An analysis of the stability of a general-purpose 3D subgridding method

In this work, we intend to study stability of a FDTD subgridding method based on a 1:2 ratio transition and whose equations are directly obtained by using a main-dual grid formalism. We provide three different approaches in order to obtain a clear view of the stability: an heuristic study, an analytical scheme based on integration lines and surfaces and an spectral analysis. We show that all three methods provide similar results, obtaining that roughly a 65% time-step reduction is enough to achieve stability.