# American Institute of Mathematical Sciences

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June  2015, 8(3): 419-434. doi: 10.3934/dcdss.2015.8.419

## Radar cross section reduction of a cavity in the ground plane: TE polarization

 1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China 2 Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States

Received  October 2013 Revised  March 2014 Published  October 2014

The reduction of backscatter radar cross section(RCS) in TE polarization for a rectangular cavity embedded in the ground plane is investigated in this paper. It is established by placing a thin, multilayered radar absorbing material(RAM) with possibly different permittivities at the bottom of the cavity. A minimization problem with respect to the backscatter RCS is formulated to determine the synthesis of RAM. The underlying scattered field is governed by a generalized Helmholtz equation with transparent boundary condition. The gradient with respect to the material permittivity is derived by the adjoint state method. A fast solver for the Helmholtz equation is presented for the optimization scheme. Numerical examples are presented to show the efficiency of the algorithm for RCS reduction.
Citation: Gang Bao, Jun Lai. Radar cross section reduction of a cavity in the ground plane: TE polarization. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 419-434. doi: 10.3934/dcdss.2015.8.419
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