Analysis and Mitigation of Discretization Errors in the Orthogonalized Integral-Based Subgridding FDTD Algorithm

Accuracy is a key aspect to be considered when assessing results from subgridding algorithms in the finite-difference time-domain (FDTD) method. This work focuses on the accuracy of a newly developed orthogonalized integral-based subgridding (OI-SG) algorithm and is divided into two main parts. First, we identify and quantify spurious reflections present in OI-SG by considering a set of free-space simulations containing a subgridded region illuminated by a plane wave and measuring the (spurious) far-field scattering. We find that the most relevant parameter of merit in these cases is the points-per-wavelength (PPW) criterion used for the spatial discretization. Second, we study near-field effects produced by the interaction between material objects and subgridding interlevel boundaries. We observe that the PPW criterion is not sufficient to determine accuracy in these cases. We find out that an important role is also played by the buffering distance between the subgrid boundaries and the material objects. We consider a variety of application examples in our analysis: a frequency selective surface (FSS), an all-angle negative refraction (AANR) metasurface, a conducting sphere, and a NASA almond. In all cases, we measure the error as a function of the spacing between the objects and the lowest-level subgridding boundary (buffering distance). We observe significant accuracy improvements in all cases.