Shape optimization for radar cross sections by a gradient method

Abstract

SUMMARYA gradient method for optimization of shape and materials for radar cross section (RCS) reduction is derived from Maxwell's equations. The method uses the adjoint problem and finds the derivatives of the RCS with respect to all design parameters from a single solution of the scattering problem. The method is tested in two-dimensional test problems to minimize the RCS in specified angular intervals at a single frequency, and finds configurations with strongly reduced RCS in a small number of iterations. In the absence of other constraints, the optimal shapes of perfectly electrically conducting (PEC) scatterers have sharp corners pointing in the directions where the RCS is minimized and shapes optimized at a single or small number of frequencies exhibit corrugations with about half the wavelength of the incident wave. The corrugations can be suppressed by means of penalty functions, and this gives only moderate increases of the RCS. After such regularization, the optimal shapes agree well with expectations from geometrical optics; they have almost flat surfaces whose normals lie outside the intervals chosen for RCS optimization, and sharp edges at locations where the surface normal points into the intervals in which the RCS is minimized. Shape optimization of PEC wing profiles aiming at both good aerodynamical properties and low RCS show give conflicting requirements on the shape.

Computational optimization of the thermal performance of internally finned ducts

“…Other examples of the applications of the gradient method inc1ude the optimization of a radar cross section [Bondeson et al (2004)], and the optimization of a shaft cross-section using an adaptive shape refinement technique akin to an automatic adjustment of the number of control points on a spline [Kohli and Carey (1993)]. An adaptive shape refinement technique, based on the gradient and the finite element methods, has been used by Schleupen et al (2000) to optimize sorne mechanical objects subjected to applied stresses.…”

On the Influence of Coupling Amc Resonances for RCS Reduction in the SHF Band

“…For many years, Radar Cross Section (RCS) [1][2][3][4][5][6][7][8][9] reduction has been a field of interest for different applications where the goal is the reduction of the scattered electromagnetic field when illuminating the objectof-interest by an incident wave [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Depending on the emitting and receiving device, RCS can be monostatic (the transmitter and the …”

Determination of Interrogating Frequencies to Maximize Electromagnetic Backscatter from Objects with Material Coatings

“…For example, the papers [9,12,22,23] consider multidisciplinary shape optimization problems for an airfoil where the aim is to minimize the electromagnetic backscattering together with aerodynamical constraints and maximization. In [11,17] an optimization for the shape and material parameters for the coating layer is performed to minimize the RCS in a sector when the shape of outer boundary of the airfoil is fixed. The paper [8] considers the optimization of the material parameters of a coating layer.…”