A Hybrid High-Order Algorithm for Radar Cross Section Computations

We describe a high-order method for computing the monostatic and bistatic radar cross section (RCS) of a class of three-dimensional targets. Our method is based on an electric field surface integral equation reformulation of the Maxwell equations. The hybrid nature of the scheme is due to approximations based on a combination of tangential and nontangential basis functions on a parametric reference spherical surface. A principal feature of the high-order algorithm is that it requires solutions of linear systems with substantially fewer unknowns than existing methods. We demonstrate that very accurate RCS values for medium (electromagnetic-) sized scatterers can be computed using a few tens of thousands of unknowns. Thus linear systems arising in the highorder method for low to medium frequency scattering can be solved using direct solves. This is extremely advantageous in monostatic RCS computations, for which transmitters and receivers are co-located and hence the discretized electromagnetic linear system must be solved for hundreds of right-hand sides corresponding to receiver locations. We demonstrate the high-order convergence of our method for several three-dimensional targets. We prove the high-order spectral accuracy of our approximations to the RCS for a class of perfect conductors described globally in spherical coordinates.