Computational Electromagnetics in complex linear media with the TLM method

Description

Volumic time-domain computational methods such as FDTD or Transmission-Line Matrix method (TLM) are widely used for full-wave simulation of structures with arbitrary geometry. While FDTD is a direct discretization of curl Maxwell's equation using finite-difference operators, TLM is seen as a discretized version of Huygens' principle of wave propagation. Fields are computed by linear combination of local ordinary waves. Local medium properties are accounted for by correcting the field values at every time step in a way that can be fundamentally described by a filtering process. Generally, the Symmetrical Condensed Node (SCN) proposed by Johns is used, owing to its very good dispersion characteristics and the fact that it always operates at the maximum time-step, computes all field components at the cell center and at the same time-step. Another advantage of the SCN is that continuity of tangential field components is automatically enforced at interfaces between media as fields are always updated in a homogeneous medium. As a result, SCN-TLM remains very accurate for high contrast of constitutive parameters. The price to pay is larger computer expenditure per iteration than when using FDTD, for instance. However, some recent work have shown that, even if the SCN-TLM requires more operations and storage, it substantially outperforms FDTD in terms of computer cost for high contrasted media or zones with irregular mesh with large mesh size ratio. This is due to the local properties of the SCN-TLM. In this paper, a brief review of the TLM method is presented. Then, a unified TLM algorithm for complex linear media is described. These media include dispersive, anisotropic or media with both characteristics. Some aspects of the TLM method regarding its performances for high contrast heterogeneous media are discussed. Also, some issues regarding dispersion and stability when dealing with complex media are presented. Examples in the case of dispersive, non-isotropic media such as ferrite will be shown. Finally, when dealing with highly heterogeneous medium such as encountered in human dosimetry, the use of block- meshing brings some obvious advantage. However, when local time-step is used some stability issue occurs. Some current results and related discussion are presented.

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