Nonorthogonal Finite-difference Time-domain Method Research Articles

Characterization of the Specific Absorption Rate of the Cell Phone in the Human Head, Using the LN-FDTD Method

In this work we show how the study of the absorption of electromagnetic energy will be approached in biological tissues of the human head, originating from cell phones in a 900MHz band, and the development of a program to calculate the Specific Absorption Rate (SAR) in the cell phone user’s head. The implementation of the Local Non-Orthogonal Finite-Difference Time Domain method is presented (LN-FDTD), and the use of Uniaxial Perfectly-Matched Layer (UPML), comparing the results obtained with the existing results in the literature.

Calculation of induced voltages on curved overhead transmission lines: analysis by using the non-orthogonal finite difference method

It is carried out a study regarding the catenaries of the lines of a three-phase transmission system with its neutral conductor grounded at two points. It is investigated the effect of electromagnetic field impinging on such transmission lines (due to lightning currents) by performing the calculation of induced voltages on the conductors. The numerical solution of Maxwell's equations is obtained by using the non-orthogonal finite-difference time-domain method.

Three-Dimensionally Nonorthogonal Alternating-Direction Implicit Finite-Difference Time-Domain Algorithm for the Full-Wave Analysis of Microwave Monolithic Circuit Devices

An alternating-direction implicit finite-difference time-domain (FDTD) algorithm is applied to the full wave analysis of microwave integrated circuit devices. A 3-D multidomain method is developed in nonorthogonal coordinates. Nonorthogonal grids are only used for the anomalistic regions of a complex structure, whereas the standard FDTD lattice is used for the other regions. By using the Jacobian coordinate transformation, curvilinear coordinates can be converted into conventional FDTD format expediently. The perfectly matched layer is used to truncate the boundary. Accurate griddings using the new scheme are obtained, and the complexity of the algorithm is minimal. To illustrate the theory, a sinusoidal plane wave and a Gaussian pulse that propagate through a localized nonorthogonal grid space is used, and the stability of our code is examined. A newly developed compact microstrip bandpass filter is analyzed using the proposed method. The simulated results agree very well with measurements. As compared to other nonorthogonal FDTD (NFDTD) method, the proposed algorithm is much more efficient than other NFDTD counterpart when complex structures are analyzed.

Generalized Alternating-Direction Implicit Finite-Difference Time-Domain Method in Curvilinear Coordinate System

In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.

ADI-FDTD algorithm in curvilinear co-ordinates

The alternating direction implicit (ADI) scheme has been successfully applied to the finite-difference time-domain (FDTD) method to achieve an unconditionally stable algorithm. The ADI-FDTD method is extended to the curvilinear co-ordinate system to form an alternating direction implicit nonorthogonal FDTD (ADI-NFDTD) method. The numerical results show that the proposed ADI-NFDTD algorithm demonstrates better late time stability compared to the conventional NFDTD scheme.

Theoretical bandgap modeling of two-dimensional square photonic crystals fabricated by the interference of three noncoplanar laser beams

We have investigated numerically the photonic bandgap (PBG) and spectral properties of two-dimensional (2-D) square structures fabricated by holographic lithography. Based on the block-iterative frequency-domain method and on the nonorthogonal finite-difference time-domain method, we have calculated band structure as a function of intensity threshold and shown that the PBG of 2-D titania arrays opens only for TM polarization and that directional PBGs can be obtained simultaneously for TE- and TM-polarized waves. In addition, we have shown that symmetry reduction of the atom introduced by holographic lithography can lift the band degeneracies and create an absolute PBG for a square lattice of dielectric rods in air.

Modelling metallic discontinuities with the non-orthogonal finite difference time domain method

Numerical electromagnetic models, such as the finite difference time domain (FDTD) method, have many applications. The authors focus on the non-orthogonal FDTD method, which offers an improved geometric flexibility compared to other standard techniques. Results from numerical electromagnetic analysis methods, such as the FDTD method, are often degraded by an error known as numerical dispersion. For metallic structures this dispersion error is often higher than expected from theoretical considerations. The source of this additional error is due to the reciprocal field interpolation scheme used in the non-orthogonal FDTD algorithm. The error is illustrated by means of a microstrip waveguide and a microstrip antenna. Techniques for reducing this error are evaluated; careful construction of the mesh at the metallic boundary being the most reliable solution.

Stable non-orthogonal FDTD method

Introduction: A number of techniques have been proposed to extend the classical Yee’s finite-difference time-domain (FDTD) algorithm to a grid that is conformal to curved objects. Such methods, including the nonorthogonal FDTD (NFDTD) [1, 2], can accurately represent the curved boundaries without resorting to inefficient staircase orthogonal meshes. However, their significant advantage is offset by the fact that they suffer from late time instabilities. In [3], it is demonstrated that the instability of NFDTD is inherent. Although a ‘time-subgriding’ approach is presented there to reduce the late time instability, an unconditionally stable NFDTD is still not obtained. In this Letter, we introduce a novel approach to discretise Maxwell’s equations using only the covariant components. It is demonstrated that the new NFDTD algorithm is stable over a very long period of numerical simulation. Moreover, the algorithm is less computationally intensive than other NFDTD methods [1, 2] where both of the covariant and contravariant components are needed. The proposed technique is validated by simulation results on a circular waveguide resonator.

A program for calculating photonic band structures and Green's functions using a non-orthogonal FDTD method

We present a program which will calculate either the photonic band structure or the causal Green's function for photons incident on a complex dielectric structure. The method we use is a variant on the finite difference time domain (FDTD) method familiar to the electric engineering community, also known as the order(N) method. However, we employ a new transparent formalism which simplifies the stability analysis and identification of conserved quantities, as well as allowing the use of non-orthogonal coordinate systems without the usual computational overheads. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretisation so the technique is ideally suited to handling systems with large and complicated unit cells.

Efficient determination of Q factor by structured nonorthogonal FDTD method

A structured nonorthogonal finite-difference time-domain (FDTD) method incorporating existing perturbation techniques is used to determine the Q factor of an arbitrary three-dimensional cavity resonator. The new scheme combines the efficiency of the Cartesian mesh with the accuracy of the conformal grid. Good results are achieved with little computational effort.

Analyzing electromagnetic structures with curved boundaries on Cartesian FDTD meshes

In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by traditional FDTD formulas. Therefore, this new algorithm is more efficient than general nonorthogonal FDTD schemes in terms of computer resources such as memory and central processing unit (CPU) time. Simulation results are presented and compared to those using other methods.

A study of the nonorthogonal FDTD method versus the conventional FDTD technique for computing resonant frequencies of cylindrical cavities

The nonorthogonal finite-difference-time-domain (FDTD) technique is used to compute the resonant frequencies of dielectric-filled cylindrical cavities. Because the method is based on the nonorthogonal coordinate system, it is not restricted to specific geometries, e.g. rectangular or axially symmetric geometries, and is suitable for analyzing cavities of arbitrary shape. The advantages of this technique over the conventional FDTD algorithm with a staircase grid are shown in a convergence study, where the two methods are used to compute the dominant resonant frequency of a cylindrical cavity. The accuracy of the technique for calculating the resonant frequencies of the first few modes is demonstrated by comparing the results obtained with this technique with those derived by using two versions of the finite element method in the frequency domain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>