Two-Step Preconditioner of Multilevel Simple Sparse Method for Electromagnetic Scattering Problems

In order to efficiently solve the dense complex linear systems arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel simple sparse method (MLSSM) is used to accelerate the matrix-vector product operations. Because of the nature of EFIE, the resulting linear systems from EFIE formulation are challenging to solve by iterative methods. In this paper, the two-step preconditioner is used to alleviate the low convergence of Krylov subspace solvers, which combine the modified complex shifted preconditioner and sparse approximate inversion (SAI) preconditioner. Numerical examples demonstrate that the two-step preconditioner can greatly improve the convergence of the generalized minimal residual method (GMRES) for the dense complex linear systems and reduce the computationnal time significantly.