GO solutions with Fast Marching

摘要

We develop an approach for a fast and accurate determination of the Geometrical Optics solutions to Maxwell's equations based on the determination of the eikonal function. The approach, here presented for a 3D problem, is devised to handle scenarios involving complex spatially varying refraction indices. A new solution to a critical issue related to matching of computational grids across scatterers' boundaries is introduced. The explicit solution of the eikonal equation allows to set up an inverse ray tracing scheme, which proves particularly convenient as compared to direct ray tracing. Inverse ray tracing is performed using techniques from computer graphics improving computational performance. The field amplitude and polarization are then found by solving the relative transport equations along each ray.