A Recompressed Nested Cross Approximation for Electrically Large Bodies

A recompressed nested cross approximation (rNCA) based closely on the recent fast nested cross approximation (fNCA) algorithm is formulated in this article. The proposed method builds on previous work in which the fNCA was formulated in a purely algebraic and kernel-independent fashion, using a top-down recursive application of the adaptive cross-approximation (ACA). Our proposed method employs ACA recompression to avoid the need to compute low-rank approximations of excessively large far-field matrices, and thus mitigates the effects of high-frequency rank growth on run-time scaling for electrically large models. The low run-time and memory cost allows for efficient parallel computation of
$\mathcal {H}^{2}$
-matrices for systems of excessive electrical sizes. Radar cross sections (RCSs) are evaluated for electrically large instances of a perfectly conducting sphere and the NASA Almond. We observe near-linear scaling of memory cost and construction time.