Efficient Analytical Skeleton Approximation for Compressing Electrically Large Integral Operators

In this paper, we develop an efficient method to build a Skeleton Approximation to compress electrically large integral operators. By introducing auxiliary plates and analytically selecting a reduced set of auxiliary points, an accurate low-rank approximation can be generated in a time complexity of
$O(kn)$
, as compared to existing
$D(n^{3})$
or
$O(k^{2}n)$
methods, where
$k$
is the rank and
$n$
is the matrix size. Numerical experiments have demonstrated its accuracy and efficiency.