Finite-difference Time-domain Code Research Articles

Numerical analysis of the limits of effective medium theory for nonlinearly propagating dispersive waves

Acoustic metameterials are an increasingly popular approach to control both linear and nonlinear sound propagation. In this approach, heterogeneous structures are engineered to behave as predetermined continuous media. A key requirement for a system to be accurately approximated as a homogeneous material for wave motion is that the smallest length scale of the waveform be much larger than any length scale associated with the microscale structure of the system. However, the fact that the characteristic length scales of a finite-amplitude waveform can change due to nonlinear effects means that care must be taken when analyzing such signals in an acoustic metamaterial. This talk presents recent work toward understanding the breakdown of effective medium theory as finite-amplitude waves propagate in a heterogeneous system and weak shocks or solitons begin to form. A finite-difference time-domain code was used to model the propagation of a pulse of sound in a one-dimensional propagation domain using both a full description of the system and an effective-medium description accounting for effective mass density, compressibility, coefficient of nonlinearity, and dispersion. The difference between the solutions of the two models provides a method by which one can estimate the error associated with using effective properties.

Feasibility of a finite-difference time-domain model in large-scale acoustic simulations.

Wave-based techniques for room acoustics simulations are commonly applied to low frequency analysis and small-sized simplified environments. The constraints are generally the inherent computational cost and the challenging implementation of proper complex boundary conditions. Nevertheless, the application field of wave-based simulation methods has been extended in the latest research decades. With the aim of testing this potential, this work investigates the feasibility of a finite-difference time-domain (FDTD) code simulating large non-trivial geometries in wide frequency ranges. A representative sample of large coupled-volume opera houses allowed demonstration of the capability of the selected FDTD model to tackle such composite geometries up to 4 kHz. For such a demanding task, efficient calculation schemes and frequency-dependent boundary admittances are implemented in the simulation framework. The results of in situ acoustic measurements were used as benchmarks during the calibration process of three-dimensional virtual models. In parallel, acoustic simulations performed on the same halls through standard ray-tracing techniques enabled a systematic comparison between the two numerical approaches highlighting significant differences in terms of input data. The ability of the FDTD code to detect the typical acoustic scenarios occurring in coupled-volume halls is confirmed through multi-slope decay analysis and impulse responses' spectral content.

Benchmarking 2D against 3D FDTD codes for the assessment of the measurement performance of a low field side plasma position reflectometer applicable to IDTT

O-mode reflectometry, a technique to diagnose fusion plasmas, is foreseen as a source of real-time (RT) plasma position and shape measurements for control purposes in the coming generation of machines such as DEMO. It is, thus, of paramount importance to predict the behavior and capabilities of these new reflectometry systems using synthetic diagnostics. Finite-difference time-domain (FDTD) time-dependent codes allow for a comprehensive description of reflectometry but are computationally demanding, especially when it comes to three-dimensional (3D) simulations, which requires access to High Performance Computing (HPC) facilities, making the use of two-dimensional (2D) codes much more common. It is important to understand the compromises made when using a 2D model in order to decide if it is applicable or if a 3D approach is required. This work attempts to answer this question by comparing simulations of a potential plasma position reflectometer (PPR) at the Low Field-Side (LFS) on the Italian Divertor Tokamak Test facility (IDTT) carried out using two full-wave FDTD codes, REFMULF (2D) and REFMUL3 (3D). In particular, the simulations consider one of IDTT’s foreseen plasma scenarios, namely, a Single Null (SN) configuration, at the Start Of Flat-top (SOF) of the plasma current.

A Fast and Fully Parallel Analog CMOS Solver for Nonlinear PDEs

A general-purpose analog computing method is proposed to compute the continuous-time solutions of nonlinear partial differential equations (PDEs). The discrete-time difference operator in the standard finite difference time domain (FDTD) method is replaced by continuous-time delay operators that can be realized using analog all-pass filters. The resulting spatially discrete time-continuous (SDTC) update equations are realized using analog circuits which compute continuous-time solutions of the PDE with prescribed initial and boundary conditions. The proposed concept is demonstrated in simulation via an integrated circuit (IC) design of a nonlinear acoustic wave equation solver in 180 nm CMOS technology. Analog arithmetic operations (multiply, scale, and add) are realized in parallel using fully differential op-amps and analog multipliers. The proposed IC computes the PDE solution in parallel at 33 discrete spatial points and has a simulated bandwidth and power consumption of approximately 2 MHz and 3 W, respectively. The performance of the IC is simulated using foundry-supplied device models and quantified using i) the mean squared difference between the circuit simulation results and FDTD simulations, and ii) the noise to signal energy ratio. Acceptable accuracy is obtained, with error metric values varying between -7 and -30 dB for various configurations of the problem. Comparison of the custom analog IC simulations with MATLAB- and C-based FDTD code running on a modern workstation shows an expected average speedup of 205× and 140×, respectively.

On the edge turbulence effects on the density profile reconstruction using O-mode reflectometers

The effect of turbulence in the position measurements of the DEMO Plasma position reflectometer is evaluated at the high field side equatorial plane location using REFMULF, a 2D finite-difference time-domain full-wave code for reflectometry simulations. Different levels of turbulence (1–10%) of a Kolmogorov-like k-spectrum are analysed statistically with random generated density fluctuations. The study shows that for turbulence amplitudes in the range 1–7% most of the measurements are not affected significantly and the reflectometer can provide the position measurements within the DEMO requirements. For higher levels of turbulence, the mean error becomes negative and its absolute value and the standard deviation increases for values in the order of 0.5 cm. One of the reasons for this behavior is the deviation of the effective cut-off position. In these cases, part of the measurements are out of the requirements, and a study must be done to understand if the reconstruction of the separatrix stills possible for the order of error of the failed measurements (1–2 cm). Other possibility is to apply a correction based on the mean position value as function of the turbulence amplitude to the position measurements. This could be applied dynamically during the plasma pulse.

A Trial Acoustic Improvement in a Lecture Hall with MPP Sound Absorbers and FDTD Acoustic Simulations

Sound absorbing micro-perforated panels (MPPs) are being increasingly used because of their high quality in terms of hygiene, sustainability and durability. The present work investigates the feasibility and the performance of MPPs when used as an acoustic treatment in lecture rooms. With this purpose, three different micro-perforated steel specimens were first designed following existing predictive models and then physically manufactured through 3D additive metal printing. The specimens’ acoustic behavior was analyzed with experimental measurements in single-layer and double-layer configurations. Then, the investigation was focused on the application of double-layer MPPs to the ceiling of an existing university lecture hall to enhance speech intelligibility. Numerical simulations were carried out using a full-spectrum wave-based method: a finite-difference time-domain (FDTD) code was chosen to better handle time-dependent signals as the verbal communication. The present work proposes a workflow to explore the suitability of a specific material to speech requirements. The measured specific impedance complex values allowed to derive the input data referred to MPPs in FDTD simulations. The outcomes of the process show the influence of the acoustic treatment in terms of reverberation time (T30) and sound clarity (C50). A systematic comparison with a standard geometrical acoustic (GA) technique is reported as well.

Assessment of measurement performance for a low field side IDTT plasma position reflectometry system

The Italian Divertor Test Tokamak (IDTT) facility will study advanced exhaust solutions applicable to DEMO. This new machine also opens the possibility to test and validate relevant non-magnetic control diagnostics in support of a DEMO design implementation. Reflectometry, compatible with a full grade reactor implementation, has been proposed as a source of real-time (RT) plasma position and shape measurements for control purposes, in replacement or complement of standard magnetic measurements, to ensure reliability and safety on the machine. Additionally, such a system can be useful to obtain the characteristics of edge turbulence, useful for Neoclassical Tearing Mode (NTM) control or to improve the efficiency of other diagnostics as Collective Thomson Scattering (CTS). This new control technique based on multiple, poloidally distributed, non-magnetic measurements, must be tested, in all of its aspects, before it can be fully implemented in future fusion reactors. IDTT will be one of the best candidates to implement and build a knowledge database of nonstandard reflectometry (away from the equatorial plane) that will be needed on DEMO and is currently unavailable. The performance of three Ordinary mode (O-mode) Plasma Position Reflectometers (PPR) at the Lower Field Side (LFS) on IDTT is assessed using the two-dimensional (2D) full-wave Finite-Difference Time-Domain (FDTD) code, REFMULF, in two of the foreseen IDTT plasma scenarios: 5MA Single Null (SN) and Double Null (DN) configurations.

A Radio Frequency Analog Computer for Computational Electromagnetics

Software-programmable analog computing is proposed for power- and area-efficient acceleration of computational electromagnetics. All-pass filters are employed to realize a continuous-time finite-difference time-domain (FDTD) algorithm. A CMOS realization of an analog computer (AC) that solves the 1-D wave equation using this time-continuous FDTD algorithm at an equivalent temporal update rate of 625 MHz is reported (180-nm CMOS, chip area of 4 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , supply voltage = 1.8 V, and power = 200 mW). The AC operates at up to 30 MHz over 18 discrete spatial points. Analog arithmetic operations (multiply and add) are realized in parallel using op-amps with gain-bandwidth product > 500 MHz. Computational grid boundaries can be configured to simulate multiple propagation scenarios. The AC is calibrated using a stochastic optimization algorithm. The normalized mean squared error of the AC varies between -10 and -20 dB within the computational grid. The power- and area-normalized performance of the design improves on earlier integrated ACs by up to three orders of magnitude. The chip is also 26$\times $ faster than a C-based software FDTD solver running on an Intel Xeon CPU and $420\times $ faster than CUDA FDTD code running on an NVIDIA GeForce GTX 1080 Ti GPU, albeit at lower accuracy (~6 bits). Finally, the AC is $2.8\times $ faster than a digital systolic array FDTD processor realized using a Xilinx RFSoC ZCU1275 and has 15$\times $ better power efficiency (computations/W).

All-optical 1 × 2 decoder based on the self-collimated beam method in 2D photonic crystals

The design, analysis, and simulation of a 1 × 2 decoder based on self-collimated beams was the aim of this work. The proposed structure consists of two-dimensional (2D) photonic crystals with their silicon rods in air. The device, of a relatively simple structure with a footprint of 228.71 μm2, comprises two inputs (I and Iref) and three outputs (Q1, Q2, and QI). It, furthermore, contains two beam splitters, produced by point defects. 2D Finite Difference Time Domain (FDTD) and Plane Wave Expansion (PWE) codes have been used for the simulation. Contrast ratio of 2.02 dB and a bit rate of 2.8 Tb/s were obtained for this device - potential candidate for all-optical digital integrated circuits.

Exact analytical calculation and numerical modelling by finite-difference time-domain method of the transient transmission of electromagnetic waves through cold plasmas

The transient transmission of an electromagnetic wave through cold, unmagnetized and collisionless plasmas is described both analytically and numerically for its normal incidence from vacuum upon a plasma half-space. Exact formulas for the electromagnetic field are written in integral forms, which are convenient for approximate analysis and comparison with the results of direct numerical simulations. The time when the plasma particle oscillations become self-consistent with the electromagnetic field can be calculated from the simplified formulas for an arbitrary distance from the plasma–vacuum interface. Special attention is paid to the formation of the electrostatic oscillation in the case when the frequency of the incident wave is equal to the plasma frequency. The amplitudes of the vanishing magnetic field and the forming electrostatic oscillation are calculated as functions of time and the distance from the plasma–vacuum interface. The formation of the electrostatic oscillation is a slow process because the electromagnetic power penetrating into the plasma tends to zero with time. The transmitted plasma electromagnetic field is also simulated by the a finite-difference time-domain (FDTD) code. The difficulties of the numerical simulation of the quasi-electrostatic field are discussed. The analytical results can be used for the validation of the FDTD codes for plasma waves.

Full-Wave Modeling of Doppler Backscattering from Filaments

It is recognized that the filaments have a significant effect on the anomalous energy and particle transport in the tokamak periphery. They are actively investigated using various diagnostics in this regard. Recently studies of filaments using the Doppler backscattering method have been performed in the Globus-M and the ASDEX-Upgrade tokamaks. Backscattering from filaments manifests itself as a burst of quasi-coherent fluctuations of the signals of detectors. Such signals are easy to describe in the Born approximation using the diagnostic weighting function. However, the filaments in tokamaks differ noticeably in their size and intensity. With an increase in the amplitude of the filaments, it is necessary to consider the transition from linear scattering to nonlinear one and further up to the transition from backscattering to reflection from a moving filament. This problem can be solved only using a full wave code. Our simulation was carried out using the finite-difference time-domain code IPF-FD3D in slab geometry. We did not resort to using well-known non-linear MHD codes to determine filament parameters. In the simulation artificial filament-like perturbations were used, the parameters of which varied over a wide range. Modeling Doppler backscattering signal was focused on the identification of the influence of the amplitude of the filament and its size on the shape and the size of the Doppler backscattering output signal. The results obtained largely explain the similarity of the IQ detector data registered in different tokamaks.

2D full-wave simulations of conventional reflectometry using 3D gyro-fluid plasma turbulence

A synthetic reflectometer based on the 2D finite-difference time-domain full-wave code REFMUL is applied to data from 3D numerical simulations of edge and scrape-off layer plasma turbulence obtained with the GEMR code. Full-wave simulations are performed using the conventional reflectometry set-up with O-mode waves, fixed frequency probing and an equivalent I/Q detection scheme. Results show a significant spectral broadening of the synthetic reflectometry complex amplitude A(t)eiφ(t) with increasing probing frequency. The reflectometry response displays phase jumps which are due to the self-consistent evolution of turbulent density structures. The range ∼3%–6% of moderate turbulence amplitude is studied here, in the transition from the linear to nonlinear regimes of conventional reflectometry. While a phase jump removal algorithm is applied, spectral broadening of the phase with increasing probing frequency is nevertheless observed. Linear scaling of phase fluctuations with is also retrieved. REFMUL simulations with turbulence data rendered on both the GEMR field aligned coordinates (drift planes, neglecting circular magnetic flux surfaces) and on polar geometry (poloidal planes, taking into account plasma curvature) are carried out revealing similar trends on both coordinate systems. However, phase fluctuations obtained from poloidal planes display higher root mean square values, compared to drift planes. This could be expected from an increased sensitivity of the reflectometer to higher wavenumbers, due to plasma curvature effects.

Engineering the Eigenspace Structure of Massive MIMO Links Through Frequency-Selective Surfaces

We propose an efficient finite-difference time-domain (FDTD) computational paradigm to estimate the channel matrix of generic massive multiple-input–multiple-output (MIMO) systems. Working with a practical scenario with 196 base station (BS) elements and 6 equispaced user-equipment devices, we compute the dominant eigenspace for the uplink channel. The full-wave results are compared to conventional ray-tracing methods, with emphasis laid upon observing and understanding the electromagnetic (EM) impact of interelement mutual coupling and spherical wavefront illumination on the wireless MIMO channel properties. In particular, we investigate EM manipulation of massive MIMO channel structures by utilizing, especially, engineered wire-grid frequency-selective surfaces placed in the vicinity of the BS massive MIMO array. Using the in-house FDTD code, we demonstrate the capability of such passive structures to redistribute the illumination Poynting vector magnitude over the BS array aperture, as well as modifying the dominant eigenspace at certain design frequencies. This letter demonstrates the advantage of the synergy between rigorous EM analysis and stochastic communication theories and techniques, with expected applications in emerging wireless technologies (5G and beyond).

A first full wave simulation assessment of reflectometry for DTT

The Divertor Test Tokamak (DTT) facility is being proposed to study the exhaust solutions in tokamaks with a special look on DEMO, searching for alternatives to ITER's detached condition operation, for the case this solution proves inadequate. To know about the physical processes occurring in the plasma or for engineering needs and control uses, diagnostics play a major role and reflectometry, foreseen in the forthcoming generation of machines such as ITER and DEMO, is a useful asset for DTT. Assessing the different areas and applications that could be deployed on DTT is of significant importance from an early stage. We propose, therefore, to use numerical simulation using finite-difference time-domain codes (FDTD) of the REFMUL* family to implement synthetic reflectometry diagnostics. Different aspects are included such as propagation in the plasma, optimisation of the system location within the vacuum vessel, its access to the plasma (waveguide and antennas), or the signal processing techniques.

Fictitious wave domain modelling and analysis of marine CSEM data

SUMMARY Modelling marine controlled-source electromagnetic (CSEM) responses in the fictitious time domain is a novel approach, which facilitates the full exploration of EM diffusive properties in the fictitious wave domain (FWD). Concepts, such as reflections, refractions, diffractions and transmissions, which are used for the analysis of elastic wave propagation can thus be adopted in FWD for interpreting CSEM data. In this paper, we use a high-order finite difference time domain (FDTD) algorithm for modelling marine CSEM responses in both the fictitious time domain and the diffusive frequency domain. A complex frequency shifted perfectly matched layer (CFS–PML) boundary condition is adopted to the FDTD modelling. We demonstrate the performance of the CFS–PML boundary condition and validate the high-order FDTD code in the FWD with the half-space sea water model and in the frequency domain with the 1-D canonical reservoir model. We investigate and analyse the propagation characteristics of electromagnetic fields in the FWD, where we apply wave propagation concepts to interpret marine CSEM data. Similarities between wave and field propagations relevant for marine CSEM data are demonstrated through several 1-D to 3-D numerical examples.

High-frequency displacement current transformer with just one winding

PurposeThis paper aims to describe a new concept of transformer based on the displacement current. The paper shows how this idea can be translated into reality and presents an example of a working design.Design/methodology/approachThe authors replace the primary winding of the transformer with a capacitor. The displacement current between the capacitor plates induces a magnetic flux in the core. This flux in turn induces electromotive force in the classical secondary winding.FindingsThe basic mathematical aspects illustrated by results obtained from a simulation developed using a commercial software ANSYS-HFSS are given. The saturation of the magnetic core due to the applied high-frequency range is investigated and simulated using a finite difference time domain code implemented in MATLAB. A prototype transformer was built and tested; the obtained results confirm the previous ones from simulations.Originality/valueA new concept of the single winding transformer was used as a pulse forming circuit.

SURROGATE MODELING OF INDOOR DOWN-LINK HUMAN EXPOSURE BASED ON SPARSE POLYNOMIAL CHAOS EXPANSION

Human exposure induced by wireless communication systems increasingly draws the public attention. Here, an indoor down-link scenario is concerned and the exposure level is statistically analyzed. The electromagnetic field (EMF) emitted by a WiFi box is measured and electromagnetic dosimetry features are evaluated from the whole-body specific absorption rate as computed with a Finite-Difference Time-Domain (a.k.a. FDTD) code. Due to computational cost, a statistical analysis is performed based on a surrogate model, which is constructed by means of so-called sparse polynomial chaos expansion (PCE), where the inner cross validation (ICV) is used to select the optimal hyperparameters during the model construction and assess the model performance. However, the ICV error is optimized and the model assessment tends to be overly optimistic with small data sets. The method of cross-model validation is used and outer cross validation is carried out for the model assessment. The effects of the data preprocessing are investigated as well. Based on the surrogate model, the global sensitivity of the exposure to input parameters is analyzed from Sobol' indices.

Design and measuring performance of the ITER plasma position reflectometer in-port-plug antennas

Design parameters of the ITER Plasma Position Reflectometer (PPR) in-port-plug antennas are determined and their measurement performance is assessed using 2D full wave analysis. Two ITER scenarios were selected in order to determine the optimum antenna position and orientation, namely the ITER QDT = 10 baseline scenario (15 MA) and the low density one planned for the initial non-active phase at 7.5 MA. Using them to feed a 3D ray tracing code, the spatial position and optimum orientation angles of each set of emission and detection antennas were determined. Additionally, a far field analysis of the launching radiation patterns led to the definition of the antenna dimensions in terms of optimal power coupling. After this preliminary work, 2D full wave simulations using a finite difference time domain (FDTD) code were carried out to assess the measurement performance of the system. To this end, the detected wave amplitudes and phases were evaluated for each scenario and two models of the scrape-off layer (SOL) density profiles. By calculating the spectrogram of the complex amplitude of the detected wave, the reconstruction of the plasma density profile can be made and be directly compared with the input profiles. As a result from this synthetic diagnostic analysis, an estimation of the error in the determination of the last closed flux surface position was possible.

A Novel Dispersive Time-Domain Interaction Code for Helix TWT by Collocated Space and Staggered Time Scheme Pseudospectral Analytical Time-Domain Method

Remarkable advantages are achieved by pseudospectral techniques such as pseudospectral analytical time-domain (PSATD) method in numerical simulations. Examples are, but not limited to discretization effects reduction (e.g., numerical dispersion error) and geometrical dispersion consideration. In this paper, a novel well-organized version [a newly presented particle-wave interaction code (PaWaIC)], employing collocated space and staggered time scheme PSATD method is introduced: PaWaIC-PSATD-CSST. Validity of the new code is investigated. It is shown that a more accurate phase velocity is realized by PaWaIC-PSATD-CSST in comparison with PaWaIC-pseudospectral arbitrary order finite-difference time-domain (PaWaIC-PSAOFDTD) code for an identical time step and grid size. The fast single-run capability of this novel code for simulating pulse response of wideband tubes is also presented.

Turbulence level effects on conventional reflectometry using 2D full-wave simulations

Numerical simulations are critical in improving the capabilities of microwave diagnostics. In this work, the 2D finite-difference time-domain full-wave code REFMUL was applied to broadband turbulent plasmas using the conventional reflectometry setup. Simulations were performed with O-mode waves, fixed frequency probing, and I/Q detection. The plasma density, determining O-mode propagation, was modeled as the sum of a slab background plasma with a fluctuating component following a Kolmogorov-like amplitude k-spectrum. The density turbulence level δn e/n e was scanned over several orders of magnitude for simulated plasma flows of constant plasma velocity in either the radial or the poloidal direction. Simulations show trends, such as spectral broadening of the complex A(t)eiφ(t) signals and increasing fluctuations in A(t) and φ(t) with increasing δn e/n e, that are similar for both plasma flow directions. These together with possibilities to reconstruct a poloidal wavenumber spectrum are discussed in view of extending the measuring capabilities. The onset of non-linear effects associated with phase runaway, as previously observed with other 1D and 2D codes, as well as radial Doppler effects is also observed and discussed.