Efficient matrix filling of multilevel simply sparse method via multilevel fast multipole algorithm

In this paper, an improved multilevel simply sparse method (MLSSM) is proposed for solving electromagnetic scattering problems that are formulated using the electric field integral equation approach. Previously, the matrix filling procedure of the conventional MLSSM is based on the adaptive cross approximation (ACA) method. Although the ACA is more efficient than direct filling, it requires a longer filling time for the far-field matrix than that of the multilevel fast multipole algorithm (MLFMA). Three problems with moderate electrical sizes are used to demonstrate that the far-field matrix filling memory of the ACA is also higher than that of the MLFMA. Hence, the MLFMA is utilized to reduce both the far-field matrix filling time and memory of the conventional MLSSM. Since the MLSSM recompresses the far-field interaction matrix of the MLFMA, the matrix-vector multiplication of the proposed method is more efficient than that of the MLFMA. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.