This paper describes a novel time-domain node for the TLM method. It has the unique feature of modeling arbitrary inhomogeneous media on a generally graded rectangular TLM mesh without using stubs. Variations in material properties and arbitrary aspect ratios of mesh cells are modeled by allowing different characteristic impedances in a cell, maintaining impulse synchronism throughout the mesh. The complete theory of the new node is given and its implementation on a general TLM mesh is discussed. Numerical results for a canonical resonator loaded with dielectric layers are presented for different grading cases. Substantial savings in computer storage and run-time as well as improved accuracy compared to the uniform mesh are achieved when an appropriate nonuniform grading of the TLM mesh is used. >

Theory of the symmetrical super-condensed node for the TLM method

Propagation of electromagnetic waves in three-dimensional (3D) space is studied using the Transmission-Line Modelling (TLM) method. The theoretical foundation, generalization and more advanced versions of the symmetrical condensed node (SCN), a basic structure for 3D TLM modelling, are presented. 

A unified approach to the derivation of TLM schemes capable of modelling nonuniform anisotropic materials on an arbitrarily graded mesh is introduced. The parameters and the scattering properties for a general symmetrical condensed node (GSCN) constructed from link lines with arbitrary characteristic impedances and up to six stubs are described. 

For the first time in 3D TLM modelling it is shown that stubs can be removed completely from the SCN, whilst still allowing general inhomogeneous problems to be modelled. This development, described as the symmetrical super-condensed node (SSCN), contributes significant reductions in memory storage and computer run-time in TLM simulations.
In order to assess accuracy and numerical dispersion in the various TLM schemes based on the GSCN, dispersion relations are studied. A general approach for the analytical expansion of the general dispersion relation is introduced, enabling the derivation of dispersion relations in algebraic form for all currently available nodes.

Based on the results obtained from the dispersion analysis, work aimed at constructing an optimal node is described. A class of adaptable symmetrical condensed nodes (ASCN) is derived, with superior propagation characteristics compared to other known TLM nodes.

The development and characterisation of advanced nodes for the TLM method

New formulas for the maximum permissible time step in TLM hybrid nodes modeling anisotropic media are introduced and analyzed. It is shown that the value of the time step in most cases can be higher than that suggested by the minimum node dimension. The chosen value of the time step has significant impact on the dispersion characteristics of the hybrid symmetrical condensed node. >

On the time step in hybrid symmetrical condensed TLM nodes

In this paper, a validation study for the metamaterial accurate modelling using the electromagnetic numerical transmission line matrix (TLM) computation method is presented In our work, the three-dimensional symmetrical condensed node (SCN) TLM algorithm has been modified to fully simulate non-linear and dispersive metamaterial structures The modification code principles have been explained theoretically The propagation computation using our modifying TLM code has been tested for a metamaterial ground slab loaded by split ring resonator structure The tested structure acts as a metamaterial radar absorber Moreover, experimental measurements were carried out and compared to the computed ones The results confirmed the good agreement between measured and TLM computed results Furthermore, the propagation computation was confirmed by measuring the backscattering for different incident angles which demonstrate very good agreement for our modified TLM code The measurement results confirm the versatility a

Accurate propagation computation through metamaterial RAM structures using modified 3D SCN transmission line matrix method for different incidence angles

An improvement of the wave concept iterative procedure (WCIP) is proposed that avoids excessive computational storage and simulation times for bulky devices. The description of such features has been a major difficulty since both small and large dimensions exist which led to hardened constraints when accuracy is required. An alternative consists in the use of appropriate modifications and interfaces of coarse numerical meshes (macropixel), which allows implementation of fine features within the circuit area. These concepts are tested and validated through comparison between measurement and simulated results. This method is applied on multi-scale circuits that could not be simulated before because of memory storage limitation.

Different spectral scale level in the wave concept iterative procedure to solve multi-scale problems

The paper describes a modification of the transmission line matrix (TLM) method of numerical analysis in three dimensions. The traditional 3D distributed node (cubic cell) TLM algorithms are generalized for cuboid cells of arbitrary aspect ratio. The basic theory of the cuboid 3D distributed node is described in detail. A full dispersion analysis of the cuboid mesh is performed for the general case, and the results are compared to the characteristics of the traditional cubic mesh. Some applications are shown in this paper. Numerical results for a canonical rectangular waveguide cavity are compared with those obtained with a cubic cell to demonstrate the validity of the algorithm. Based on those comparisons, we demonstrate that the cuboid cell offers greater flexibility in discretization and can save memory as well as CPU time. >

Qi Zhang

Papers

Characteristics of 3D distributed node TLM mesh with cells of arbitrary aspect ratio