Fast iterative solution of integral equation with matrix decomposition algorithm and multilevel simple sparse method

In order to efficiently solve large dense complex linear systems arising from the electric field integral equations formulation of electromagnetic problems, matrix decomposition algorithm-singular value decomposition (MDA-SVD) is used to accelerate the matrix-vector product (MVP) operation. Based on the symmetry of the impedance matrix, a modified multilevel simple sparse method (M-MLSSM) is proposed. Combining MDA and M-MLSSM, the authors obtain a sparse representation of the impedance matrix and construct a fast MVP operation. A perfectly electrically conducting sphere and the series-fed microstrip antenna array are simulated to demonstrate the validity of the proposed method. Moreover, numerical experiments demonstrate that combined MDA and M-MLSSM can accelerate the MVP operation and reduce memory requirements by at least half an order of magnitude compared to MDA-SVD.