Multilevel Fast Multipole Algorithm-Based Direct Solution for Analysis of Electromagnetic Problems

In this communication, a multilevel fast multipole algorithm (MLFMA)-based direct method is proposed for solving electromagnetic scattering problems that are formulated using the electric-field integral equation (EFIE) approach. The method is based on the multilevel compressed block decomposition (MLCBD) algorithm. Previously, the matrix filling procedure of the MLCBD is based on the matrix decomposition algorithm-singular value decomposition (MDA-SVD) method. Although the MDA-SVD is more efficient than direct filling, it requires a longer filling time for the far-field matrix than for the MLFMA. The problems are used to demonstrate that the matrix filling memory requirement of the MDA-SVD is also higher than that of the MLFMA. Hence, the MLFMA is utilized to reduce both the matrix filling time and memory of the MLCBD. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.