Fast Direct Solution with Mixed Skeletons and Equivalences Approximation for Electromagnetic Scattering from Conducting Objects

In this paper, we propose a kernel-independent fast direct solver with nested equivalent source approximation (NESA) for electromagnetic scattering from conducting objects at low to moderate frequencies. With strong admissibility condition in this work, to achieve a high efficiency computation, NESA with skeletons is employed to compress the far field interactions via the adaptive cross approximation (ACA) at the leaf level. NESA with equivalent sources is employed at higher levels. Subsequently, the system matrix is factorized by two kinds of elimination matrices corresponding to far and near field interactions respectively. During the factorization, the radiation and receiving matrices are updated from the leaf level up to the top level with prescribed accuracy to account for the contributions of fill-in blocks generated from the near interactions elimination. The complexities of both computation and memory scale as O(N) for constant-rank problems. Several numerical results are presented to verify the accuracy and complexity of our method.