Conventional Finite-difference Time-domain Method Research Articles

An overlapping Yee finite-difference time-domain method for material interfaces between anisotropic dielectrics and general dispersive or perfect electric conductor media

SUMMARY A novel stable anisotropic finite-difference time-domain (FDTD) algorithm based on the overlapping cells is developed for solving Maxwell's equations of electrodynamics in anisotropic media with interfaces between different types of materials, such as the interface between anisotropic dielectrics and dispersive medium or perfect electric conductor (PEC). The previous proposed conventional anisotropic FDTD methods suffer from the late-time instability due to the extrapolation of the field components near the material interface. The proposed anisotropic overlapping Yee FDTD method is stable, as it relies on the overlapping cells to provide the collocated field values without any interpolation or extrapolation. Our method has been applied to simulate electromagnetic invisibility cloaking devices with both anisotropic dielectrics and PEC included in the computational domain. Numerical results and eigenvalue analysis confirm that the conventional anisotropic FDTD method is weakly unstable, whereas our method is stable. Copyright © 2013 John Wiley & Sons, Ltd.

A Krylov Stability-Corrected Coordinate-Stretching Method to Simulate Wave Propagation in Unbounded Domains

The Krylov subspace projection approach is a well-established tool for the reduced-order modeling of dynamical systems in the time domain. In this paper, we address the main issues obstructing the application of this powerful approach to the time-domain solution of exterior wave problems. We use frequency-independent perfectly matched layers to simulate the extension to infinity. Pure imaginary stretching functions based on Zolotarev's optimal rational approximation of the square root are implemented leading to perfectly matched layers with a controlled accuracy over a complete spectral interval of interest. A new Krylov-based solution method via stability-corrected operator exponents is presented which allows us to construct reduced-order models (ROMs) that respect the delicate spectral properties of the original scattering problem. The ROMs are unconditionally stable and are based on a renormalized bi-Lanczos algorithm. We give a theoretical foundation of our method and illustrate its performance through a number of numerical examples in which we simulate two-dimensional electromagnetic wave propagation in unbounded domains, including a photonic waveguide example. The new algorithm outperforms the conventional finite-difference time-domain method for problems on large time intervals.

Alternating‐direction explicit algorithms for crank–nicolson‐based FDTD methods

AbstractThis article proposes a new unconditionally stable explicit finite‐difference time‐domain (FDTD) scheme for 3D Maxwell equation.The proposed scheme is based on alternating‐direction explicit method and Crank–Nicolson (CN)‐based FDTD method, and we present two versions of the proposed method. Numerical stability and dispersion analysis of the new algorithm were also presented. The results by the proposed method are compared with the results by the conventional FDTD method, alternating‐direction implicit method, and CN‐based FDTD method. As a result, it is confirmed that the proposed method is unconditionally stable and the efficiency is superior to the conventional method if the minimum cell size in the computational domains is required to be much smaller than the wavelength. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:1269–1273, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26802

Time-reversal transcranial ultrasound beam focusing using a k-space method

This paper proposes the use of a k-space method to obtain the correction for transcranial ultrasound beam focusing. Mirroring past approaches, a synthetic point source at the focal point is numerically excited, and propagated through the skull, using acoustic properties acquired from registered computed tomography of the skull being studied. The received data outside the skull contain the correction information and can be phase conjugated (time reversed) and then physically generated to achieve a tight focusing inside the skull, by assuming quasi-plane transmission where shear waves are not present or their contribution can be neglected. Compared with the conventional finite-difference time-domain method for wave propagation simulation, it will be shown that the k-space method is significantly more accurate even for a relatively coarse spatial resolution, leading to a dramatically reduced computation time. Both numerical simulations and experiments conducted on an ex vivo human skull demonstrate that precise focusing can be realized using the k-space method with a spatial resolution as low as only 2.56 grid points per wavelength, thus allowing treatment planning computation on the order of minutes.

Implementation of Absorbing Boundary Conditions Based on the Second-Order One-Way Wave Equation in the LOD- and the ADI-FDTD Methods

This letter describes the implementation of second-order one-way wave-equation absorbing boundary conditions (ABCs) in two unconditionally stable finite-difference time-domain (FDTD) methods-namely the locally one-dimensional (LOD)- and the alternating-direction implicit (ADI)-FDTD methods. The Higdon second-order absorbing operator is discretized in the same way as when it is used with the conventional FDTD method. The resulting discrete expression is directly applied to the electric field in each time substep of the LOD- and the ADI-FDTD methods. Numerical examples are given to illustrate the validity of the proposed approach.

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

A k-Space Method for Moderately Nonlinear Wave Propagation

A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.

WCS-FDTD Algorithm for Periodic Structures

In this letter, the weakly conditional technique is applied to the finite-difference time-domain (FDTD) method, called WCS-FDTD in short. It is combined with periodic boundary condition (PBC), so periodic structures can be solved by using this method conveniently. When the explicit difference calculations are performed in the directions with larger spatial increments, the time-step is thus determined by the larger spatial increments, and the stability condition is less strict than the conventional FDTD method. In order to save the CPU running time, the Sherman–Morrison formula is used to solve the nontridiagonal linear systems. Compared to ADI-FDTD method, this method has better accuracy and computational efficiency. Numerical results are given to demonstrate the effectiveness of the proposed method.

A Hybrid Approach for Solving Coupled Maxwell and Schrödinger Equations Arising in the Simulation of Nano-Devices

A hybrid numerical technique for solving coupled Schrodinger and Maxwell's equations for the simulation of nano-devices is presented. The finite-difference time-domain (FDTD) method is applied to Schrodinger's equation, while the locally one-dimensional finite-difference time-domain (LOD-FDTD) method is applied to Maxwell's equations for efficient simulation of the coupled equations. Results of the proposed approach are compared to those obtained via the conventional FDTD method.

A Nonorthogonal ADI-FDTD Algorithm for Solving Two Dimensional Scattering Problems

In this paper, an alternating-direction implicit (ADI) scheme is applied to the finite-difference time-domain (FDTD) method for solving electromagnetic scattering problems in a generalized coordinate system. A formulation for two dimensional problems is presented and its numerical dispersion and stability property are discussed. In our generalized approach, the nonorthogonal grid is used to model the complex region of a scatterer only, whereas the standard FDTD lattice is used for the remaining regions. As a result, accurate griddings with a simple algorithm can be obtained using the new scheme, and the complexity of the algorithm is minimal. The perfectly matched layer (PML) is used to truncate the boundary. To illustrate the theory, a sinusoidal plane wave and a Gaussian pulse that propagates through a space modeled by locally nonorthogonal grids are used, with the stability of the code examined. The radar cross section of a perfectly conducting cylinder with a thin coating, a large curvature, and/or a sharp edge is calculated using the proposed method, and the result is compared with those using other conventional FDTD methods. It is found that the proposed algorithm is much more efficient than its FDTD counterpart when a complex object is analyzed.

Three-dimensional hybrid implicit–explicit finite-difference time-domain method in the cylindrical coordinate system

A novel hybrid implicit–explicit (HIE) finite-difference time-domain (FDTD) method, which is extremely useful for problems with very fine structures along the ϕ-direction in cylindrical coordinate system, is presented. This method has higher computation efficiency than conventional cylindrical FDTD methods, because the time step in this method is only determined by the space discretisations in the radial and vertical directions. The numerical stability of the proposed HIE–FDTD method is presented analytically. Compared with the cylindrical alternating-direction implicit (ADI)–FDTD method, this HIE–FDTD method has higher accuracy, especially for larger time step size. At each time step, the HIE–FDTD method requires the solution of two tridiagonal matrices and four explicit updates. While maintaining the same size of time step, the central processing unit (CPU) time for this weakly conditionally stable FDTD method can be reduced to about 3/5 of that for the ADI–FDTD scheme. The numerical performance of the proposed HIE–FDTD over the conventional cylindrical FDTD method and cylindrical ADI–FDTD method is demonstrated through numerical examples.

Meshless Radial Basis Function Method for Transient Electromagnetic Computations

We propose a novel numerical method to simulate transient electromagnetic problems. The time derivatives are still tackled with the customary explicit leapfrog time scheme. But in the space domain, the fields at the collocation points are expanded into a series of radial basis functions and are treated with a meshless method procedure. Our method solves numerically Maxwell's equations with various assigned boundary conditions and current source excitation. Furthermore, the numerical stability condition of our method is obtained through a one-dimensional (1-D) wave equation and thus the relationship between control parameters is accounted for. To verify the accuracy and effectiveness of the new formulation, we compare the results of the proposed method with those of the conventional finite-difference time-domain method through a 1-D case study with different boundary conditions.

An Efficient FDTD Method for Axially Symmetric LWD Environments

In this paper, an unconditionally stable finite- difference time-domain (FDTD) method in cylindrical coordinates is developed to analyze electromagnetic responses under axially symmetric measure-while-drilling/logging-while-drilling (MWD/LWD) environments. The method is based on the application of the Crank-Nicholson scheme to the FDTD method in cylindrical coordinates. To accelerate the solution of this approach, an algebraic multigrid method is applied. For several MWD/LWD electromagnetic simulations, it is observed that the proposed method can be close to 20 times faster than the conventional FDTD method.

局所境界要素法によるイメージセンサの３次元波動光学シミュレーション

A novel wave optical simulation method (a localized boundary element method) has been developed. This method enables us to execute 3-D wave optical simulation with much smaller memory space and much shorter calculation time than conventional boundary element methods or FDTD (Finite Difference Time Domain) methods. The color shading characteristics of inner lens structures in CCD image sensors and the light-gathering power and crosstalk of light waveguide structures in CMOS image sensors can be analyzed by this method. This method was found to be powerful and useful for wave optical analysis of image sensors.

Two-Dimensional FDTD Analysis of the Readout Characteristics of an Optical Near Field Disk

Various kinds of optical near-field apertures have been proposed for higher throughput and smaller spot size. However, few studies have mentioned the readout characteristics of the recorded marks on an optical disk illuminated by a near field optical light. In this paper, we have investigated the scattering light by a two-dimensional recorded mark on a phase change disk with Finite-Difference Time-Domain (FDTD) simulations. Instead of using Recursive Convolution (RC) and Piecewise Linear Recursive Convolution (PLRC) scheme, we integrated the motion equation of free electron into conventional FDTD method to solve the electromagnetic field in the metallic materials. The validity of the proposed method is illustrated by comparing its results with those from the analytic exact solution. We analyzed the distributions of optical near-field around a two-dimensional metallic nano-aperture, and then calculated the far-field scattering pattern from a two-dimensional recorded mark on a phase change disk while it was illuminated by an optical near-field though a nanoaperture. The sum signal by a condenser lens was calculated from far-field pattern, and its relationships with the width of recorded mark and the thickness of each layer in the phase change disk were illustrated. The cross-talk between the recorded marks was also discussed.

Analysis of microstrip discontinuities by FDTD method combined with SOC technique

In this paper, the application of the finite-difference time-domain (FDTD) algorithm combined with the short-open calibration SOC technique to three-dimensional microstrip discontinuity is presented. This SOC technique is directly accommodated in the FDTD algorithm. It is used to remove the unwanted parasitic errors brought by the approximation of the impressed voltage sources and the feed lines. The FDTD is formulated in such a way that the port voltages and currents are explicitly represented through relevant network matrices. This new method is also used to analyze finite periodic structures. The scattering parameters of the whole periodic structure can be approximately obtained through analyzing only one cell of it. The results for microstrip discontinuities and finite periodic structures are compared with the conventional FDTD method.

A compact one‐dimensional modal FDTD method

AbstractThe finite‐difference time‐domain (FDTD) method is an effective technique for computing wideband electrical parameters such as scattering parameters of waveguide structures. in the computations, a known incident is normally required and is usually obtained with a simulation of a long uniform structure. For a three‐dimensional problem, simulation of a long structure can be very memory‐ and CPU time‐intensive. In addition, effective absorbing boundary conditions are needed to effectively terminate the structure even at and below the cutoff frequencies. To address these issues, many one‐dimensional FDTD methods and absorbing schemes were proposed. However, they all have dispersion characteristics different from those of the conventional FDTD method, leading to undesired errors or reflections. In this paper, a new one‐dimensional scheme is developed that has numerical dispersion characteristics very similar to that of the conventional FDTD method. When used as the absorbing boundary condition, it generates reflections of less than −200 dB even at and below the cutoff frequencies for the considered modes. When used to obtain the incident wave, its results have difference of less than −200 dB from that produced by the conventional FDTD method. Copyright © 2007 John Wiley & Sons, Ltd.

A novel and efficient subgridding scheme in FDTD method using the Crank‐Nicolson algorithm

AbstractSubgridding algorithms in the finite‐difference time‐domain (FDTD) method are applicable and efficient in handling problems containing fine structural features. Only regions surrounding the fine features need to be discretized with a finer spatial grid to avoid finely discretizing the whole computation domain but still maintaining the desired accuracy. A novel subgridding scheme using the Crank‐Nicolson (CN) method to update the field components in the fine grid region is proposed in this article. Combined with the Douglas‐Gunn algorithm to convert the block tri‐diagonal matrix of the CN method into pure tri‐diagonal form, the proposed method is efficient at solving circuit problems and scattering problems. Accuracy of the proposed method is verified by comparison with results from a conventional FDTD method with fine spatial increment. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 3103–3106, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22932

Accurate modeling of the optical properties of left-handed media using a finite-difference time-domain method

This paper contains an important message regarding the numerical modeling of left-handed media (LHM) using the finite-difference time-domain (FDTD) method which remains at the moment one of the main techniques used in studies of these exotic materials. It is shown that conventional implementation of the dispersive FDTD method leads to an inaccurate description of evanescent waves in the LHM. This defect can be corrected using spatial averaging at the interfaces. However, a number of results obtained using the conventional FDTD method have to be reconsidered. For instance, accurate simulation of subwavelength imaging by the finite-sized slabs of left-handed media does not reveal the cavity effect reported by Chen [Phys. Rev. Lett. 92, 107404 (2004)]. Hence the finite transverse dimension of LHM slabs does not have significant effects on the subwavelength image quality, contrary to previous assertions.

FDTD Characterization of UWB Indoor Radio Channel Including Frequency Dependent Antenna Directivities

This letter presents a modeling of ultrawideband (UWB) indoor radio channel using the finite-difference time-domain (FDTD) method. By dividing the frequency band (3-11 GHz) into eight subbands, the conventional FDTD method is applied to calculate the channel impulse responses (CIRs). At the centre frequency of each subband, measured frequency dependent dielectric constant/loss factor of different indoor materials are used and antenna patterns are taken into account by applying the equivalence principle with the total-field/scattered-field approach. Radio channel modeling results show that the base station antenna pattern variations at different frequencies can considerably influence the channel behavior in a UWB indoor environment