Accuracy Limitations of the Locally One-Dimensional FDTD Technique

While the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method preserves the second-order temporal accuracy of the conventional FDTD technique, the locally one-dimensional (LOD)-FDTD method exhibits a first-order in time splitting error. Despite this difference, the numerical dispersion analyses of these methods reveal that both present similar accuracy properties. For this reason, the characteristic noncommutativity error of the LOD-FDTD scheme has not received much attention. In this letter, we determine the closed form of the local truncation error for the 3D-LOD-FDTD scheme. We find that it presents error terms that depend on the time-step size multiplied by the spatial derivatives of the fields. Numerical results confirm that these terms become a significant source of error that is not revealed in the dispersion analyses.