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

Abstract

AbstractThis letter introduces an unconditionally 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) in homogeneous media. The second spatial derivatives in the WE are discretized by using a three‐point compact (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 tridiagonal matrices, 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.