Nested Pseudoskeleton Approximation Algorithm for Generating H 2 -Representation of Electrically Large Surface Integral Operators

Abstract

In this paper, we develop a fast nested pseudoskeleton approximation algorithm to generate a low-rank $\mathcal{H}^{2}$ -matrix to represent electrically large surface integral equations (SIEs). The algorithm only uses $O (N\log N)$ entries of the original dense SIE matrix of size $N$ to generate the $\mathcal{H}^{2}$ -representation. It also provides a closed-form expression of the cluster bases and coupling matrices using original matrix entries. The resultant $\mathcal{H}^{2}$ -matrix is then directly solved for electrically large scattering analysis. Numerical experiments have demonstrated the accuracy and efficiency of the proposed algorithm.