Mixed-Form Nested Approximation for Wideband Multiscale Simulations

We propose a mixed “skeleton” and “equivalence” nested approximation method to compress the impedance matrix of the method of moments for the wideband multiscale simulations. We first introduce a nested skeleton approximation, where the impedance matrix is expressed recursively by sampling the dominant basis functions (e. g., <italic>skeletons</italic>) with a fully algebraic implementation from the original basis functions. The idea is to introduce the automatically constructed test surface around the interface between near- and far-field regions, for each group the dominant RWGs are sampled recursively with the adaptive cross approximation to compress the matrix against the test surface. Second, we introduce a mixed-form algorithm of “skeleton” and “equivalence” nested approximation method, at low levels, the nested skeleton approximation is employed, and it is smoothly transferred to standard wideband nested equivalence approximation (WNESA) at high levels. An accurate number of skeletons can be always found with a predetermined threshold at a low level, which will improve computation efficiency, with respect to WNESA. The computational complexity of the proposed algorithm is <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N\log {N})$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is the number of unknowns. Numerical wideband multiscale simulations demonstrate the efficiency of the proposed algorithm.