Overcoming Memory Bandwidth Limitations In GPU-Accelerated Finite-Difference Time-Domain Simulations: A systolic update scheme

To date, numerical analysis for sound wave propagation in time domain has been investigated widely as a result of advances in computer technology. The finite difference time domain (FDTD) methods are very widely used for time domain numerical analysis. The following is a family of FDTD method, for example, the standard FDTD method based on Yee’s algorithm, wave equation FDTD (WE-FDTD) method, the FDTD(2,4) method, and so on. The FDTD and WE-FDTD methods cause numerical dispersion error due to using second order finite difference (FD) approximation. To overcome this problem, the FDTD(2,4) method using higher order spatial FDs have been proposed. On the other hand, the settings of the interface between different media are important issue to solve acoustic wave propagation in non-uniform media. In this study, we examine the dependence on calculation parameters in the settings of interface for some FDTD methods. The present study shows dependence on the CFL number and ratio of sound velocity and impedance between the boundaries. We demonstrate that accuracy of the interface between different media strongly depend on calculation parameters and the ratio of sound velocity. Moreover, the proposal settings of the interface for the FDTD(2,4) methods are more accurate.

The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the time-dependent Schrödinger equation (TDSE) in imaginary time. The TDSE is numerically solved with an initial random wave function and after enough simulation time, the wave function converges to the ground state wave function. The excited states are determined by using the same procedure for the ground state with additional constraints that the wave function must be orthogonal with all lower energy wave functions. The numerical results for energies and wave functions for different parameters of confinement potentials are given and compared with published results using other numerical methods. It is shown that the FDTD method gives accurate energies and wave functions.

Photonic crystals have shown a great deal of promise for the realization of true integrated optics. Waveguides with small bends may be formed allowing compact integrated photonic circuits to be formed. Full three- dimensional (3D) photonic simulations are required in order to realize very low loss, integrated photonic crystal circuits. Needless to say, the design and fabrication of such fully 3D structures is challenging, and thus efficient simulation tools are necessary to identify the optimum structures for different applications. Researchers at the Department of Defense (DoD) and Arizona State University (ASU) have independently developed parallel Finite Difference Time Domain (FDTD) codes, with the goal of scaling up each simulator for complicated structures such as 3D optical integrated circuits (OIC). As the name implies, FDTD is a popular time-domain method for solving Maxwell's equations for the electric and magnetic fields. These two curl equations are solved explicitly in time over half-step intervals, where the values of one set of field values (e.g., electric fields) are used at the successive interval to solve for the other field (e.g., magnetic field) in a time marching fashion. The goal of our current work is to realize a fully parallel FDTD code scalable to 108 FDTD grid points in order to have sufficient resolution to model even a relatively limited number of periods of a given waveguide structure. This requires both a scalable parallel FDTD code, as well as one with the proper boundary conditions and more efficient algorithms to reduce run. The work and results discussed herein address both the scalability and the efficiency of the time-domain algorithm. Index Terms: Finite-difference time-domain (FDTD) methods, photonic crystals, parallel processing, electromagnetic analysis.

In this paper, we consider electromagnetic (EM) wave propagation in nonlinear optical media in one spatial dimension. We model the EM wave propagation by the time-dependent Maxwell’s equations coupled with a system of nonlinear ordinary differential equations (ODEs) for the response of the medium to the EM waves. The nonlinearity in the ODEs describes the instantaneous electronic Kerr response and the residual Raman molecular vibrational response. The ODEs also include the single resonance linear Lorentz dispersion. For such model, we will design and analyze fully discrete finite difference time domain (FDTD) methods that have arbitrary (even) order in space and second order in time. It is challenging to achieve provable stability for fully discrete methods, and this depends on the choices of temporal discretizations of the nonlinear terms. In Bokil et al. (J Comput Phys 350:420–452, 2017), we proposed novel modifications of second-order leap-frog and trapezoidal temporal schemes in the context of discontinuous Galerkin methods to discretize the nonlinear terms in this Maxwell model. Here, we continue this work by developing similar time discretizations within the framework of FDTD methods. More specifically, we design fully discrete modified leap-frog FDTD methods which are proved to be stable under appropriate CFL conditions. These method can be viewed as an extension of the Yee-FDTD scheme to this nonlinear Maxwell model. We also design fully discrete trapezoidal FDTD methods which are proved to be unconditionally stable. The performance of the fully discrete FDTD methods are demonstrated through numerical experiments involving kink, antikink waves and third harmonic generation in soliton propagation.

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing

In this study, we examine the acoustic simulation method combining the wave equation finite difference time domain (WE FD-TD) method and compact FDs (CPFDs) for the second derivative.The wave equation compact finite difference time domain (WE CPFD-TD) method does not require calculation of the particle velocity; therefore, it can reduce the calculation time and memory used.Furthermore, for acceleration of simulation, we employ the recursive filtering algorithm and graphics processing unit (GPU) computing.As a result, we clarified that the threedimensional WE CPFD-TD acoustic simulation using GPU is ca.25-30 times faster than that using CPU with OpenMP.

In this study, we examine the acoustic simulation method combining the wave equation finite difference time domain (WE FD-TD) method and compact FDs (CPFDs) for the second derivative. The wave equation compact finite difference time domain (WE CPFD-TD) method does not require calculation of the particle velocity; therefore, it can reduce the calculation time and memory used. Furthermore, for acceleration of simulation, we employ the recursive filtering algorithm and graphics processing unit (GPU) computing. As a result, we clarified that the three-dimensional WE CPFD-TD acoustic simulation using GPU is ca. 25–30 times faster than that using CPU with OpenMP.

The finite difference time-domain (FDTD) method was used to study the nuclear electromagnetic pulse (NEMP) waves and the continuous sinusoidal wave of different frequency coupling into one metallic container through a small aperture in one face of the container. The incident electric fields of NEMP were expressed by double exponential functions with two different decay constants. Based on the algorithm of thin material sheets in the FDTD method, the finite-difference expressions of the electromagnetic components at the common boundary of two thin sheets are dealt with distinguishingly. A method to compute the shielding effectiveness of the metal enclosure with an aperture and thin walls is introduced. The time-domain behavior of the electric field inside the metallic container excited by the waves was obtained by the FDTD method. The results of FDTD and ETL method are compared in order to verify the validity of FDTD modeling.

Photonic crystals have shown a great deal of promise for the realization of true integrated optics. Waveguides with small bends may be formed allowing compact integrated photonic circuits to be formed. Full three dimensional (3D) photonic simulations are required in order to realize very low loss, integrated photonic crystal circuits. Needless to say, the design and fabrication of such fully 3D structures is challenging, and thus efficient simulation tools are necessary to identify the optimum structures for different applications. Researchers at the Department of Defense (DoD) and Arizona State University (ASU) have independently developed parallel Finite Difference Time Domain (FDTD) codes, with the goal of scaling up each simulator for complicated structures such as 3D optical integrated circuits (OIC). As the name implies, FDTD is a popular time-domain method for solving Maxwell's equations for the electric and magnetic fields. These two curl equations are solved explicitly in time over half-step intervals, where the values of one set of field values (e.g., electric fields) are used at the successive interval to solve for the other field (e.g., magnetic field) in a time marching fashion. In previously reported work, a fully parallel FDTD code scalable to 107 FDTD grid points was presented and showed good scalability up to 200 processors. The goal of our current work has been to realize a more optimized and efficient implementation requiring significantly less memory and scalable to thousands of processors. This requires both a scalable parallel FDTD code, as well as one with improved absorbing boundary conditions and more efficient algorithms to reduce runtime. The work and results discussed herein address both the scalability and the efficiency of the time-domain algorithm.

Dielectric resonator antennas (DRAs) are a relatively new class of antenna that utilizes the radiation phenomena of dielectric resonators in open space. Since mainly analytical approaches have been applied to investigate DRA designs, the current DRA forms are limited to simple geometric shapes and high‐performance DRAs with complex shapes have not yet been developed. Topology optimization is capable of yielding high‐performance structures, and has been extensively applied to a variety of structural optimization problems. Applying it to the task of DRA design may be extremely useful for the design of high‐performance antennas. On the other hand, the finite difference time domain (FDTD) method has been used to numerically evaluate general antenna performance, since it is numerically robust during time domain analyses and can handle complex models. Thus, the integration of topology optimization with the FDTD method has the potential to enable innovative designs of advanced antennas that offer exceptional performance. In this research, we propose a new topology optimization method for the design of DRAs that aim to operate with enhanced bandwidths, using the FDTD method. First, the concept of topology optimization is briefly discussed, and a way to integrate topology optimization with the FDTD method is proposed. Next, design requirements are clarified and the corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several DRA design examples are presented to confirm the usefulness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

Environmental haptic sensations are reproduced by means of machine admittance control. Conventional reproduced environments are expressed by a stiffness and viscosity model and Finite Element Method(FEM) . In this research, multi-inertia environmental haptic sensations that are composed of multiple mass, stiffness, and viscosity values are reproduced based on machine admittance control by using the finite difference time domain (FDTD) method. In this study, we observe the frequency characteristics from the external force to be stored for the position response, calculate the complex equation from the motion equation for each frequency, and obtain the characteristic matrix of the environment by means of the least squares method. The obtained parameter can be used, as it is as a parameter of the FDTD method. This method is suitable for the method of rendering the environmental haptic sensations using the FDTD method and machine admittance control.

This article presents an explicit fourth‐order accurate Finite Difference Time Domain (FDTD) method, in which the fourth‐order accurate staggered Adams‐Bashforth time integrator is used for temporal discretization and the fourth‐order accurate Taylor Central Finite Difference scheme for spatial discretization. The analysis shows that the numerical dispersion of the new FDTD method is much lower than that of the Fang‐FDTD method and the stability restraint of the new FDTD methods is relaxed in comparison with that of the FDTD method using the Staggered Backward Differentiation time integrator. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 910–912, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22303

Antireflection structured surface was analyzed by a finite difference time domain (FDTD) method in the visible light spectrum. The antireflection structured array was conical moth-eye structures. Comparing the reflectance of different aspect ratios by the FDTD method, we found that the reflectance was less than 1% when the aspect ratio was larger than 0.8 in the visible light spectrum. In order to confirm the results by this simulation method, the conical structured arrays of a polymer film were fabricated by the holographic lithography and a following replicating process. The conical structured arrays were fabricated with the periodic length of 350nm and the height of 300nm. The simulation results by FDTD method were compared with those by the fabricated sub-wavelength structures. The experimental results showed highly consistent with the simulation results.

In this paper, the propagation characteristics of the fields in a planar waveguide, a synchronous-waveguides and a s-bended waveguide were simulated with the Finite Difference Time Domain (FDTD) method. The distribution graphs of the field intensities for the simulated optical waveguides were obtained. Coupling lengths were gained from the data of graphs. By comparing these results with that simulated with beam propagating method (BPM), it is concluded that during simulating waveguide with relatively simple structure the simulation performed by the FDTD method are better in accord with the BPM analysis, but with relative complex structure such as the s-bended waveguide the FDTD method can simulated much better than the BPM dose. So during simulating waveguide with complex structure the FDTD method is the better option.

This paper presents a new hybrid method for the calculation of the radiation field outside the shielding enclosure. The method computes the tangential component of the electric field on the opening by finite difference time domain (FDTD) method to determine the equivalent magnetic current source. This magnetic current, once determined, can be used to ascertain the radiate field anywhere external to the opening in a shielding enclosure. The accuracy of the proposed method is verified by comparing the exterior radiation fields with those calculated by full FDTD and the traditional hybrid method. Simulation results show that the new hybrid method significantly reduces the computational effort and time, but still maintains satisfactory results. It also shows that the proposed method is very effective for the far field in that the computational effort, as compared with that of the near field, does not increase remarkably.