O(N) matrix-vector multiplication in periodic MoM

Tihon, Denis;Craeye, Christophe
(2019) 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA) — Location: Granada, Spain (9.September.2019)

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Using the periodic Green's function, periodic structures can be simulated with the Method of Moments. In classical implementation, first the periodic impedance matrix of the structure is filled. Then, it is inverted. The computational complexity of these steps scale as O(N 2 ) and O(N 3 ), respectively, with N the number of basis and testing functions used to discretize the geometry. When dealing with large structures, iterative techniques are preferred due to their lower complexity, which ranges between O(N) and O(NlogN). In this paper, we propose an algorithm for matrix-vector multiplication that is specialized for the simulation of elongated structures and scales as O(N). The algorithm is based on a plane wave decomposition of the fields. The peculiarity of the proposed algorithm and its efficiency lies in the proper ordering of the operations performed. The complexity of the method is validated through the simulation of an array of dielectric nanowires of various sizes.
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Tihon, D., & Craeye, C. (2019). O(N) matrix-vector multiplication in periodic MoM. Proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), p. 1145-1148. https://doi.org/10.1109/ICEAA.2019.8879273