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.