基于离散伴随方程的三维雷达散射截面几何敏感度计算

针对有限差分法计算雷达散射截面（RCS）梯度效率低，采用高精度雷达散射截面评估时计算代价高的问题，提出了一种基于麦克斯韦积分方程离散伴随方程的RCS梯度高效计算方法。基于伴随方程的梯度计算可以通过一次雷达散射截面求解、一次伴随方程求解获得RCS关于所有设计变量的梯度。其中麦克斯韦积分方程离散伴随方程的形式与原方程基本一致，可以采用矩量法（MOM）及多层快速多极子算法（MLFMA）求解。伴随方程求解计算量与直接雷达散射截面评估基本一致，存储量在直接雷达散射截面评估的基础上增加不明显。通过双椎体模型、导弹模型对基于矩量法、多层快速多极子算法的伴随梯度进行验证，证明了基于伴随方法的RCS梯度计算可以实现复杂外形中RCS梯度的高效、高精度求解，为基于梯度的高精度气动/隐身一体化优化提供了基础。

Three dimensional radar cross section geometric sensitivity calculation based on discrete adjoint equation

A Radar Cross Section (RCS) gradient calculation method based on adjoint equation of Maxwell integral equation is proposed. This method aims to overcome the high cost and low efficiency in the traditional finite difference calculation method. The adjoint method can obtain the gradients of all design variables by one radar cross-section solution and one adjoint solution. The required calculation amount of the gradient solution is basically independent of the number of design variables. The form of adjoint equation is similar to the original equation, and can be solved by the Method of Moment (MOM) and Multilevel Fast Multipole Algorithm (MLFMA). The calculation and storage amount in solving adjoint equation is basically the same as the calculation of RCS. By adopting the double ogive model and a missile model, two test cases are adopted to ve-rify the reliability and precision of the adjoint method. Gradients calculated based on the adjoint method of MOM and MLFMA are compared with the finite difference results. Numerical results prove the accuracy of the adjoint method, and demonstrate that it can be applied in complex shapes, providing a basis for the construction of gradient-based aerodynamics-stealth optimization framework.