A three‐point compact LOD‐FDTD method for solving the 2D scalar wave equation

Abstract

This letter introduces anunconditionally stable finite‐difference time domain (FDTD) method, based on the locally one‐dimensional (LOD) technique, for the solution of the two‐dimensional scalar wave equation (WE) inhomogeneous media. The second spatial derivatives in the WE are discretized by using a three‐pointcompact (implicit) finite‐difference formula with a free parameter. This formula has second‐order accuracy and becomes fourth‐order by properly selecting the parameter value. Moreover, the resulting algorithm only involves tridiagonalmatrices, as when using standard (explicit) second‐order finite differences. Additionally, a stability analysis is performed and the numerical dispersion relation of the method is derived.The proposed compact LOD‐WE‐FDTD technique has been applied to the calculation of resonant frequencies in a metallic ridge cavity. The accuracy of the results obtained has been studied as a function of the parameter value.