Explicit Finite-difference Time-domain Research Articles

An Explicit and Unconditionally Stable FDTD Method for Electromagnetic Analysis

In this paper, an explicit and unconditionally stable finite-difference time-domain (FDTD) method is developed for electromagnetic analysis. Its time step is not restricted by the space step, and its accuracy is ensured for the time step chosen based on accuracy. The strength of the conventional explicit FDTD is thus preserved in avoiding a system matrix solution, while the shortcoming of the conventional FDTD is eliminated in the time step's dependence on space step. Numerical experiments in both 2-D and 3-D simulations have demonstrated the performance of the proposed method in stability and efficiency without sacrificing accuracy.

Simulations and measurements of 3-D ultrasonic fields radiated by phased-array transducers using the westervelt equation.

The purpose of this work is to validate, by comparing numerical and experimental results, the ability of the Westervelt equation to predict the behavior of ultrasound beams generated by phased-array transducers. To this end, the full Westervelt equation is solved numerically and the results obtained are compared with experimental measurements. The numerical implementation of the Westervelt equation is performed using the explicit finite-difference time-domain method on a three-dimensional Cartesian grid. The validation of the developed numerical code is first carried out by using experimental data obtained for two different focused circular transducers in the regimes of small-amplitude and finite-amplitude excitations. Then, the comparison of simulated and measured ultrasonic fields is extended to the case of a modified 32-element array transducer. It is shown that the developed code is capable of correctly predicting the behavior of the main lobe and the grating lobes in the cases of zero and nonzero steering angles for both the fundamental and the second-harmonic components.

A Novel 3-D HIE-FDTD Method With One-Step Leapfrog Scheme

This paper presents a novel 3-D leapfrog hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method. By first adopting the Peaceman–Rachford scheme and then the one-step leapfrog scheme, the proposed HIE-FDTD algorithm is implemented in the same manner as the traditional finite-difference time-domain method in which the implicit scheme was applied only in the direction where a fine grid was applied and the explicit scheme was applied in two other directions where a larger grid was used. Further, by introducing auxiliary field variables denoted by $e$ and $h$ , the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical analysis demonstrated that the Courant–Friedrichs–Lewy stability condition of the proposed HIE-FDTD method is determined only by one grid cell size, which is more relaxed than those of the existing HIE-FDTD methods, and the numerical dispersion error is less than that of the alternating-direction implicit method.

Alternating Direction Implicit Methods for FDTD Using the Dey-Mittra Embedded Boundary Method

The alternating direction implicit (ADI) method is an attractive option to use in avoiding the Courant- Friedrichs-Lewy (CFL) condition that limits the size of the time step required by explicit finite-difference time-domain (FDTD) methods for stability. Implicit methods like Crank-Nicholson offer the same advantages as ADI methods but they do not rely on simple, one-dimensional, tridiagonal system solves for which there are well-known fast solution methods. To date, the ADI method applied to the FDTD method for curved domains has been used within the context of subgridding (i.e., local refinement) or for stairstepped boundaries that are only first-order accurate. A popular second- order accurate approach to representing smooth domains with the FDTD method is the Dey-Mittra embedded boundary method. However, to be useful in a realistic setting, the cells with only a small fraction of their volume inside the domain need to be discarded from simulations for stability considerations or else the time step size will be prohibitively small. Using the ADI method instead of the explicit method implies that time step can be chosen to depend on accuracy and no cells need discarding. We show in this paper the ability to maintain stability beyond the CFL limit for the Dey-Mittra method without discarding any cells. We also consider convergence of the ADI method as compared to the standard explicit method that is limited by the CFL condition.

3P2-2 Reflective boundary condition with arbitrary boundary shape for compact explicit-finite difference time domain method(Poster Session)

3P2-2 Reflective boundary condition with arbitrary boundary shape for compact explicit-finite difference time domain method(Poster Session)

Numerical study of the effect of defect layer on unmagnetized plasma photonic crystals

In this paper an explicit finite-difference time domain scheme developed in staggered grids is used to solve the Maxwell's equations in Drude medium. Besides the preservation of discrete zero-divergence condition in electric and magnetic fields, we also aim to conserve the inherent conservation laws in simple medium all the time using the temporally second-order accurate explicit symplectic partitioned Runge-Kutta scheme. Within the framework of a semidiscretized method, the first-order spatial derivative terms in Faraday's and Ampere's equations are approximated to get an accurate numerical dispersion relation equation. The derived numerical angular frequency is accurately related to the wavenumber of Maxwell's equations for the space centered scheme of fourth-order accuracy. The resulting symplectic finite difference scheme developed in the time domain minimizes the difference between the exact and numerical group velocities. This newly proposed scheme is applied to model EM waves in the unmagnetized plasma crystal which contains a defect layer in photonic crystal. Our purpose is to numerically study the effects of defect layers on the propagation insight.

Three-Dimensional Sound Field Analysis Using Compact Explicit-Finite Difference Time Domain Method with Graphics Processing Unit Cluster System

In this study, the compact explicit-finite difference time domain (CE-FDTD) method is applied to the three-dimensional sound field analysis to reduce computer resources. There are various derivative schemes in the CE-FDTD method. They are first examined theoretically to evaluate the numerical accuracy. As a theoretical result, it is found that the interpolated wide band (IWB) scheme has the widest bandwidth in which the cut-off frequency is in agreement with the Nyquist frequency. The calculation performance is theoretically estimated, then experimentally evaluated with the graphics processing unit cluster system. As a result, it is found that the memory usage of the IWB scheme is less than one-third of that of the standard leapfrog (SLF) scheme to achieve the same cut-off frequency. It is also found that the calculation time of the IWB scheme with the shared memory is about 19% compared with that of the SLF scheme with the graphics processing unit (GPU) cluster system. The impulse response is calculated for a large room with a volume capacity of about 4500 m3 in which the sampling rate was 40 kHz. It is confirmed that the three-dimensional sound field with the natural reverberation can be calculated by the IWB scheme.

Large-scale sound field rendering with graphics processing unit cluster for three-dimensional audio with loudspeaker array

The sound field rendering is a technique to simulate the sound field from the three-dimensional numerical models constructed in the computer, and it is the same concept as the graphics rendering in the computer graphics. In this paper, a graphics processing unit (GPU) cluster system is applied to the sound field rendering for a large room simulation. The compact explicit finite difference time domain (CE-FDTD) method is implemented on the GPU cluster system. The CE-FDTD method is a kind of the finite difference method in which the wave equation is directly discretized based on the central differences. The developed GPU cluster system consists of eight PC nodes in which four GPUs are mounted respectively. The rendering results are reproduced by a speaker array system in which 157 speakers surround a small room. The sound field renderings are performed for a large room with a volume capacity of about 5000 cubic meters, in which the impulse responses of one-second length with a sampling rate of 40 kHz are calculated at 157 points corresponding to the loudspeaker positions. The impulse responses are then convoluted with dry music sources. The sound field rendering with the 157ch loudspeaker array system provides the realistic sound field reproduction with natural reverberation.

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.

Unconditionally Stable Fundamental LOD-FDTD Method With Second-Order Temporal Accuracy and Complying Divergence

An unconditionally stable fundamental locally one-dimensional (LOD) finite-difference time-domain (FDTD) method with second-order temporal accuracy and complying divergence (CD) (denoted as LOD2-CD-FDTD) is presented for three-dimensional (3-D) Maxwell's equations. While the conventional LOD-FDTD method does not have complying divergence, the LOD2-CD-FDTD method has complying divergence in a manner analogous to the conventional explicit FDTD method. The update procedures for a family of LOD-FDTD methods that employ similar splitting matrix operators are presented. By extending the previous concept of achieving second-order temporal accuracy for the LOD2-FDTD method via implicit output processing, we hereby propose novel, explicit output processing that not only retains second-order temporal accuracy, but also complying divergence for the LOD2-CD-FDTD method. The current source implementation for the LOD2-CD-FDTD method involves source-incorporation in only the first procedure. To further enhance efficiency, the LOD2-CD-FDTD method is formulated into the fundamental LOD2-CD-FDTD method with efficient matrix-operator-free right-hand sides. Subsequently, detailed implementation for the fundamental LOD2-CD-FDTD method is presented. Analytical proof is provided to ascertain the second-order temporal accuracy of the LOD2-CD-FDTD method. Numerical results and examples are also presented to validate the divergence-complying property of the LOD2-CD-FDTD method.

Application of the Z-transform technique to modeling the linear lumped networks in the HIE-FDTD method

In this work, a new lumped-network hybrid implicit–explicit finite-difference time-domain (LN-HIE-FDTD) method has been proposed. This method is derived from combining the 3D HIE-FDTD method with the Z-transform technique for the hybrid system including linear lumped networks. It possesses the advantage of deriving the updating equations immediately for complex circuits. The accuracy of the proposed method is verified from the comparison of calculated results given by the proposed method and the conventional lumped-network FDTD (LN-FDTD) method. The efficiency of the proposed method is verified from the comparison of the CPU time by the two methods. It is demonstrated that the proposed method is numerically efficient while time-saving.

Finite difference time domain analysis of extended composite right/left-handed transmission line equations

In this article, a set of differential equations to model the behavior of the extended composite right/left handed transmission line in time domain is proposed. These equations are solved by an explicit finite difference time domain algorithm. To investigate the numerical stability of the proposed algorithm, the amplification matrix is extracted. The results of the proposed algorithm are confirmed by the results of the Agilent ADS commercial software. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:68–76, 2014.

Parallelized finite difference time domain room acoustic simulation

A parallelized room acoustics simulator based on the finite difference time domain (FDTD) method is developed, utilizing a Blue Gene/L supercomputer. Wave-based methods such as FDTD are desirable for use in room acoustics simulations since they account for effects such as diffraction and interference. However, such methods require large amounts of computational power and memory, especially when simulating large volumes or high frequencies. To utilize the power of modern computing systems and move toward large-scale simulations of realistic concert halls, a parallel FDTD implementation is written in the C++ programming language with the Message Passing Interface (MPI) library. The volume to be simulated is partitioned into blocks, which efficiently update shared interfaces between nearest neighbors using the Blue Gene architecture's point-to-point communication network. Several compact explicit FDTD schemes are compared using simulations of various spatial volumes, executed on varying numbers of processors. The use of a Blue Gene/L supercomputer demonstrates substantial speedup over an equivalent serial implementation.

Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.

A locally one‐dimensional finite difference time domain method for the analysis of a periodic structure at oblique incidence

An implicit finite difference time domain (FDTD) method is developed to analyze periodic structures at oblique incidence. The split‐field technique is applied to the locally one‐dimensional (LOD) FDTD method with the periodic boundary condition. In addition, the dispersion control parameters are introduced to reduce the numerical dispersion error. The effectiveness of the present method is investigated through the analysis of a photonic band gap structure. It is shown that the computational time is reduced to ≅16% of that of the explicit FDTD method with acceptable results being maintained. As an application, a broadband mirror consisting of a subwavelength grating is analyzed and discussed.

Alternating-direction explicit scheme for the 2D finite-difference time-domain method for TEz waves

In this article, a new explicit finite-difference time-domain (FDTD) method is proposed to eliminate the Courant–Friedrich–Levy (CFL) condition restraint. This new algorithm is based on an alternating-direction explicit (ADE) method and Crank–Nicolson (CN) scheme. Called CN-ADE-FDTD method, and we present two versions of the proposed method. Numerical stability analysis of the new algorithm was also presented. Furthermore, the results by the CN-ADE-FDTD method are compared with the results by the conventional FDTD method. As a result, it is confirmed that the proposed method is unconditionally stable and superior to the conventional one. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2689–2694, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26346

Frequency-Dependent 3-D LOD-FDTD Method for the Analysis of Plasmonic Devices

A simple trapezoidal recursive convolution technique is utilized to develop a frequency-dependent locally one-dimensional finite-difference time-domain (FDTD) method for the three-dimensional analysis of dispersive media. A gap plasmonic waveguide is analyzed and the numerical results are compared with those of the traditional explicit FDTD. A time step ten times as large as that determined from the stability criterion can be allowed to reduce computational time by 40%, offering acceptable numerical results. A plasmonic grating is analyzed as an application.

Room Acoustics Simulation Using 3-D Compact Explicit FDTD Schemes

This paper presents methods for simulating room acoustics using the finite-difference time-domain (FDTD) technique, focusing on boundary and medium modeling. A family of nonstaggered 3-D compact explicit FDTD schemes is analyzed in terms of stability, accuracy, and computational efficiency, and the most accurate and isotropic schemes based on a rectilinear grid are identified. A frequency-dependent boundary model that is consistent with locally reacting surface theory is also presented, in which the wall impedance is represented with a digital filter. For boundaries, accuracy in numerical reflection is analyzed and a stability proof is provided. The results indicate that the proposed 3-D interpolated wideband and isotropic schemes outperform directly related techniques based on Yee's staggered grid and standard digital waveguide mesh, and that the boundary formulations generally have properties that are similar to that of the basic scheme used.

An Elliptical Cylindrical FDTD Algorithm for Modeling Conformal Patch Antenna

An explicit finite-difference time-domain (FDTD) method is described using a uniform elliptical cylindrical spatial grid for time-domain Maxwell's equations to accurately and efficiently model conformal elliptical cylindrical line-fed patch antennas and overcome stair-casing errors. Such errors are encountered when a Cartesian spatial grid is used for modeling curved surfaces. In addition, the method described in this paper obviates coding complexity encountered in modeling of curved surfaces which is manifest using CP-FDTD or CFDTD techniques. Characterizing expressions representing the absorbing boundary condition and Courant stability condition are presented and used to provide a highly effective algorithm to simulate conformal microstrip antennas. The proposed FDTD algorithm is validated against HFSS results showing excellent correlation.

Improved hybrid implicit–explicit finite-difference time-domain method with higher accuracy and user-defined stability condition

An improved hybrid implicit–explicit finite-difference time-domain (IHIE-FDTD) method is presented in this paper. Compared with the conventional hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method, this new method has higher accuracy. The time-step size in the IHIE-FDTD is determined by a user-defined parameter and is arbitrarily alterable. The numerical performance of the proposed method over the conventional HIE-FDTD method and alternating-direction implicit finite-difference time-domain method is demonstrated through numerical examples.