Two-Level Preconditioning Techniques for Electromagnetic Wave Scattering Problems

We investigate preconditioned iterative solutions of large dense complex valued matrices arising from discretizing the hybrid integral equations of electromagnetic scattering. Due to the specific data pattern, we propose to construct two-level (TL) preconditioners to treat the conducting and dielectric parts more efficiently. The main purpose of this study is to show that the TL preconditioning is effective with the MLFMA and can reduce the number of Krylov iterations substantially by using subdivided domain of the near part matrix for each level. Our experimental results indicate that the TL preconditioning maintains the computational complexity of the MLFMA, but converges much faster, thus effectively reduces the overall simulation time for the coated material objects.