Solution box: SOLBOX-15

From computational point of view, frequency-selective structures are challenging to analyze since they involve resonating elements. In fact, resonances are essential for the operation of these structures, i.e., they generally provide the required responses (shadowing, focusing, full transmission, etc.) when their elements resonate. These resonances can be studied well via analytical approaches, e.g., by using circuit representations to model unit cells. However, as for other structures, numerical simulations — particularly those based on three-dimensional models — can be extremely useful for complete analyses of electromagnetic characteristics of complex frequency-selective structures before their realizations. The challenge is that when there are resonating elements, linear systems constructed in numerical simulations tend to become very ill-conditioned. For example, when using iterative solvers, iteration counts can be extremely large, while a convergence to a given error threshold may not guarantee an accurate result.