Fundamentals of the three-dimensional spatial harmonic analysis (SHA) approach are reviewed, and the advantages of a fast-converging formulation versus the initial SHA formulation are proved using the examples of periodic plasmonic nanostructures. First, two independent parallel versions with the initial and a fast-converging formulations are implemented using the scattering matrix algorithm for multilayer cascading. Then, by comparing the results from both versions, it is shown that choosing the advanced fast-converging scheme could be essential for accurate and efficient modeling of plasmonic structures. Important obstacles to the fast parallel implementation of this approach are also revealed. The results of the test simulations are finally validated using the data obtained from the experimental characterization of fabricated samples.