Simulation of the interaction of electromagnetic fields with multiple rough scatterers in three dimensions

We describe a fully discrete high-order algorithm for simulating low to medium frequency electromagnetic waves scattered by an ensemble of perfectly conducting three dimensional particles with rough non-convex surfaces. A key component of our surface integral algorithm is the high-order approximation of the tangential surface current on each obstacle in the ensemble, which leads to linear systems with considerably fewer unknowns than low order boundary element methods. This allows us to obtain high-order solutions using a fast iterative solver for multiple scattering problems (based on reflections from the obstacles) that takes advantage of fast solution of single obstacle scattering problems with multiple right hand sides (corresponding to the reflections) using LU factorisation.