Adjoint-based RCS surface sensitivity calculation for very large electrical size object

The primary concern in stealth aircraft design is the very large electrical size objects. However, the computational and storage requirements of these objects present significant obstacles for current high-fidelity design methods, particularly when addressing high-dimensional complex engineering design problems. To address these challenges, we developed a surface sensitivity technique based on the multilevel fast multipole algorithm (MLFMA). An access and storage of sparse partial derivative tensor was improved to significantly enhanced the computation performance. The far-field interactions of the surface sensitivity equation were realized by differential the multipole expansion. In addition, we proposed a fast far-field multiplication method to accelerate the multiplication process. The surface mesh derivative with respect to the design variables was calculated by analytical and complex variable methods, substantially improving computational efficiency. These advancements enabled the MLFMA-based surface sensitivity method to millions meshes and large-scale gradients, extending gradient-based optimization for very large electrical size problems. Test cases have verified the effectiveness of this method in optimizing very large electrical objects in terms of both accuracy and efficiency.