Abstract

A methodology is presented that allows the derivation of low-truncation-error finite-difference representations of the two-dimensional Helmholtz equation,specific to waveguide analysis. This methodology is derived from the formal infinite series solution involving Bessel functions and sines and cosines. The resulting finite-difference equations are valid everywhere except at dielectric corners, and are highly accurate (from fourth to sixth order, depending on the type of grid employed). Nonetheless, they utilize only a nine-point stencil,and thus lead to only minor increases in numerical effort compared with the standard Crank-Nicolson equations.

[IEEE ]

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