Rigorous Solutions of Electromagnetic Problems Involving Hundreds of Millions of Unknowns

Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be easily achieved, even when using the most powerful computers with state-of-the-art technology. Hence, many electromagnetic problems in the literature have been solved by resorting to various approximation techniques, without controllable error. In this paper, we present full-wave solutions of scattering problems discretized with hundreds of millions of unknowns by employing a parallel implementation of the Multilevel Fast Multipole Algorithm. Various examples involving canonical and complicated objects, including scatterers larger than 1000 lambda, are presented, in order to demonstrate the feasibility of accurately solving large-scale problems on relatively inexpensive computing platforms.