Computational Electromagnetics Research Laboratory
Development and Characterization of Generalized TLM Networks for Electromagnetic Modeling
Qi Zhang, University of Victoria, March 1996.
A set of two- and three-dimensional TLM node structures with cells of arbitrary aspect ratio for the time domain analysis of electromagnetic field problems have been developed. These node structures increase the flexibility of space discretization and allow the modeling of media with arbitrary constitutive parameters without the need for reactive stubs. They provide substantial improvement in accuracy when modeling microwave and millimeter-wave structures. The algorithms were implemented in a numerically efficient manner and validated extensively by applying them to solve field problems.
It is shown that the anisotropic rectangular or cuboid TLM network can be built in such a way that the propagation vector remains independent of the direction of propagation in the infinitesimal approximation. The dispersion error related to the modeling of the TLM method is studied. A full dispersion analysis of the rectangular and cuboid meshes is performed for the general case, and results are compared to those of the traditional square and cubic cells.
In order to verify the conformity of the rectangular TLM algorithm with Maxwell's equations, and to place it on a sound field-theoretical basis, the properties of the rectangular TLM were derived using the Method of Moments (MOM). This derivation extends the work by Krumpholz and Russer from the square to the more general rectangular case. Hilbert space representation was also extended to the general rectangular case; it represents the most elegant and compact formulation of the new TLM scheme. This approach leads to more efficient analysis of structures sustaining waves with different wave numbers in two coordinate directions.
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