An efficient adjoint method for the aero-stealth shape optimization design

Sensitivity analysis is an important part of gradient-based aero-stealth shape optimization design. An efficient Radar Cross Section (RCS) gradient evaluation method based on the adjoint approach is proposed in this paper. The merits of this proposed method mainly include the following two aspects. First, the adjoint field will be obtained from a single solution of the scattering problem without solving the adjoint equation. Second, the residual derivatives computing code is generated through the adjoint mode of Automatic Differentiation (AD) technique and is optimized by changing the “two-sweeps” architecture into the “inner-loop two-sweeps” architecture. The time consumption and memory usage are tested and the results show that the AD adjoint mode with “inner-loop two-sweeps” architecture is high-efficiency while the memory consumption is friendly. In addition, the accuracy of the adjoint method is verified through the finite differences method. After that, a gradient-based aero-stealth optimization design method is developed and employed to study the shape requirements of aerodynamic and stealth performance. The cost function is composed of the drag coefficient and the RCS. The results show that several trade-off configurations would be obtained by selecting different weight factors and the pure stealth optimization design would lead to a screwy shape. Further studies illustrate that the RCS reduction comes from two aspects. On the one hand, the sharp leading edge could reduce the surface current magnitude and avoid the specular back-scattering. On the other hand, the undulations could change the phases and weaken the superimposed effect.