Multilayer Iterative Solutions of Large-Scale Electromagnetic Problems Using MLFMA

We present multilayer solutions of large-scale electromagnetic problems using the multilevel fast multipole algorithm (MLFMA). With the conventional algebraic preconditioners based on the available near-field interactions, the cost of iterative solutions may exceed the linearithmic complexity, particularly for ill-conditioned systems, despite the efficient matrix-vector multiplications by MLFMA. We show that, using a multilayer approach employing approximate and full versions of MLFMA, the complexity can be reduced to the desired levels without deteriorating the accuracy. The proposed approach significantly accelerates iterative solutions also for well-conditioned system, while it does not require any extra memory as opposed to memory-hungry algebraic preconditioners. Numerical results of scattering problems involving both canonical and complicated structures are presented to demonstrate the efficiency of the multilayer strategy.