Optimal design of a cavity for RCS reduction
Jun Lai, CIMS

We study  the reduction of backscatter radar cross section (RCS) for a cavity embedded in the ground plane. One approach is through shape optimization.  RCS reduction for the cavity is formulated as a shape optimization problem involving the Helmholtz equation. The existence of the minimizer is proved under an appropriate constraint. Descent directions of the objective function with respect to the boundary can be found via the domain derivative. It is used in a gradient-based optimization scheme to find the optimal shape of the cavity. Another approach for RCS reduction is through the coating material. Assume the bottom of the cavity is coated by a thin, multilayered radar absorbing material (RAM) with possibly different permittivities. The objective is to minimize the backscatter RCS by the incidence of a plane wave over a single or a set of incident angles and frequencies. By formulating the scattering problem as a Helmholtz equation with artificial boundary condition, the gradient with respect to the material permittivities is determined efficiently by the adjoint state method, which is integrated into a nonlinear optimization scheme. Numerical example shows the RCS may be significantly reduced through these approaches.