Reduced order models of refined Yee's cells

This letter introduces a new approach to increasing the accuracy of Finite Difference (FD) methods by means of local mesh refinement. The area slightly larger than single Yee's cell is covered by dense mesh and its macromodel is created by the Model Order Reduction (MOR) of state equations in the frequency domain. Such macromodels are subsequently used in the Finite Difference Time Domain (FDTD) or the Finite Difference Frequency Domain (FDFD) analysis of the entire structure. Unlike a popular subgridding technique, the model order reduction approach does not affect the stability or convergence properties of underlying numerical schemes.