Numerical Solution of the GO Equations for GRIN Lens Antennas by Using the Lax-Friedrichs Sweeping Method

This paper introduces a novel method for analyzing inhomogeneous lenses by numerically solving the Eikonal and transport equations on a computational grid, eliminating the need for ray tracing.The approach employs the sweeping method, a numerical technique that iteratively solves the governing equations across the grid.By alternating the traversal directions and incorporating Gauss-Seidel updates, the method ensures convergence while accounting for boundary conditions and neighboring grid values.The proposed algorithm, known as the Lax-Friedrichs Sweeping Method (LFSM), offers an efficient solution to the factored Eikonal and transport equations.It enables highly accurate computation of the Eikonal Laplacian, which significantly improves amplitude accuracy.This method outperforms traditional ray-tracing techniques in terms of speed, precision, computational efficiency, and robustness.The inputs required for LFSM-based GRIN lens analysis include a computational grid, a refractive index map, and the type and position of the source.The implementation of the LFSM is here presented, as well as the application of it to the analysis of a Maxwell fish eye lens.