Finite-difference Time-domain Solver Research Articles

Retrospective 3D Modeling of RF Coils Using a 3D Tracker for EM Simulation

ABSTRACTThe 3D geometry of the RF coil in use is often unavailable when the RF coil is a commercial one or the RF coil has been developed through ad hoc modification of the coil shape at the laboratory. Without the coil geometry information, making a 3D model of the RF coil may be necessary to simulate the RF coil performance using a finite difference time domain (FDTD) solver. We used a stylus‐type 3D tracker to measure the 3D positions of the landmarks on the coil wires. From the measured landmark positions, we built 3D models of the coil wires using a 3D design tool. We also carried out FDTD simulation of the RF coil performances after transferring the 3D model data to the FDTD solver. For demonstration, we built 3D models of a shoulder coil and a 36‐channel helmet‐style array coil, and we computed B1 field maps of the coils using the FDTD solver. We think the proposed method can be greatly used for FDTD simulation of the RF coils in use whose geometries are unknown. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 43B: 126–132, 2013

High-Order Error-Optimized FDTD Algorithm With GPU Implementation

This paper presents the development of a two-dimensional (2-D) finite-difference time-domain (FDTD) solver that features reliable calculations and reduced simulation times. The accuracy of computations is guaranteed by specially-designed spatial operators with extended stencils, which are assisted by an optimized version of a high-order leapfrog integrator. Both discretization schemes rely on error-minimization concepts, and a proper least-squares treatment facilitates further control in a wideband sense. Given the parallelization capabilities of explicit FDTD algorithms, considerable speedup compared to serialized CPU calculations is accomplished by implementing the proposed algorithm on a modern graphics processing unit (GPU). As our study shows, the GPU version of our technique reduces computing times by several times, thus confirming its designation as a highly-efficient algorithm.

Solving 3D anisotropic elastic wave equations on parallel GPU devices

Efficiently modeling seismic data sets in complex 3D anisotropic media by solving the 3D elastic wave equation is an important challenge in computational geophysics. Using a stress-stiffness formulation on a regular grid, we tested a 3D finite-difference time-domain solver using a second-order temporal and eighth-order spatial accuracy stencil that leverages the massively parallel architecture of graphics processing units (GPUs) to accelerate the computation of key kernels. The relatively small memory of an individual GPU limits the model domain sizes that can be computed on a single device. To circumvent this constraint and move toward modeling industry-sized 3D anisotropic elastic data sets, we parallelized computation across multiple GPU devices by using domain decomposition and, for each time step, employing an interdevice communication protocol to exchange data values falling within interior boundaries of each subdomain. For two or more GPU devices within a single compute node, we use direct peer-to-peer (i.e., GPU-to-GPU) communication, whereas for networked nodes we employed message-passing interface directives to route data over the network. Our 2D GPU-based anisotropic elastic modeling tests achieved a [Formula: see text] speedup relative to an OpenMP CPU implementation run on an eight-core machine, whereas our 3D tests using dual-GPU devices produced up to a [Formula: see text] speedup. The performance boost afforded by the GPU architecture allowed us to model seismic data for 3D anisotropic elastic models at lower hardware cost and in less time than has been previously possible.

OpenCL‐based acceleration of the FDTD method in computational electromagnetics

SUMMARYThe evolution of processors into multi‐core architectures has led to the acceleration of scientific codes using numerous highly specialized processors, that is, multi‐core central processing units (CPUs), graphics processing units (GPUs) and also devices that merge both technologies in a single‐die chip. Development of parallel codes that are both scalable and portable between the processor architectures is challenging. To overcome this limitation, we investigated the acceleration of the finite‐difference time‐domain (FDTD) method in computational electromagnetics on modern computing architectures, that is, multi‐core CPUs and GPUs, through the use of Open Computing Language (OpenCL). Further extension of the OpenCL parallel programing model with the Message Passing Interface allows for the targeting of standard distributed memory computer clusters as well as clusters accelerated by GPUs. Portability between hardware manufactured by different vendors and highly specialized and parallel computing architectures is the main advantage of the developed FDTD solvers. The codes were coupled with a commercial simulation platform to evaluate the performance of the solvers in real‐world industrial scenarios. Although the portability resulted in a slightly reduced performance (10–35%) of the OpenCL‐accelerated FDTD simulations compared with the native Compute Unified Device Architecture or Open Multiprocessing implementations, the obtained benchmarking results of the OpenCL FDTD solvers on distributed memory systems show that the communication overhead can be hidden by computations for sufficiently large simulation domains with a scaling efficiency higher than 90%. Copyright © 2012 John Wiley & Sons, Ltd.

FDTD simulations of localization and enhancements on fractal plasmonics nanostructures

A parallelized 3D FDTD (Finite-Difference Time-Domain) solver has been used to study the near-field electromagnetic intensity upon plasmonics nanostructures. The studied structures are obtained from AFM (Atomic Force Microscopy) topography measured on real disordered gold layers deposited by thermal evaporation under ultra-high vacuum. The simulation results obtained with these 3D metallic nanostructures are in good agreement with previous experimental results: the localization of the electromagnetic intensity in subwavelength areas ("hot spots") is demonstrated; the spectral and polarization dependences of the position of these "hot spots" are also satisfactory; the enhancement factors obtained are realistic compared to the experimental ones. These results could be useful to further our understanding of the electromagnetic behavior of random metal layers.

An efficient time domain solver for the acoustic wave equation

An efficient numerical solver for time domain solution of the wave equation for the purpose of propagation in small and large acoustic spaces is presented. It is based on the adaptive rectangular decomposition technique that subdivides a space into rectangular partitions and within each partition utilizes the analytical solution of the wave equation for spatially invariant speed of sound. This technique allows numerical computations in kilohertz range for auralization and visualization purposes. This can help engineers to quickly locate geometric features responsible for acoustical defects in practical engineering applications like noise control. It is demonstrated that by carefully mapping all the components of the technique on the GPU architecture, significant improvement in performance can be achieved while maintaining accuracy comparable to a high-order finite difference time domain (FDTD) solver. It is an order of magnitude faster than corresponding CPU-based solver and three orders of magnitude faster than the CPU-based FDTD solver. This technique can perform a 1 s long simulation on complex-shaped 3D scenes of air volume 7500 cu m till 1650 Hz within 18 min on a desktop machine. The ideal session for this work is “Computational Acoustics”.

Interfacing Thin-Wire and Circuit Subcell Models in Unstructured Time-Domain Field Solvers

A method for driving and terminating Holland-Simpson based thin-wire models by arbitrary lumped-element circuits is proposed. The approach uses the fact that these thin-wire models result in modified Telegrapher's equations, and interfacing transmission lines and lumped-element circuits is straightforward. The thin-wire voltage and current at a circuit/wire junction can be written in terms of circuit nodal voltages and branch currents, permitting the circuit solution to act as a boundary condition for the thin-wire system. In this work, we provide the circuit/wire interfacing conditions and combine circuits with Edelvik's Holland-Simpson model that permits thin-wires to be arbitrarily oriented within an unstructured mesh. Edelvik's work, previously implemented for finite-difference and finite-element time-domain solvers is formulated for the finite-volume method. Numerical and experimental results for circuit-driven thin-wire antennas are provided to validate the method.

Parallelization of the FDTD method based on the open computing language and the message passing interface

A novel approach for parallelization of the finite-difference time-domain (FDTD) method based on open computing language (OpenCL) and the message passing interface (MPI) was presented. Because of the portability of OpenCL, the developed code targets not only distributed shared memory computer clusters based on multicore central processing units but also clusters accelerated by graphics processing units. Subsequently, this article shows the results of numerical tests to evaluate the hybrid MPI-OpenCL FDTD solver in electromagnetic simulations. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:785–789, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26610

Full-Wave Analysis of Traveling-Wave Field-Effect Transistors Using Finite-Difference Time-Domain Method

Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD) method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs), together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.

Multiphysics simulation of high-frequency carrier dynamics in conductive materials

We present a multiphysics numerical technique for the characterization of high-frequency carrier dynamics in high-conductivity materials. The technique combines the ensemble Monte Carlo (EMC) simulation of carrier transport with the finite-difference time-domain (FDTD) solver of Maxwell’s curl equations and the molecular dynamics (MD) technique for short-range Coulomb interactions (electron-electron and electron-ion) as well as the exchange interaction among indistinguishable electrons. We describe the combined solver and highlight three key issues for a successful integration of the constituent techniques: (1) satisfying Gauss’s law in FDTD through proper field initialization and enforcement of the continuity equation, (2) avoiding double-counting of Coulomb fields in FDTD and MD, and (3) attributing finite radii to electrons and ions in MD for accurate calculation of the short-range Coulomb forces. We demonstrate the strength of the EMC/FDTD/MD technique by comparing the calculated terahertz conductivity of doped silicon with available experimental data for two doping densities and showing their excellent agreement.

An efficient GPU-based time domain solver for the acoustic wave equation

An efficient algorithm for time-domain solution of the acoustic wave equation for the purpose of room acoustics is presented. It is based on adaptive rectangular decomposition of the scene and uses analytical solutions within the partitions that rely on spatially invariant speed of sound. This technique is suitable for auralizations and sound field visualizations, even on coarse meshes approaching the Nyquist limit. It is demonstrated that by carefully mapping all components of the algorithm to match the parallel processing capabilities of graphics processors (GPUs), significant improvement in performance is gained compared to the corresponding CPU-based solver, while maintaining the numerical accuracy. Substantial performance gain over a high-order finite-difference time-domain method is observed. Using this technique, a 1 s long simulation can be performed on scenes of air volume 7500 m 3 till 1650 Hz within 18 min compared to the corresponding CPU-based solver that takes around 5 h and a high-order finite-difference time-domain solver that could take up to three weeks on a desktop computer. To the best of the authors’ knowledge, this is the fastest time-domain solver for modeling the room acoustics of large, complex-shaped 3D scenes that generates accurate results for both auralization and visualization.

On the use of the method of moments in plasmonic applications

In the last 40 years the method of moments (MOM) has been a cornerstone in the field of computational electromagnetics. Traditionally, this method has been used to solve integral equations formulated for antennas and other components in the microwave frequency range and below. In this paper, the application of MOM in the field of plasmonics is briefly reviewed. First, existing literature is referenced. Then the differences with the classical implementations are pointed out. Finally, its applicability, advantages, and disadvantages are discussed. This is done by comparing it with a numerical finite difference time domain solver well‐known in the plasmonics research community for a number of example structures. It is shown that also at these higher frequencies, namely in the IR and optical range, MOM is a very powerful technique.

Optical Dispersion Models for Time-Domain Modeling of Metal-Dielectric Nanostructures

We discuss second-order complex Padé approximants which give a systematic approach to time-domain modeling of dispersive dielectric functions. These approximants, which also reduce to the classical Drude, Lorentz, Sellmeier, critical points and other models upon appropriate truncation, are used to compare frequency domain (FD) versus time-domain (TD) simulations of local optical responses and the transmission-reflection spectra for a plasmonic nanostructure. A comparison is also made using auxiliary differential equations (ADE), and second order recursive convolution (RC) formulations embedded in finite-difference, finite-volume, and finite-element time-domain solvers.

The influence of the reflective environment on the absorption of a human male exposed to representative base station antennas from 300 MHz to 5 GHz

The environment is an important parameter when evaluating the exposure to radio-frequency electromagnetic fields. This study investigates numerically the variation on the whole-body and peak spatially averaged-specific absorption rate (SAR) in the heterogeneous virtual family male placed in front of a base station antenna in a reflective environment. The SAR values in a reflective environment are also compared to the values obtained when no environment is present (free space). The virtual family male has been placed at four distances (30 cm, 1 m, 3 m and 10 m) in front of six base station antennas (operating at 300 MHz, 450 MHz, 900 MHz, 2.1 GHz, 3.5 GHz and 5.0 GHz, respectively) and in three reflective environments (a perfectly conducting wall, a perfectly conducting ground and a perfectly conducting ground + wall). A total of 72 configurations are examined. The absorption in the heterogeneous body model is determined using the 3D electromagnetic (EM) finite-difference time-domain (FDTD) solver Semcad-X. For the larger simulations, requirements in terms of computer resources are reduced by using a generalized Huygens' box approach. It has been observed that the ratio of the SAR in the virtual family male in a reflective environment and the SAR in the virtual family male in the free-space environment ranged from −8.7 dB up to 8.0 dB. A worst-case reflective environment could not be determined. ICNIRP reference levels not always showed to be compliant with the basic restrictions.

Optimization of Reduced-Size Smooth-Walled Conical Horns Using BoR-FDTD and Genetic Algorithm

An accurate optimization tool has been developed to design arbitrarily-shaped axis-symmetrical devices. It is based on the combination between a genetic algorithm (GA) and a finite-difference time-domain (FDTD) solver formulated in a cylindrical coordinate system. For validation purposes, this tool is applied to design several smooth-walled compact conical horns with a large flare angle (90°) in the 60-GHz band. The unavoidable phase distortions appearing in the horn aperture are compensated by loading the horn mouth with thin shaped dielectric lenses made in Rexolite. Based on these test cases, several synthesis strategies are discussed and compared in order to select the best antenna prototype among those synthesized. A scaled version of this prototype has been fabricated to operate around 29.5 GHz. The numerical and experimental results are in excellent agreement. Horn size reduction rates up to 80% have been reached.

Compact 3-D Envelope ADI-FDTD Algorithm for Simulations of Coherent Radiation Sources

A modified complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain solver for electromagnetic (EM) fields is presented. Like the conventional ADI scheme, the modified scheme is based on splitting the time step into two halves. In each substep, Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The new scheme is a combination of the conventional CE-ADI scheme and the leapfrog ADI scheme that was recently reported. The main features are a more compact form of the tridiagonal equations and greater flexibility in the application of boundary conditions. The boundary conditions on the six faces of the solution box are general and can be specified either as perfect conductor, symmetry boundary conditions, cavity modes, or arbitrary external specification. The new compact CE-ADI scheme is unconditionally stable; thus, the time step can be larger than the one imposed by the Courant-Friedrichs-Lewy (CFL) condition. Fast stable EM simulations of a planar slow-wave structure are demonstrated, with time steps exceeding the CFL limit by two orders of magnitude.

FDTD modeling of realistic semicontinuous metal films

We have employed a parallelized 3D FDTD (finite-difference time-domain) solver to study the electromagnetic properties of random, semicontinuous, metal films. The structural features of the simulated geometries are exact copies of the fabricated films and are obtained from SEM images of the films themselves. The simulation results show good agreement with the experimentally observed far-field spectra, allowing us to also study the nonlinear moments of the optical responses for these realistic nanostructures.

Ground effects in time-domain simulations of outdoor sound propagation.

Finite-difference, time-domain (FDTD) methods are precise and powerful tools to solve linearized Euler equations. Interaction between the acoustic waves with local wind or temperature gradients as well as a complex topography can be taken into account. Recently, a time-domain boundary condition has been proposed [Cotté et al., AIAA J. 47, 2391–2403 (2009)] and has been implemented in a FDTD solver using methods developed in the computational aeroacoustics community [Bogey and Bailly, J. Comput. Phys. 194, 194–214 (2004)]. Propagation of an initial pulse over a distance of 500 m in a two-dimensional geometry is considered in a frequency band up to 1200 Hz. Surface waves which propagate close to and parallel to impedance grounds are exhibited. To validate the obtained results, a comparison is made in the time-domain with an analytical solution. Ground effects are discussed depending on the impedance of the ground. [This work was performed using HPC resources from GENCI-IDRIS (Grant 2009-022203).]

Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique

We present terahertz-frequency characterization of doped silicon via a multiphysics numerical technique that couples ensemble Monte Carlo (EMC) simulation of carrier transport and a finite-difference time-domain (FDTD) solver of Maxwell’s curl equations. We elucidate the importance of rigorous enforcement of Gauss’s law, in order to avoid unphysical charge buildup and enhance solver accuracy. The calculated complex conductivity of doped bulk silicon shows excellent agreement with available experimental data. This comprehensive microscopic simulator is a valuable predictive tool in the terahertz frequency range, where experimental data are scarce and the Drude model inadequate.

Rotman lens design and simulation in software [Application Notes

Since its invention in the early 1960s (Rotman and Turner, 1963), the Rotman Lens has proven itself to be a useful beamformer for designers of electronically scanned arrays. Inherent in its design is a true time delay phase shift capability that is independent of frequency and removes the need for costly phase shifters to steer a beam over wide angles. The Rotman Lens has a long history in military radar, but it has also been used in communication systems. This article uses the developed software to design and analyze a microstrip Rotman Lens for the Ku band. The initial lens design will come from a tool based on geometrical optics (GO). A second stage of analysis will be performed using a full wave finite difference time domain (FDTD) solver. The results between the first-cut design tool and the comprehensive FDTD solver will be compared, and some of the design trades will be explored to gauge their impact on the performance of the lens.