Contour Path Finite-difference Time-domain Research Articles

A systematic and topologically stable conformal finite-difference time-domain algorithm for modeling curved dielectric interfaces in three dimensions

A systematic conformal finite-difference time-domain (FDTD) algorithm for the direct modeling of dielectric interfaces in three dimensions is presented in this paper. The straightforward procedure is based on the proper reformation of the grid cells in the vicinity of the dielectric surface, leading thus to the creation of five-faced prisms on the primary grid, apart from the standard hexagonal ones. The new scheme overcomes any topological deficiency that forbids the contour path FDTD and conformal FDTD technique to directly simulate dielectric boundaries, since it maintains the lattice duality. Therefore, no instabilities, even late-time ones, are observed. On the other hand, the accuracy obtained, even with very coarse meshes, is very good as is proved by the numerical analysis of various resonance problems.

Analysis of shielded membrane microstrip line using the finite-difference time-domain method

A simple and efficient analysis method of the shielded membrane microstrip (SMM) line using the finite-difference time-domain (FDTD) method is presented. New FDTD equations are derived using the contour path FDTD concept for the Yee cell which contains three thin dielectric sheets of membrane. The characteristic impedance and the effective dielectric constant of the SMM line are calculated using our proposed method. The method is validated by comparison with the results shown by Robertson et al. [1996].

A novel contour-path finite-difference time-domain (CPFDTD) algorithm for modeling objects with curved surfaces

A novel CPFDTD algorithm for modeling smooth curved surfaces is presented. This scheme subdivides electric fields on the distorted grid into the extended contour field, the nondistorted field, and the quasiavailable field to avoid the collinear borrowing approximation. Several earlier methods are applied to the E-plane sectoral horn antenna to obtain far-field patterns. To show the validity and applicability of our method, computed far-field patterns are compared with measured values. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 285–287, 2001.

FDTD simulations of TEM horns and the implications for staircased representations

Two-dimensional (2-D) TEM horns are modeled using the finite-difference time-domain (FDTD) method. The boundary walls are perfect electric conductors and one wall, which does not align with the Cartesian grid, is approximated using a staircased representation. By carefully comparing the FDTD results to those of the analytic solution, one can make conclusions about the coarseness with which a boundary can be represented. It is found that staircasing errors are small when the staircase diagonal (the hypotenuse of the right triangle created by the stairstep) is smaller than half a wavelength at the highest significant frequency in the excitation. This rule-of-thumb is put forward as a necessary condition for the discretization of general problems. Results are also provided for some simple FDTD schemes that are designed to reduce staircasing errors. By using large aspect-ratio cells, a grid can be constructed that satisfies the rule-of-thumb given above. While this approach eliminates general staircasing errors, some errors persist owing to the presence of step discontinuities immediately adjacent to the horn feed. These errors can be further reduced by using a cell-splitting approach. It is shown that the contour path FDTD technique can be used to eliminate nearly all staircasing errors, while some additional improvement is shown to be provided by using a stabilized contour path FDTD approach. Finally, a recently proposed conformal technique that permits simple implementation is shown to provide results comparable with those of the stabilized contour path approach.

Stabilised CPFDTD algorithm for the analysis of arbitrary 3D PEC structures

The use of the contour path finite difference time domain (CPFDTD) method with locally distorted contours is well known to give accurate results for curved metal structures. The numerical stability of this scheme is, however, not guaranteed and this can pose problems, especially in the analysis of closed resonant structures. In addition, the generation of the distorted mesh is itself not a trivial task. In this contribution, we present a modification to the three-dimensional CPFDTD scheme which, without sacrificing accuracy, renders it numerically stable, robust and easy to generate. A step-by-step procedure is given whereby the distorted mesh can be automatically generated for any desired metal structure. The accuracy of the modified scheme is demonstrated for the analysis of a circular cylindrical resonant cavity which is tilted with respect to the Cartesian FDTD mesh.

The analysis of general two-dimensional PEC structures using a modified CPFDTD algorithm

The use of the contour path finite difference time domain (CPFDTD) method with locally distorted contours has been shown to give accurate results for curved metal structures. However, the numerical stability of this scheme is not guaranteed and significant skill is required in order to generate an appropriate grid. In this contribution, we present a modification to the CPFDTD scheme which ensures stability and give a step-by-step procedure for simple generation of the distorted grid. Examples are presented to demonstrate that the modified scheme yields results superior to those obtained using the standard staircased finite difference time domain (FDTD) approach. Example geometries are cylindrical cavities having complex cross-sections with smooth surfaces and right-angle bends. The accuracy of the method is demonstrated by comparison to analytical results where available.

Derivation and application of a passive equivalent circuit for the finite difference time domain algorithm

The widely used finite difference time domain (FDTD) algorithm in its standard form is conditionally stable, the condition being the well-known Courant criterion. Much research has focussed on modifying the standard algorithm to improve its characterisation of geometrical detail and curved surfaces; these modified algorithms, however, may easily be conditionally stable-there is no value of time step that stabilizes the algorithm. The authors present a passive electrical circuit that, by virtue of its formal equivalence with FDTD, provides a criterion by which unconditionally unstable algorithms may be avoided. As an example the passive circuit criterion is used to remove the instability from a contour-path FDTD algorithm.

Analysis of general 3-D PEC structures using improved CPFDTD algorithm

The contour path finite difference time domain (CPFDTD) method, employing locally distorted integration contours, has been shown to give accurate results for curved three-dimensional metal structures. The numerical stability of this scheme is not, however, guaranteed and significant skill is required to generate an appropriate grid. The authors present a modification to the three-dimensional CPFDTD method which ensures stability and which permits simple generation of the locally distorted grid. The accuracy of the scheme is demonstrated through the calculation of the resonant frequencies of circular cylindrical and spherical resonators.

Improved locally distorted CPFDTD algorithm with provable stability

The contour path finite difference time domain (CPFDTD) method has been shown to give accurate results for curved metal structures. However, the numerical stability of this scheme is not guaranteed and significant skill is required to generate an appropriate grid. The authors present a modification to the two-dimensional CPFDTD method which ensures stability and which permits simple generation of the locally distorted grid. The accuracy of the scheme is demonstrated through calculation of the resonant frequencies of circular cylindrical resonators.

A Monte-Carlo FDTD technique for rough surface scattering

A Monte-Carlo finite-difference time-domain (FDTD) technique is developed for wave scattering from randomly rough, one-dimensional surfaces satisfying the Dirichlet boundary condition. Both single-scale Gaussian and multiscale Pierson-Moskowitz surface roughness spectra are considered. Bistatic radar cross sections are calculated as a function of scattering angle for incident angles of 0, 45, 70, and 80 degrees measured from the vertical. The contour path FDTD method is shown to improve accuracy for incident angles greater than 45 degrees. Results compare well with those obtained using a Monte-Carlo integral equation technique.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Contour path FDTD method for analysis of pyramidal horns with composite inner E-plane walls

The contour path finite-difference time-domain (FDTD) method is used for modeling pyramidal horn antennas with or without composite E-plane inner walls. To model the pyramidal horn surface, a locally distorted grid is used. Modified equations are obtained based on the locally distorted grid and the assumptions of the contour path method. The developed algorithm is validated by comparing computed antenna gain patterns, with and without the presence of composite material, with available measurements. >