A higher-order multilevel fast multipole algorithm for 3D scattering

In this paper, we present a higher-order multilevel fast multipole algorithm (MLFMA) for solving integral equations of electromagnetic wave scattering by three-dimensional conducting objects. We first employ higher-order parametric elements to provide an accurate modeling of the scatterer´s geometry and then higher-order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer´s surface. The resultant numerical system of equations is then solved using the MLFMA with a reduced computational complexity. Appropriate preconditioning techniques are employed to speedup the MLFMA solution.