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Time-domain electromagnetic simulations employing unstructured tetrahedral meshes can be sensitive to local mesh characteristics. In particular, the maximum permissible time step for stable operation can be unacceptably small. In this paper, a cell clustering technique is described for the transmission line modeling algorithm that reduces the sensitivity to local mesh characteristics and permits substantial increases in time step to be made without compromising accuracy or stability.

This paper presents a transmission-line modeling (TLM) algorithm, which is based upon unstructured tetrahedral meshes. In comparison with the conventional, usually Cartesian, scheme, the use of such meshes provides a significant enhancement in the flexibility and accuracy of the TLM simulations, permitting both smooth boundary approximations and the use of diversely sized elements in multiscale problems. A full theoretical development of the unstructured algorithm is presented for the first time and canonical problems are used to demonstrate the computational advantages available. Particular consideration is given to practical meshing constraints and the merging of adjacent tetrahedra into larger cells used to avoid the use of undesirably small time steps.

Transmission-line modeling (TLM) is an established numerical simulation method for electromagnetics that has been employed in a wide variety of application areas. To date, TLM has been formulated primarily for structured (usually Cartesian) meshes. This paper presents and illustrates the application of a new TLM algorithm suitable for use with unstructured two-dimensional meshes based upon triangular elements.

The paper describes the development of a class of adaptable symmetrical condensed (ASCN) transmission-line modeling (TLM) nodes. The parameters and numerical properties of the ASCN are expressed in terms of arbitrary weighting functions which can be selected in a manner that minimizes dispersion and improves accuracy. It is shown that this approach is effective and can be used to optimize nodal properties according to problem requirements.

A general symmetrical condensed node (GSCN) for the transmission line modeling (TLM) method, with six different link line characteristic impedances, six stubs, and six lossy elements is described for the first time. It unifies all the currently available condensed nodes into a single formulation and provides the basis for the derivation of an infinite set of new nodes, including nodes with improved numerical characteristics. The GSCN is derived in two ways: (1) from an equivalent network model and (2) directly from Maxwell's equations using central differencing and averaging. The direct correspondence established between the GSCN TLM and a finite difference scheme for Maxwell's equations provides a rigorous theoretical foundation for all available TLM methods with condensed nodes.

A method for obtaining analytical solutions of the general transmission line modeling (TLM) dispersion relation for condensed node schemes is described. Exact analytical forms of the dispersion relation for currently available nodes are derived, enabling the efficient study of dispersion solutions without resorting to a numerical solver. Using these analytical relations, the range and behavior of propagation errors are fully explored and visualized, not only for propagation along the axes and diagonals or in a coordinate plane, but for arbitrary angles of propagation in three-dimensional space. Comparisons are presented of the numerical performance of different TLM condensed node schemes.

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. >

An important aspect in the application of transmission-line modelling (TLM) to microwave circuit and electromagnetic compatibility (EMC) simulation studies is the accurate modelling of wires and wire-like structures. This paper outlines the cause of errors arising from simplified descriptions often used when modelling wires by integrated solution methods in TLM. It proposes a simple solution which is validated against experimental results for a number of test configurations. >

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. >