Radar Cross Section Gradient Calculation of Coated Aircraft Based on the Adjoint Method and Improved Self-Dual Integral Equations

This study presents an efficient method for calculating the gradient of the radar cross section (RCS) of coated aircraft. The method is based on adjoint theory and an improved formulation of self-dual integral equations (SDIE), incorporating the multilevel fast multipole algorithm (MLFMA) and impedance boundary conditions (IBC). To address the computational limitations of conventional SDIE methods, such as inaccuracies from extraneous integral terms at coated interfaces and ill-conditioning with nonuniform IBC, we propose an improved SDIE formulation that incorporates MLFMA and IBC. The numerical properties of the adjoint and control equations derived from the improved SDIE are analyzed, and a novel right preconditioning technique is introduced to improve solver convergence and computational efficiency, thus significantly accelerating gradient computation. Numerical experiments conducted on a flying wing model validate the accuracy and efficiency of the proposed method for RCS gradient calculation. The results confirm that the method is both efficient and reliable for computing RCS gradients of coated aircraft.