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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
References:
[1]

H. Ammari, G. Bao, and A. W. Wood, An integral equation method for the electromagnetic scattering from cavities,, Math. Meth. Appl. Sci., 23 (2000), 1057. doi: 10.1002/1099-1476(200008)23:12<1057::AID-MMA151>3.0.CO;2-6. Google Scholar

[2]

H. Ammari, G. Bao and A. W. Wood, Analysis of the electromagnetic scattering from a cavity,, Japan J. Indust. Appl. Math., 19 (2002), 301. doi: 10.1007/BF03167458. Google Scholar

[3]

H. Ammari, G. Bao and A. W. Wood, A cavity problem for maxwells equation,, Meth. Appl. Anal., 9 (2002), 249. Google Scholar

[4]

H. T. Anastassiu, A review of electromagnetic scattering analysis for inlets, cavities and open ducts,, IEEE Antennas and Propagation Magazine, 45 (2003), 27. doi: 10.1109/MAP.2003.1282177. Google Scholar

[5]

G. Bao, J. Gao and P. Li, Analysis of direct and inverse cavity scattering problems,, Numer. Math. Theor. Meth. Appl., 4 (2011), 419. doi: 10.4208/nmtma.2011.m1021. Google Scholar

[6]

G. Bao, J. Gao, J. Lin and W. Zhang, Mode matching for the electromagnetic scattering from three-dimensional large cavities,, IEEE Antennas Wireless Propagat., 60 (2012), 2004. doi: 10.1109/TAP.2012.2186255. Google Scholar

[7]

G. Bao and J. Lai, Radar cross section reduction of a cavity in the ground plane,, Commun. Comput. Phys., (). Google Scholar

[8]

G. Bao and W. Sun, A fast algorithm for the electromagnetic scattering from a large cavity,, SIAM J. Sci. Comput., 27 (2005), 553. doi: 10.1137/S1064827503428539. Google Scholar

[9]

G. Bao, K. Yun and Z. Zhou, Stability of the scattering from a large electromagnetic cavity in two dimensions,, SIAM J. Math. Anal., 44 (2012), 383. doi: 10.1137/110823791. Google Scholar

[10]

G. Bao and W. Zhang, An improved mode-matching method for large cavities,, IEEE Antennas Wireless Propagat. Lett., 27 (2005), 393. doi: 10.1109/LAWP.2005.859375. Google Scholar

[11]

R. Burkholder and P. Pathak, Analysis of em penetration into and scattering by electrically large open waveguide cavities using gaussian beam shooting,, Proc. IEEE, 79 (1991), 1401. doi: 10.1109/5.104215. Google Scholar

[12]

R. Chou and S. Lee, Modal attenuation in multilayered coating waveguide,, IEEE Trans. Microwave Theory Tech., 36 (1988), 1167. Google Scholar

[13]

D. C. Dobson, Optimal design of periodic antireflective structures for the helmholtz equation,, Euro. J. Appl. Math., 4 (1993), 321. doi: 10.1017/S0956792500001169. Google Scholar

[14]

R. Hemon, P. Pouliguen, H. He, J. Saillard and J. F. Damiens, Computation of em field scattered by an open-ended cavity and by a cavity under radome using the iterative physical optics,, Progress In Electromagnetics Research, 80 (2008), 77. Google Scholar

[15]

P. Huddleston, Scattering from conducting finite cylinders with thin coatings,, IEEE Trans. Antennas Propagat., 35 (1987), 1128. doi: 10.1109/TAP.1987.1143984. Google Scholar

[16]

J. Jin, A finite element-boundary integral formulation for scattering by threedimensional cavity-backed apertures,, IEEE Trans. Antennas Propagat., 39 (1991), 97. Google Scholar

[17]

J. Jin, The Finite Element Method in Electromagnetics,, 2nd edition. Wiley, (2002). Google Scholar

[18]

J. H. Kim and Y. J. Lee, Optimization of gradient-index antireflection coatings,, J. Opt. Soc. Korea, 4 (2000), 86. doi: 10.3807/JOSK.2000.4.2.086. Google Scholar

[19]

E. Knott, J. Shaeffer, and M. Tuley, Radar Cross Section,, Second edition. Scitech Publishing Inc, (2004). Google Scholar

[20]

H. Ling, R. Chou and S. Lee, Shooting and bouncing rays: Calculating the rcs of an arbitrarily shaped cavity,, IEEE Trans. Antennas Propagat., 37 (1989), 194. doi: 10.1109/8.18706. Google Scholar

[21]

J. Liu and J. Jin, A special higher order finite-element method for scattering by deep cavities,, IEEE Trans. Antennas Propagat., 48 (2000), 694. Google Scholar

[22]

P. Monk, Finite Element Methods for Maxwell's Equation,, Oxford University Press, (2003). doi: 10.1093/acprof:oso/9780198508885.001.0001. Google Scholar

[23]

H. Mosallaei and Y. Rahmat-Samii, Rcs reduction of canonical targets using genetic algorithm synthesized ram,, IEEE Trans. Antennas Propagat., 48 (2000), 1594. doi: 10.1109/8.899676. Google Scholar

[24]

J. Nocedal and S. J. Wright, Numerical Optimization,, Second Edition, (2006). Google Scholar

[25]

S. Ohnuki and T. Hinata, RCS of material partially loaded parallel-plate waveguide cavities,, IEEE Trans. Antennas Propagat., 51 (2003), 337. doi: 10.1109/TAP.2003.809855. Google Scholar

show all references

References:
[1]

H. Ammari, G. Bao, and A. W. Wood, An integral equation method for the electromagnetic scattering from cavities,, Math. Meth. Appl. Sci., 23 (2000), 1057. doi: 10.1002/1099-1476(200008)23:12<1057::AID-MMA151>3.0.CO;2-6. Google Scholar

[2]

H. Ammari, G. Bao and A. W. Wood, Analysis of the electromagnetic scattering from a cavity,, Japan J. Indust. Appl. Math., 19 (2002), 301. doi: 10.1007/BF03167458. Google Scholar

[3]

H. Ammari, G. Bao and A. W. Wood, A cavity problem for maxwells equation,, Meth. Appl. Anal., 9 (2002), 249. Google Scholar

[4]

H. T. Anastassiu, A review of electromagnetic scattering analysis for inlets, cavities and open ducts,, IEEE Antennas and Propagation Magazine, 45 (2003), 27. doi: 10.1109/MAP.2003.1282177. Google Scholar

[5]

G. Bao, J. Gao and P. Li, Analysis of direct and inverse cavity scattering problems,, Numer. Math. Theor. Meth. Appl., 4 (2011), 419. doi: 10.4208/nmtma.2011.m1021. Google Scholar

[6]

G. Bao, J. Gao, J. Lin and W. Zhang, Mode matching for the electromagnetic scattering from three-dimensional large cavities,, IEEE Antennas Wireless Propagat., 60 (2012), 2004. doi: 10.1109/TAP.2012.2186255. Google Scholar

[7]

G. Bao and J. Lai, Radar cross section reduction of a cavity in the ground plane,, Commun. Comput. Phys., (). Google Scholar

[8]

G. Bao and W. Sun, A fast algorithm for the electromagnetic scattering from a large cavity,, SIAM J. Sci. Comput., 27 (2005), 553. doi: 10.1137/S1064827503428539. Google Scholar

[9]

G. Bao, K. Yun and Z. Zhou, Stability of the scattering from a large electromagnetic cavity in two dimensions,, SIAM J. Math. Anal., 44 (2012), 383. doi: 10.1137/110823791. Google Scholar

[10]

G. Bao and W. Zhang, An improved mode-matching method for large cavities,, IEEE Antennas Wireless Propagat. Lett., 27 (2005), 393. doi: 10.1109/LAWP.2005.859375. Google Scholar

[11]

R. Burkholder and P. Pathak, Analysis of em penetration into and scattering by electrically large open waveguide cavities using gaussian beam shooting,, Proc. IEEE, 79 (1991), 1401. doi: 10.1109/5.104215. Google Scholar

[12]

R. Chou and S. Lee, Modal attenuation in multilayered coating waveguide,, IEEE Trans. Microwave Theory Tech., 36 (1988), 1167. Google Scholar

[13]

D. C. Dobson, Optimal design of periodic antireflective structures for the helmholtz equation,, Euro. J. Appl. Math., 4 (1993), 321. doi: 10.1017/S0956792500001169. Google Scholar

[14]

R. Hemon, P. Pouliguen, H. He, J. Saillard and J. F. Damiens, Computation of em field scattered by an open-ended cavity and by a cavity under radome using the iterative physical optics,, Progress In Electromagnetics Research, 80 (2008), 77. Google Scholar

[15]

P. Huddleston, Scattering from conducting finite cylinders with thin coatings,, IEEE Trans. Antennas Propagat., 35 (1987), 1128. doi: 10.1109/TAP.1987.1143984. Google Scholar

[16]

J. Jin, A finite element-boundary integral formulation for scattering by threedimensional cavity-backed apertures,, IEEE Trans. Antennas Propagat., 39 (1991), 97. Google Scholar

[17]

J. Jin, The Finite Element Method in Electromagnetics,, 2nd edition. Wiley, (2002). Google Scholar

[18]

J. H. Kim and Y. J. Lee, Optimization of gradient-index antireflection coatings,, J. Opt. Soc. Korea, 4 (2000), 86. doi: 10.3807/JOSK.2000.4.2.086. Google Scholar

[19]

E. Knott, J. Shaeffer, and M. Tuley, Radar Cross Section,, Second edition. Scitech Publishing Inc, (2004). Google Scholar

[20]

H. Ling, R. Chou and S. Lee, Shooting and bouncing rays: Calculating the rcs of an arbitrarily shaped cavity,, IEEE Trans. Antennas Propagat., 37 (1989), 194. doi: 10.1109/8.18706. Google Scholar

[21]

J. Liu and J. Jin, A special higher order finite-element method for scattering by deep cavities,, IEEE Trans. Antennas Propagat., 48 (2000), 694. Google Scholar

[22]

P. Monk, Finite Element Methods for Maxwell's Equation,, Oxford University Press, (2003). doi: 10.1093/acprof:oso/9780198508885.001.0001. Google Scholar

[23]

H. Mosallaei and Y. Rahmat-Samii, Rcs reduction of canonical targets using genetic algorithm synthesized ram,, IEEE Trans. Antennas Propagat., 48 (2000), 1594. doi: 10.1109/8.899676. Google Scholar

[24]

J. Nocedal and S. J. Wright, Numerical Optimization,, Second Edition, (2006). Google Scholar

[25]

S. Ohnuki and T. Hinata, RCS of material partially loaded parallel-plate waveguide cavities,, IEEE Trans. Antennas Propagat., 51 (2003), 337. doi: 10.1109/TAP.2003.809855. Google Scholar

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