Second-order absorbing boundary conditions for the FD-TLM method analysis of open-region scattering problems

Voelker and Lomax (1990) developed the finite-difference transmission-line-matrix (FD-TLM) method for the full-wave time domain analysis of the electromagnetic properties of integrated circuits, with perfectly conducting boundary conditions to terminate the computational domain. The present paper extends the utility of the FD-TLM method for solving open region scattering problems in remote sensing applications, by developing and evaluating second-order absorbing boundary conditions (ABCs) for the method. First-order ABCs for the FD-TLM method have been developed in Zhang et al. (1993). The derivation of the ABCs in Cartesian coordinates starts from the Halpern and Trefethen's second-order approximation of the rational polynomial in the dispersion relation of the one-way wave equation (Trefethen and Halpern, 1986). The ABCs for the edges and corners are obtained by associating sets of approximate PDEs corresponding to the boundaries. The finite-difference time domain (FD-TD) expressions for the ABCs are derived by using a two-level discretization scheme which is proved to be stable (Renaut, 1992). The implementation of the ABCs into the FD-TLM method is finally accomplished through the equivalence between the FD-TD and FD-TLM methods.<
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