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

Abstract

This 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 WEare discretized by using a three-point compact (implicit) finite-differenceformula with a free parameter. This formula has second-order accuracyand becomes fourth-order by properly selecting the parameter value.Moreover, the resulting algorithm only involves tridiagonal matrices, aswhen using standard (explicit) second-order finite differences. Addition-ally, a stability analysis is performed and the numerical dispersionrelation of the method is derived. The proposed compact LOD-WE-FDTDtechnique has been applied to the calculation of resonant frequencies in ametallic ridge cavity. The accuracy of the results obtained has beenstudied as a function of the parameter value.