Direct solution of electromagnetic scattering from perfect electric conducting targets using multilevel characteristic basis function method with adaptive cross approximation algorithm

The adaptive cross approximation (ACA) enhanced multilevel characteristic basis function method (MLCBFM) is studied in this article. It is well known that the impedance submatrices containing the reaction terms of low-level basis functions such as Rao-Wilton-Glisson basis functions have low-rank property. However, the authors find that the high-level impedance matrices between nonoverlapping high-level blocks are also low rank and can be compressed efficiently. This property is used to efficiently calculate the high-level reduced matrix of the MLCBFM through the ACA algorithm in this study. Furthermore an efficient scheme for the high-level characteristic basis functions (CBFs) generation is given, which reduces the redundant operations in the high-level CBFs generation step without loss of accuracy. Numerical results are given to demonstrate the accuracy and efficiency of the presented method.