Finite-difference Time-domain Grid Research Articles

Stochastic Reduced-Order Electromagnetic Macromodels in FDTD

To enable an efficient stochastic-based design optimization methodology for multiscale structures of electrical devices, circuits, and systems, we propose the infusion of stochastic modeling with the electromagnetic macromodel in the method of finite-difference time domain (FDTD). We enhance the computational efficiency of the stochastic macromodel by applying the model order reduction techniques to produce the stochastic reduced-order macromodel. In addition, we provide a methodology and algorithms for the efficient generation and application of the stochastic reduced-order macromodel in the FDTD grid. The proposed methodology quantifies the impact of uncertainty in the electromagnetic system response that is manifested as random material and structural variations, through modeling and simulation. We demonstrate the proposed methodology by applying it to the computation of the stochastic transient electromagnetic fields in a 3-D bandgap structure comprising a rectangular waveguide, which contains an array of dielectric posts that exhibit uncertainty.

Huygens Excitation in Debye Media in the FDTD Method

The total-field/scattered-field method, also called the Huygens surface method, is a common method to enforce an incident wave in a finite-difference time domain grid filled with a vacuum. In this communication, it is shown that it can also be used in such dispersive media as the Debye media. The incident wave to be enforced on the Huygens surface is computed either by an analytical calculation in the general case or by means of the auxiliary grid technique in special cases. As in a vacuum, the leakage of energy outside the Huygens surface is lower than −40 dB with the analytical incident wave and it can be far lower with the auxiliary grid incident wave.

Deterministic Reduced-Order Macromodels for Computing the Broadband Radiation-Field Pattern of Antenna Arrays in FDTD

The enhanced nodal-order reduction (ENOR) technique is used to perform model-order reduction (MOR) on a macromodel of a subgridded finite-difference time domain (FDTD) region which contains the deterministic fine structural features [1] of an aperture antenna array laying in a larger and relatively coarser FDTD grid, to solve the broadband time-varying electromagnetic fields emanating from the antenna array and to obtain the far-field radiation patterns. The far-field radiation pattern computed in FDTD is correlated against results computed through physical optics approximation . This work lays the foundation for a separate but related work to follow, in which we further develop the above deterministic macromodel into a stochastic macromodel that addresses the problem of uncertainty in fine features of structures with disparate spatial scales.

A 2-D enlarged cell technique (ECT) for elastic wave modelling on a curved free surface

The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of the structured grid. This is similar to the situation for the FDTD method in electromagnetics when it is applied to model a curved perfect conductor surface, where the conformal FDTD methods have been recently developed to avoid this error. In this work a stable and second-order accurate 2-D FDTD method for elastic wave modelling on a curved free surface is presented based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the meantime, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability even for small irregular cells. This method is verified by several 2-D numerical examples. Results show that the method is second-order accurate and stable at the Courant stability limit for a regular FDTD grid.

FDTD Computation for Sar Induced in Human Head Due to Exposure to EMF from Mobile Phone

This aim of this paper is to investigate the specific absorption rate (SAR) distribution in a human head by using the finite-difference time-domain (FDTD) calculations, due to exposure to EMF radiation from a mobile phone at frequencies 900 MHz Mobile Phone model with a λ/2 monopole antenna and a hand head phone model dimensions are 100 mm x 50 mm x 20 mm. The head model used is a sphere with a diameter of 18 cm. The FDTD grid size used in the computation was 2.5 mm. The distance between the antenna and head was 5 mm. To simplify the FDTD simulation, the SAR in the head was calculated without the effect of the human body. It was found that the SAR induced in the head decreases with the distance from the radiating source.

Numerical simulation of pressure waves in the cochlea induced by a microwave pulse.

The pressure waves developing at the cochlea by the irradiation of the body with a plane wave microwave pulse are obtained by numerical simulation, employing a two-step finite-difference time-domain (FDTD) algorithm. First, the specific absorption rate (SAR) distribution is obtained by solving the Maxwell equations on a FDTD grid. Second, the temperature rise due to this SAR distribution is used to formulate the thermoelastic equations of motion, which are discretized and solved by the FDTD method. The calculations are performed for anatomically based full body human models, as well as for a head model. The dependence of the pressure amplitude at the cochlea on the frequency, the direction of propagation, and the polarization of the incident electromagnetic radiation, as well as on the pulse width, was investigated.

Incorporating Effective Media in the Finite-Difference Time-Domain Method for Spherical Nanoparticle Modeling

A computational formulation is presented for the low frequency single-cell finite-difference time-domain (FDTD) modeling of nanospheres. The methodology is developed based on the observation that the electrostatic field inside a dielectric sphere is similar in nature to that of an FDTD cell, or equivalently by considering the electromagnetic correspondence between the single electric field component across an FDTD cell edge, and the electric dipole moment induced in an electrically small dielectric sphere when the latter is excited by a plane wave. By rigorously applying effective medium theory the physical existence of a subcell dielectric sphere in the FDTD grid is translated into an equivalent material, characterized by an effective permittivity that obeys the Clausius-Mossotti (CM) mixing rule, appropriately defined across the cell edge parallel to the excitation plane wave. A circuit based methodology is devised that allows to easily incorporate the effective medium representation of a subcell dispersive dielectric sphere into FDTD update equations. The theoretically derived results are supported by numerical experiments.

Analytical Expression for the Time-Domain Discrete Green's Function of a Plane Wave Propagating in the 2-D FDTD Grid

In this letter, a new closed-form expression for the time-domain discrete Green's function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of AFP requires computations of time-domain DGF for the plane wave with the use of multiple-precision arithmetic. Then, excitations at the TFSF interface can be computed as a time-domain convolution of a source function with DGF. The developed time-domain implementation of AFP demonstrates the leakage error across the TFSF interface around the numerical noise level that validates the correctness of the DGF derivation.

Computation of tightly-focused laser beams in the FDTD method.

We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method. We provide an error analysis, and guidelines for the discrete approximation. We analyze the scattering of the beam from layered spaces and individual scatterers. The described method should be useful for the simulation of confocal microscopy and optical data storage. An implementation of the method can be found in our free and open source FDTD software ("Angora").

Introduction of Oblique Incidence Plane Wave to Stratified Lossy Dispersive Media for FDTD Analysis

In the application of finite-difference time-domain (FDTD) method to the wideband plane wave scattering analysis of objects embedded in stratified lossy dispersive media, it is a challenge to solve the obliquely incident wave. In this work, a novel configuration of auxiliary one-dimensional (1-D) FDTD grids is proposed to provide the obliquely incident plane wave at the total-field scattered-field (TFSF) boundary in stratified lossy dispersive media. Thus a closed TFSF boundary is formed, where the incident waves are directly obtained from the auxiliary simulations without any interpolation. The formulations of the auxiliary simulations are presented by the modified 1-D Maxwell's equations. Given the dispersion characteristic, perfectly matched layer (PML) is implemented to the 1-D simulations. Examples demonstrate the effectiveness of the proposed technique of obliquely incident wave introduction.

A hybrid finite‐element/finite‐difference method with an implicit–explicit time‐stepping scheme for Maxwell's equations

SUMMARYThis paper describes a hybrid technique in time domain that combines the explicit finite‐difference time‐domain (FDTD) method and the implicit finite‐element time‐domain (FETD) method based on the discontinuous Galerkin method to analyze transient electromagnetic problems. In the hybrid method, the FETD part uses the unconditionally stable Crank–Nicholson method with a triangular mesh, whereas the standard FDTD part employs a staggered Cartesian grid for spatial discretization and the leap‐frog scheme for time stepping. Nonconforming meshes are allowed between the structured FDTD grid and unstructured FETD meshes. The hybrid method takes advantages of the modeling flexibility of the FETD method for complex structures and the efficiency of the FDTD method for simple structures. The hybrid implicit–explicit time‐stepping scheme allows a time‐step increment as large as the stability limit for the FDTD method, which can be much larger than the stability criterion of the explicit FETD scheme with small elements. The hybrid scheme has second‐order accuracy. Numerical examples demonstrate the efficiency of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Subcell FDTD Based on Z Transforms Modeling of Electrically Thin Dispersive Layers

A novel technique for treating electrically thin dispersive layers with the finite-difference time-domain (FDTD) method based on Z transforms is introduced. The proposed model is based on the subcell technique, where the constitutive relations are locally averaged in the FDTD grid. The most significant feature of the proposed model is its ability to model rather complicated dispersive layers having multiple pole pairs. Then, based on the model above, the model for pulse reflection from a coated ideal conductor is proposed. The models are validated with several numerical examples making comparison with the exact results.

Analytic Fields With Higher-Order Compensations for 3-D FDTD TF/SF Formulation With Application to Beam Excitations

The total-field/scattered-field (TF/SF) formulation is widely used to initiate incident waves for scattering problems in finite-difference time-domain (FDTD) simulations. An important aspect of the TF/SF formulation is the calculation of incident fields at the TF/SF boundary by methods that account for the numerical nature of the incident wave in the FDTD grid. Failure to do so can lead to high levels of field leakage errors across the TF/SF boundary. This paper presents an improved analytic time-domain method for accurately computing incident fields in the TF/SF formulation. Using analytic field expressions with higher-order dispersion and polarization compensations, the proposed method compensates for 1) the FDTD numerical dispersion; and 2) the lack of orthogonality between the frequency-dependent field polarizations and the wavevector, which was not accounted for in existing analytic time-domain methods. The higher-order compensations result in further suppression of field leakage errors in the SF region. In addition to exciting a plane wave, the proposed method can be employed to excite an incident beam. To demonstrate this, numerical experiments that source both 3-D plane wave and focused beam into a free space FDTD grid are presented and compared with existing methods.

The Huygens subgridding for the numerical solution of the Maxwell equations

The Huygens subgridding (HSG) is a subgridding technique developed for the numerical solution of the Maxwell equations. It relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents. The application of this concept to the finite-difference time-domain (FDTD) method has been previously published in the one dimensional and two dimensional cases. In this paper the HSG is extended to the general three dimensional case, the exchange of the electromagnetic energy between the two FDTD grids is investigated theoretically, and some modifications to the HSG algorithm are presented with the objective of simplifying its implementation.

Characterization of the Numerical Group Velocity in Yee's FDTD Grid

A method is introduced for the optimization of the numerical group velocity in standard finite-difference time-domain (FDTD) electromagnetic simulations. Through this method analytical expressions for the extrema of are presented for the first time, thus also characterizing its anisotropy. The knowledge of these expressions is hence essential for the evaluation of the anisotropy error in FDTD-based electrodynamics simulations of the propagation of wavepackets in 2D and 3D. This can be of assistance, for example, in the design of error-bounded FDTD simulations with pulsed sources at low computational cost.

Computation of the acoustic radiation force using the finite-difference time-domain method

The computational details related to calculating the acoustic radiation force on an object using a 2-D grid finite-difference time-domain method (FDTD) are presented. The method is based on propagating the stress and velocity fields through the grid and determining the energy flow with and without the object. The axial and radial acoustic radiation forces predicted by FDTD method are in excellent agreement with the results obtained by analytical evaluation of the scattering method. In particular, the results indicate that it is possible to trap the steel cylinder in the radial direction by optimizing the width of Gaussian source and the operation frequency. As the sizes of the relating objects are smaller than or comparable to wavelength, the algorithm presented here can be easily extended to 3-D and include torque computation algorithms, thus providing a highly flexible and universally usable computation engine.

On the FDTD Near-to-Far-Field Transformations for Weakly Scattering Objects

Recently published papers on the near-to-far-field (NTFF) transformation in the finite-difference time-domain (FDTD) method have demonstrated accuracy improvements for weakly scattering objects. The improvements are achieved by modifications of the “standard” NTFF transformation which is based on interpolation of the spatially shifted fields in the FDTD grid. In this paper, it is shown that accurate results can be obtained for such weakly scattering objects without the suggested improvements, provided that the correct FDTD NTFF transformation is used. “Correct” is referred to a transformation procedure that is consistent with the FDTD version of the equivalence principle. This NTFF transformation procedure was published in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION in 1998. Recently published results for weakly scattering objects have been reproduced using this NTFF transformation.

A modificatory algorithm for electrically thin dispersive layers base on shift operator finite-difference time-domain method

A novel technique for treating electrically thin dispersive layer with the finite difference time domain (FDTD) method is introduced. The proposed model is based on modifying the node update equations to account for the layer, where the electric and magnetic flux densities are locally averaged in the FDTD grid. Then, based on the characteristics that the complex permittivity and complex permeability of three kinds of general dispersive media model, i.e. Debye model, Lorentz model, and Drude model, may be described by rational polynomial fraction in jω, the shift operator method is then applied to obtain the recursive formulation for D and E, B and H available for FDTD computation is obtained. The model is validated with several numerical examples. The computed results illustrate the generality, memory and time step economy and the precision of presented scheme.

Transient Chip-Package Cosimulation of Multiscale Structures Using the Laguerre-FDTD Scheme

Transient simulation using Laguerre polynomials is unconditionally stable and is ideally suited for modeling structures containing both small and large feature sizes. The focus of this paper is on the automation of this technique and its application to chip-package cosimulation. Laguerre finite-difference time-domain (FDTD) requires using the right number of basis coefficients to generate accurate time-domain waveforms. A method for generating the optimal number of basis functions is presented in this paper. Equivalent circuit models of the FDTD grid have been developed. In addition, a method for simulation over a long time period is also presented that enables the extraction of the frequency response both at low and high frequencies. A node numbering scheme in the circuit model of the FDTD grid that is suitable for implementation has been discussed. Results from a chip-package example that shows the scalability of this technique to solve multiscale problems have been presented.

General finite-difference time-domain solution of an arbitrary electromagnetic source interaction with an arbitrary dielectric surface

In this study, we develop a numerical algorithm to calculate the interaction of an arbitrary electromagnetic beam with an arbitrary dielectric surface as one of the tools necessary to design and build a detector network based on surface-enhanced Raman scattering (SERS). By using the scattered-field finite-difference time-domain (FDTD) method with incident source terms in the FDTD equations, this development enables an arbitrary incident beam to be implemented onto an arbitrary dielectric surface or particle. Most importantly, in this study a scattered-field uniaxial perfectly matched layer (SF-UPML) absorbing boundary condition (ABC) is developed to truncate the computational domain of the scattered-field FDTD grid. The novel SF-UPML for the scattered-field FDTD algorithm should have a numerical accuracy similar to that of the conventional uniaxial perfectly matched layer for the source-free FDTD equations. Using the new ABC, the scattered-field FDTD method can accurately calculate electromagnetic wave scattering by an arbitrary dielectric surface or particles illuminated by an arbitrary incident beam.