeled wavefield, plus the convolution of the modeled wavefields with a reference trace from the observed wavefield. In this case, the source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the misfit function, and thus, the effects of the source wavelets are eliminated. Furthermore, because the modeled wavefields play a role of low-pass filtering, the observed wavefields in the misfit function, the frequency-selection strategy from low to high can be easily adopted just by setting the maximum frequency of the source wavelet of the modeled wavefields; and thus, no filtering is required. The gradient of the misfit function is computed by back-propagating the new residual seismograms and applying the imaging condition, similar to reverse-time migration. In the synthetic data evaluations, our waveform inversion yields inverted models that are close to the true model, but demonstrates, as predicted, some limitations when random noise is added to the synthetic data. We also realized that an average of traces is a better choice for the reference trace than using a single trace.

Time-Domain Implementation of Cooray–Rubinstein Formula via Convolution Integral and Rational Approximation

One of the most popular techniques to take into account the finite ground conductivity in the evaluation of the radial component of the electric field generated by a lightning return stroke is the Cooray-Rubinstein (CR) formula. As this formula is derived in the frequency domain, its application in time-domain simulation codes for the analysis of lightning-induced overvoltages on overhead lines might be challenging. In this paper, two methods allowing a simple time-domain implementation of the formula are discussed. The first one is an enhanced version of an algorithm recently proposed by two of the authors, while the second consists of a new technique, based on a suitable rational approximation of the impedance term appearing in the CR formula. This second approach is characterized by an intrinsic easiness in time-domain implementation and a considerable computational efficiency compared with conventional methods.

Time-Domain Implementation of Broadband Beamformer in Spherical Harmonics Domain

Most of the existing spherical array modal beamformers are implemented in the frequency domain, where a block of snapshots is required to perform the discrete Fourier transform. In this paper, an approach to real-valued time-domain implementation of the modal beamformer for broadband spherical microphone arrays is presented. The microphone array data are converted to the spherical harmonics domain by using the discrete spherical Fourier transform, and then steered to the look direction followed by the pattern generation unit implemented using the filter-and-sum structure. We derive the expression for the array response, the beamformer output power against both isotropic noise and spatially white noise, and the mainlobe spatial response variation in terms of the finite impulse response (FIR) filters' tap weights. A multiple-constraint problem is then formulated to find the filters' tap weights with the aim of providing a suitable tradeoff among multiple conflicting performance measures such as directivity index, robustness, sidelobe level, and mainlobe response variation. Simulation and experimental results show good performance of the proposed time-domain broadband modal beamforming approach.

Python Bindings for the Open Source Electromagnetic Simulator Meep

This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Pade approximants, and flexible scripting capabilities.

Seismic-Wave Propagation Modeling in Viscoelastic Media Using the Auxiliary Differential Equation Method

In many seismic applications, a constant quality factor is used to describe the constitutive laws of viscoelastic materials, characterized by frequency-independent attenuation characteristics. In such cases, the frequency dependence of the medium’s properties is not taken into account. To overcome this drawback, we proposed an elegant finite difference time domain implementation, with an auxiliary differential equation technique to explicitly solve any stress-strain relation. This scheme is inherited from the formalism of electromagnetism and is based on the separation of the propagation equations from the constitutive law defined in the stress-strain equation. The conventional assumption of a constant quality factor assumption can then be easily avoided in the modeling of seismic-wave propagation in viscoelastic media. We developed such a method and simulated synthetic traces over a simple, 2D viscoelastic homogeneous medium using a Zener model. Wave propagation phase velocities were estimated by means of dispersion analysis and appeared to match theoretical values over a reasonable frequency range. We also measured the material’s attenuation behavior by studying the quality factor, thereby validating our approach.

Efficient and accurate sound propagation using adaptive rectangular decomposition

Accurate sound rendering can add significant realism to complement visual display in interactive applications, as well as facilitate acoustic predictions for many engineering applications, like accurate acoustic analysis for architectural design. Numerical simulation can provide this realism most naturally by modeling the underlying physics of wave propagation. However, wave simulation has traditionally posed a tough computational challenge. In this paper, we present a technique which relies on an adaptive rectangular decomposition of 3D scenes to enable efficient and accurate simulation of sound propagation in complex virtual environments. It exploits the known analytical solution of the Wave Equation in rectangular domains, and utilizes an efficient implementation of the Discrete Cosine Transform on Graphics Processors (GPU) to achieve at least a 100-fold performance gain compared to a standard Finite-Difference Time-Domain (FDTD) implementation with comparable accuracy, while also being 10-fold more memory efficient. Consequently, we are able to perform accurate numerical acoustic simulation on large, complex scenes in the kilohertz range. To the best of our knowledge, it was not previously possible to perform such simulations on a desktop computer. Our work thus enables acoustic analysis on large scenes and auditory display for complex virtual environments on commodity hardware.

REAS3: Monte Carlo simulations of radio emission from cosmic ray air showers using an “end-point” formalism

In recent years, the freely available Monte Carlo code REAS for modelling radio emission from cosmic ray air showers has evolved to include the full complexity of air shower physics. However, it turned out that in REAS2 and all other time-domain models which calculate the radio emission by superposing the radiation of the single air shower electrons and positrons, the calculation of the emission contributions was not fully consistent. In this article, we present a revised implementation in REAS3, which incorporates the missing radio emission due to the variation of the number of charged particles during the air shower evolution using an “end-point formalism”. With the inclusion of these emission contributions, the structure of the simulated radio pulses changes from unipolar to bipolar, and the azimuthal emission pattern becomes nearly symmetric. Remaining asymmetries can be explained by radio emission due to the variation of the net charge excess in air showers, which is automatically taken into account in the new implementation. REAS3 constitutes the first self-consistent time-domain implementation based on single particle emission taking the full complexity of air shower physics into account, and is freely available for all interested users.

Time Domain Models for Damping-Controlled Fluidelastic Instability Forces in Tubes With Loose Supports

This paper presents simulations of a loosely supported cantilever tube subjected to turbulence and fluidelastic instability forces. Several time domain fluid force models are presented to simulate the damping-controlled fluidelastic instability mechanism in tube arrays. These models include a negative damping model based on the Connors equation, fluid force coefficient-based models (Chen, 1983, “Instability Mechanisms and Stability Criteria of a Group of Cylinders Subjected to Cross-Flow. Part 1: Theory,” Trans. ASME, J. Vib., Acoust., Stress, Reliab. Des., 105, pp. 51–58; Tanaka and Takahara, 1981, “Fluid Elastic Vibration of Tube Array in Cross Flow,” J. Sound Vib., 77, pp. 19–37), and two semi-analytical models (Price and Païdoussis, 1984, “An Improved Mathematical Model for the Stability of Cylinder Rows Subjected to Cross-Flow,” J. Sound Vib., 97(4), pp. 615–640; Lever and Weaver, 1982, “A Theoretical Model for the Fluidelastic Instability in Heat Exchanger Tube Bundles,” ASME J. Pressure Vessel Technol., 104, pp. 104–147). Time domain modeling and implementation challenges for each of these theories were discussed. For each model, the flow velocity and the support clearance were varied. Special attention was paid to the tube/support interaction parameters that affect wear, such as impact forces and normal work rate. As the prediction of the linear threshold varies depending on the model utilized, the nonlinear response also differs. The investigated models exhibit similar response characteristics for the lift response. The greatest differences were seen in the prediction of the drag response, the impact force level, and the normal work rate. Simulation results show that the Connors-based model consistently underestimates the response and the tube/support interaction parameters for the loose support case.

CUDA Implementation of <formula formulatype="inline"> <tex Notation="TeX">${\rm TE}^{z}$</tex> </formula>-FDTD Solution of Maxwell's Equations in Dispersive Media

This letter presents the graphic processor unit (GPU) implementation of the finite-difference time domain (FDTD) method for the solution of the two-dimensional electromagnetic fields inside dispersive media. The FDTD is truncated by the convolutional perfectly matched layer (CPML) and the piecewise-linear recursive-convolution (PLRC) formulation is used for modeling dispersive media. By using the newly introduced Compute Unified Device Architecture (CUDA) technology, we illustrate the efficacy of GPUs in accelerating the FDTD computations by achieving significant speedup factors with great ease and at no extra hardware/software cost. We validate our approach by comparison to exact and other simulated results, which show favorable agreements. The effect of the GPU–CPU memory transfers on the speedup factor will be also studied.

Investigating the spectral characteristics of backscattering from heterogeneous spherical nuclei using broadband finite-difference time-domain simulations

Reflectance spectra measured from epithelial tissue have been used to extract size distribution and refractive index of cell nuclei for noninvasive detection of precancerous changes. Despite many in vitro and in vivo experimental results, the underlying mechanism of sizing nuclei based on modeling nuclei as homogeneous spheres and fitting the measured data with Mie theory has not been fully explored. We describe the implementation of a three-dimensional finite-difference time-domain (FDTD) simulation tool using a Gaussian pulse as the light source to investigate the wavelength-dependent characteristics of backscattered light from a nuclear model consisting of a nucleolus and clumps of chromatin embedded in homogeneous nucleoplasm. The results show that small-sized heterogeneities within the nuclei generate about five times higher backscattering than homogeneous spheres. More interestingly, backscattering spectra from heterogeneous spherical nuclei show periodic oscillations similar to those from homogeneous spheres, leading to high accuracy of estimating the nuclear diameter by comparison with Mie theory. In addition to the application in light scattering spectroscopy, the reported FDTD method could be adapted to study the relations between measured spectral data and nuclear structures in other optical imaging and spectroscopic techniques for in vivo diagnosis.

A novel finite-difference time-domain scheme for electromagnetic scattering by stratified anisotropic plasma under oblique incidence condition

A novel finite-difference time-domain(FDTD) implementation, by which electromagnetic(EM) wave scattering characteristic can be analyzed for oblique incidence on stratified anisotropic plasma, is proposed. This method transforms two-dimensional electromagnetic wave scattering question to one-dimensional question, and avoids two-dimensional scattering problem by 2D FDTD method, by which the computational efficiency can be greatly improved. FDTD iterative formula of EM scattering by layered anisotropic plasma are deduced in the TEz and TMz wave oblique incidence situations, and the connection boundary(CB) and the absorbing boundary condition (ABC) in the oblique incidence situation are carried out the revision. The EM wave reflection coeffientes of the anisotropic plasma slab are calculated in the oblique incidence situation by the method. The computed results and the analytic solutions are in good agreement. The results show the accuracy and validity of the method. Finally, the algorithm is applied to calculate the reflection coefficients of the metal plate coated with the stratified anisotropic plasma under different incidence angles. The numerical results show the incidence angle have a great impact on the reflection coefficients.

Time-domain “wave” model of the human tympanic membrane

Middle ear models have been successfully developed for many years. Most of those are implemented in the frequency domain, where physical equations are more easily derived. This is problematic, however, when it comes to model non-linear phenomena, especially in the cochlea, and because a frequency-domain implementation may be less intuitive. This research explores a different approach, based on a time-domain implementation, fitted to impedance data. It is adapted from a previous work for the cat and focuses here on the human ear: volume velocity samples are distributed uniformly in space and updated periodically to simulate the propagation of the sound wave in the ear. The modeling approach is simple, yet it can quantitatively reproduce the major characteristics of the human middle ear transmission, and can qualitatively capture forward and reverse power transmission – a key feature of this time-domain implementation. These results suggest that complex, multi-modal propagation observed on the TM may not be critical to proper sound transmission along the ear. Besides, model predictions reveal that impedance and velocimetry measurements may be inconsistent with each other, hypothetically because velocimetry protocols could alter the middle ear.

Unified model for time-domain implementation of space block coded OFDM

A new scheme for time-domain implementation of space-frequency block coded (SFBC) OFDM is derived. The scheme has a block structure similar to that of time-domain implemented space-time block coded (STBC) OFDM, leading to a unified block structure for time-domain implementation of either STBC- or SFBC-OFDM, or for adaptive switching between the two. The new scheme is also shown to have complexity reduction advantages over existing schemes in the literature.