Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

This paper presents a multilevel fast adaptive cross-approximation (MLFACA) algorithm for accelerated iterative solution of the method of moments (MoM) matrix equation for electrically large targets. The MLFACA compresses the impedance submatrices between well-separated blocks into products of sparse matrices, constructed with the aid of the fast adaptive cross-sampling (FACS) scheme and the butterfly algorithm. As a result, the MLFACA can reduce both the computational time and the storage of the MoM to
${\mathbf{O}}({\mathbf{N}}\;{\mathbf{log}}^{\mathbf{2}}{\text{N}})$
, where
${\mathbf{N}}$
is the number of the Rao–Wilton–Glisson (RWG) basis functions in the analyzed target. Meanwhile, the MLFACA maintains the adaptive and kernel-independent properties. Furthermore, the characteristic basis function method (CBFM) is employed to decrease the size of the outer matrices of the MLFACA to further reduce the storage and iteration time. Numerical results are presented to demonstrate the advantages of the proposed method, including a successful solution of a scattering problem involving 10 861 668 RWG basis functions.