Abstract
A reformulation of the Transmission Line Matrix (TLM) method is presented to model non-dispersive anisotropic media. Two TLM-based solutions to solve this problem can already be found in the literature, each one with an interesting feature. One can be considered a more conceptual approach, close to the TLM fundamentals, which identifies each TLM in Maxwell’s equations with a specific line. But this simplicity is achieved at the expense of an increase in the memory storage requirements of a general situation. The second existing solution is a more powerful and general formulation that avoids this increase in memory storage. However, it is based on signal processing techniques and considerably deviates from the original TLM method, which may complicate its dissemination in the scientific community. The reformulation presented in this work exploits the benefits of both methods. On the one hand, it maintains the direct and conceptual approach of the original TLM, which may help to better understand it, allowing for its future use and improvement by other authors. On the other hand, the proposal includes an optimized treatment of the signals stored at the stub lines in order to limit the requirement of memory storage to only one accumulative term per field component, as in the original TLM versions used for isotropic media. The good behavior of the proposed algorithm when applied to anisotropic media is shown by its application to different situations involving diagonal and off-diagonal tensor properties.
Highlights
The Transmission Line Matrix (TLM) method is a low-frequency, time-domain numerical method originally proposed by Johns and coworkers in the early 1970s [1] to solve electromagnetic wave propagation problems from a different point of view
The TLM method is mainly based on finding an analogous transmission line circuit to describe the original problem by means of the study of the propagation of voltage and current pulses through it
As regards the antenna analysis and design—a challenging problem for a low-frequency numerical method such as the Finite-Difference Time-Domain (FDTD) or TLM methods—the addition of a specific sub-circuit representing the effects of the thin-wire antenna to the standard TLM node, shown in Figure 1, was first proposed in [16] to model antennas whose radius is significantly smaller than the node size
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Second and more importantly, obtaining the scattering matrix for a given node is usually a difficult task Despite these difficulties and under this general scheme, the TLM method has proven to be a versatile and powerful numerical technique for solving different challenging electromagnetic situations. As regards the antenna analysis and design—a challenging problem for a low-frequency numerical method such as the FDTD or TLM methods—the addition of a specific sub-circuit representing the effects of the thin-wire antenna to the standard TLM node, shown, was first proposed in [16] to model antennas whose radius is significantly smaller than the node size This was an imaginative and efficient solution which generated a number of subsequent works with new thin-wire models and even more complex situations [17,18,19,20].
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