N.R.S. Simons

Comparison of the transmission-line matrix and finite-difference time-domain methods for a problem containing a sharp metallic edge

We compare Yees finite-difference time-domain (FDTD) and symmetric condensed node transmission-line matrix (SCN-TLM) solutions for a cavity containing a metallic fin. Differential equation-based numerical methods are known to produce inaccurate results for this type of problem due to the rapid spatial variation of the field distribution in the vicinity of the singularity at the edge of the metal fin. This problem is relevant to the analysis of structures of practical interest such as microstrip and coplanar waveguides. Based on simulations, it is determined that for identical discretizations, SCN-TLM is more accurate than FDTD for this problem. We interpret this result as an indication that the symmetric condensed representation of fields (used within the SCN-TLM) lends itself to a more accurate algorithm than the distributed representation used by Yee. We estimate that the FDTD method requires 3.33 times more cells for a given three-dimensional problem than the transmission-line matrix (TLM) method (1.49 times more cells per linear dimension of the problem) in order to achieve the same accuracy. If we consider the requirements to update and store a single TLM or FDTD cell, we find the SCN-TLM algorithm is more efficient than the Yee FDTD algorithm in terms of both computational effort and memory requirements. Our conclusions regarding computational effort and memory requirements are limited to problems with homogeneous material properties.

A class of symmetrical condensed node TLM methods derived directly from Maxwell's equations

A series of general transmission line matrix (TLM)-type methods, which include the symmetrical condensed node method, are derived directly from Maxwells curl equations without recourse to transmission line models. Written as a system of conservation laws, Maxwells equations in 3-D plus time are decomposed along the orthogonal characteristic directions of a rectangular grid. The Riemann invariants in this method correspond to the voltage pulses of the TLM method. A new method of handling inhomogeneous media is proposed based on a new transfer event. The dispersive nature of these schemes is also investigated. >

Two dimensional hexagonal TLM node and velocity error correction

The original two-dimensional TLM (transmission line matrix) method is based on a rectangular lattice or orthogonal transmission lines. The authors introduce a node which is based on a lattice with hexagonal symmetry. The advantage of the node is that the velocity error is only weakly dependent on the direction of the propagation. Therefore, for a specific frequency the amount of velocity error can be determined and eliminated.<<ETX>>

Transmission-line matrix (TLM) method for scattering problems

Abstract In this paper we discuss the application of the TLM method to electromagnetic scattering and radiation problems. A general formulation based on the equivalence principle is developed for exciting structures with arbitrary field distributions. Various methods of realizing absorbing boundary conditions are presented. The sample computation provided illustrates the accuracy and efficiency of the formulation for a simple two-dimensional scattering problem.

Integer lattice gas automata for computational electromagnetics

Integer lattice gas automata (ILGA) are combined with the transmission-line matrix (TLM) method to yield a new electromagnetic-field computation algorithm using very low-precision integer variables. Lattice gas automata can be evaluated using look-up tables on special-purpose hardware and do not require floating-point arithmetic. In this paper, we present a TLM motivated ILGA with emphasis placed on algorithms that demonstrate minimal dissipation.

Computing electromagnetic fields in inhomogeneous media using lattice Gas Automata

Lattice Gas Automata (LGA) can be considered as an alternative to the conventional differential equation description of problems in electromagnetics. LGAs are discrete dynamical systems that are based on a microscopic model of the physics being simulated. The basic constituents of an LGA are discrete cells. These cells are interconnected according to certain symmetric requirements to form an extremely large regular lattice. The cells of an LGA are extremely simple, requiring only a few bits to completely describe their states. Even through they are simple however, the collective behaviour of LGA microscopic systems are capable of exhibiting those behaviours described by partial differential equations for real physical systems. One type of simple LGA, the HPP LGA, is constructed with only a few bits per cell and operated on a rectangular lattice. We have demonstrated [1] that it is capable of simulating two dimensional electromagnetic fields. Furthermore, the inherent parallelism and simplicity of LGA algorithms make them ideally suited to implementation in a parallel processing architecture.

TLM-based modal-extraction approach for the investigation of discontinuities in the rectangular waveguide and the NRD

This paper describes the development of a rigorous transmission-line matrix-based modal-extraction approach to analyze discontinuities in guided-wave structures in general, with particular attention to the nonradiative dielectric waveguide (NRD). The motivation for this paper arose from the need to ascertain the admittance of a slot in the ground plane of an NRD without relying on experimental data. These data enabled one to design an NRD-based slot array following the methodology of Malherbe (1984), Malherbe et al. (1984), and Ghosh et al.(1997). Previous work in this area relied on placing observation points sufficiently remote from the discontinuity in order to ensure the decay of scattered evanescent modes to appreciably low levels. The method discussed here obviates this requirement and allows the evaluation of generalized scattering-matrix coefficients arbitrarily close to the discontinuity, thus significantly reducing the computational overhead. Results pertaining to discontinuities in the NRD and the rectangular waveguide have been presented and shown to give good agreement with those in the literature and with measurements. The perfectly matched layer has been used as an absorbing boundary condition in our simulations. Finally, the results have been verified using the power-conservation and Poyntings theorems.

Characterization of an NRD slot for the design of an NRD based slot array

The non-radiating dielectric waveguide (NRD) has been receiving considerable attention due to its low loss nature and the ability to suppress radiation at bends and discontinuities. It is proposed to exploit the above properties to design a NRD based slot array. Previous work relied on measured data for the admittance of a single slot in the ground plane of the NRD. In the present paper, a single slot in the NRD ground plane is characterized using the TLM method. The perfectly matched layer (PML) absorbing boundary condition was used to ensure minimal reflection from the exterior boundaries of the computational domain. It is also shown that an s/sub 11/ less than -40 dB is achieved when the PML is used to terminate the NRD.

Comments on "A class of symmetrical condensed node TLM methods derived directly from Maxwell's equations" [with reply]

In the original paper, LoVetri and Simons [see ibid, vol.41, p. 1419-28,1993] derive the three-dimensional symmetrical condensed node TLM algorithm using a characteristic based field decomposition of Maxwells equations. The goal and eventual result of the investigation was to present a mathematically sound method for deriving the TLM scattering and transfer events directly from Maxwells equations (without recourse to the approximation of space by a mesh of transmission lines). The statement made by Krumpholz and Russer, that the original derivation is erroneous, is not valid and the two specific points they raise are considered. >

Formulation of lumped elements in a general (conformal) coordinate system

In this paper, the fundamental theory of modelling passive and active linear lumped elements for a generalised coordinate system is discussed. A general procedure for deriving expressions for modelling distributed lumped elements is outlined via an example of a distributed lumped voltage source.