Multilevel FFT Method for Surface-to-Volume Field Propagation in Electrically Large Dielectric Objects

We have developed a multilevel FFT (MLFFT) method to propagate known surface currents on the boundary to the interior of electrically large (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\gt }30\lambda $ </tex-math></inline-formula>) homogeneous dielectric objects with low memory. The two enabling features are: 1) a flattened hierarchy to make the fast Fourier transforms (FFTs) at the coarsest level as large as possible and 2) forgoing the disaggregation step of the MLFMM in favor of direct field evaluation. These allow the interior field to be computed on a finely sampled Cartesian grid in 10s of minutes on standard workstations for a single incident field. The method outperforms today’s commercial electromagnetic solvers in time and memory for the same application. The accuracy of the method was validated using two commercial solvers and the computation time was measured using progressively larger dielectric spheres. The primary application of the MLFFT is distorted-type imaging and inverse scattering algorithms that require the total electric field inside a homogeneous object. The specific scientific use case is the 60-MHz monostatic Juventas radar (JuRa) radar on the Hera/Juventas mission that will image the interior of asteroid Dimorphos.