$\mathcal {O}(N)$ Nested Skeletonization Scheme for the Analysis of Multiscale Structures Using the Method of Moments

We present a scheme to compress the method of moments (MoM) matrix, which is linear in complexity for low to intermediate frequency problems in electromagnetics. The method is fully kernel independent and easy to implement using existing codes. The <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(N)$</tex-math></inline-formula> complexity for both memory and time (setup and matrix–vector product) is achieved thanks to the application of a recursive skeletonization to the <inline-formula><tex-math notation="LaTeX">$\mathcal {H}^2$</tex-math> </inline-formula> matrix structure of the MoM matrix that uses the nested nature of the far interactions. The interpolative decomposition is applied in a novel manner in order to compress the “far-field signature” of the groups of basis functions. Moreover the scheme is fully characterized and it proves itself well suited for the analysis of multiscale structures.

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