MLACE-MLFMA Combined With Reduced Basis Method for Efficient Wideband Electromagnetic Scattering From Metallic Targets

In this paper, a fast interpolation algorithm [multilevel accelerated Cartesian expansion (MLACE)-multilevel fast multipole algorithm (MLFMA)-reduced basis method (RBM)] is proposed for the first time by leveraging the benefits of the MLACE, the classical MLFMA, and the RBM; furthermore, a novel nonblind sampling method (NBSM) is proposed to approximate an orthogonal subspace for the MLACE-MLFMA-RBM. By integrating the empirical interpolation method (EIM) and the error-based compensation method (EBCM) into the NBSM, we first efficiently establish a robust and precision-controllable orthogonal subspace. Next, with the accurate orthogonal subspace, the MLACE-MLFMA-RBM can simplify the iterative solution process of the MLACE-MLFMA or the MLFMA into N
_g
matrix-vector multiplications (MVMs) and the solution of a reduced N
_g
-dimensional linear equation (N
_g
is the number of orthonormal vectors). Note that only the MVMs between the far-region impedance matrix and the orthogonal vector bases are calculated. In comparison with the classical MLACE-MLFMA and the MLACE-MLFMA-RBM based on different sampling methods for wideband electromagnetic (EM) responses, our proposed algorithms require less memory and CPU time and integrate higher flexibility. The numerical results are provided to demonstrate the accuracy, efficiency, and flexibility.