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We present a subdomain formulation of the periodic method of moments (PMM) with thin-wire kernel for analyzing frequency-selective surfaces (FSSs) with rectilinear wire-type elements. Analysis of the convergence of the impedance matrix for a FSS with aligned unidirectional elements indicates the effect of individual oscillatory and decaying components. For the individual impedance elements of this FSS, we prove and demonstrate the universality of their envelopes as a function of shell size in the spectral domain. For N wire segments, the PMM converges according to O(N4). The dependence on the order of polynomial basis functions shows a geometric progression. The theory is also applied to a single-layer FSS having asymmetrically split segmented rings.