Accurate solutions of extremely large integral-equation problems in computational electromagnetics

Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknowns. Some of the complicated real-life problems (such as scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as benchmarking data for many purposes and even as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and National Aeronautics and Space Administration (NASA) Almond geometries are presented, in addition to the solution of complicated objects, such as the Flamme. The parallel implementation is also extended to solve very large dielectric problems, such as dielectric lenses and photonic crystals.