摘要
时谐电磁波入射到基面内任意形状的开洞上,此过程数学上可由Maxwell 方程组来描述.研究了逆散射问题,即利用散射场的信息来确定开洞的形状.证明了二维TM极化情形时逆散射问题的惟一性和局部稳定性.
出处
《中国科学（A辑）》
CSCD
北大核心
2005年第6期641-650,共10页
Science in China(Series A)
基金
国家基础研究重大项目(973)(批准号:G1999032802)国家自然科学基金重点项目(批准号:10431030)部分资助
参考文献11
-
1Ammari H, Bao G, Wood A W. Analysis of the electromagnetic scattering from a cavity. Japan J Indust,Appl Math, 2002, 19:301-310.
-
2Ammari H, Bao G, Wood A W. A cavity problem for Maxwell's equations. Meth Appl Anal, 2002, 9:249-260.
-
3Ammari H, Bao G, Wood A W. An integral equation method for the electromagnetic scattering from cavitys. Math Meth Appl Sci, 2000, 23:1057-1072.
-
4Asvestas J S, Kleinman R E. Electromagnetic scattering by indented screens. IEEE Trans Antennas Propag, 1994, 42:22-30.
-
5Goggans P M, Shumpert T H. Backscatter RCS for TE and TM excitations of dielectric-field cavity backed apertures in two-dimensional bidies. IEEE Trans Antennas Propag, 1991, 39:1224-1227.
-
6Senior T B A, Sarabandi K, Natzke J R. Scattering by a narrow gap. IEEE Trans Antennas Propag, 1990,38:1102-1110.
-
7李家春 周显初.数学物理中的渐近方法[M].北京:科学出版社,2002..
-
8Leis R. Initial boundary value problems in mathematical physics. New York: Wiley, 1986.
-
9Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order. New York, Berlin:Springer-Verlag, 1983.
-
10Elschner J, Schmidt G. Inverse scattering for periodic strctures, stability of polygonal interfaces. Inverse Problems, 2001, 17:1817-1829.
共引文献3
-
1刘竞,陈明文,孙仁济,王自东.二维非稳态晶体生长问题的扰动分析[J].扬州大学学报（自然科学版）,2005,8(4):32-35.
-
2刘竞,陈明文,王自东.扰动边界条件下晶体生长模型的渐近分析[J].北京工商大学学报（自然科学版）,2006,24(1):63-65.
-
3敖继军,阿其拉图,牡丹.混合气体线性化Boltzmann算子的特征值与特征函数[J].应用数学学报,2011,34(4):591-601.
同被引文献34
-
1童重亮,程晋,山本昌宏.由Dirichlet到Neumann映射重构平面上椭圆型方程对流系数的一种方法[J].中国科学（A辑）,2004,34(6):752-766. 被引量：2
-
2Kohn R V, Vogelius M. Determining conductivity by boundary measurements. Commun Pure Appl Math, 37:113-123 (1984)
-
3Liu J J, Cheng J, Nakamura G. Reconstruction and uniqueness of an inverse scattering problem with impedance boundary. Sci China Set A-Math, 45(11): 1408 -1419 (2002)
-
4Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton- Jacobi formulations. J Comput Phys, 79:12-49 (1988)
-
5Osher S, Fedkiw R. Level set methods and Dynamic Implicit surfaces. In: Applied Mathematical Sciences, Vol 153. New York: Springer, 2003
-
6Santosa F. A level set approach for inverse problems involving obstacles. ESAIM, Control Optim Calculus Variations, 1:17- 33 (1996)
-
7Dorn O, Lesselier D. Lever set method for inverse scattering. Inverse Problems, 22:67-131 (2006)
-
8Chan T F, Tai X C. Level set and total variation regularization for elliptic inverse problems with discom tinuous coefficients. J Comput Phys, 193:40-66 (2003)
-
9Chan T F, Tai X C. Identification of discontinuous coefficients in elliptic problems using total variation regularisation. SIAM J Sci Comput, 25:881-904 (2003)
-
10Mumford D, Shah J. Optimal approximation by piecewise smooth functions and associated variational problems. Commun Pure Appl Math, 42:577-685 (1989)
-
1洞穴逆散射问题解的惟一性与局部稳定性[J].中国学术期刊文摘,2005,11(23):2-2.
-
2杨孝英,马富明,杜新伟.计算开洞穴电磁散射问题的一种优化PML方法[J].吉林大学学报（理学版）,2009,47(2):185-190. 被引量：10
-
3杨绍甫,白建平,张耀举.光在不同界面反射时的Goos-Hnchen位移[J].河南大学学报（自然科学版）,2009,39(1):22-24.
-
4徐记伟,时家明.电磁波在二维等离子体光子晶体中的传播特性研究[J].微波学报,2010,26(5):78-81. 被引量：1
-
5林炎和,朱绮彪,张妍.Opposite Goos-H^inchen Displacements for TE- and TM-Polarized Beams Transmitting through a Slab of Indefinite Metamaterial[J].Chinese Physics Letters,2010,27(7):133-136. 被引量：1
-
6Gang Bao,Faouzi Triki.ERROR ESTIMATES FOR THE RECURSIVE LINEARIZATION OF INVERSE MEDIUM PROBLEMS[J].Journal of Computational Mathematics,2010,28(6):725-744. 被引量：3
-
7杨允表,黄剑源.四面开洞核心简体在承受竖向集中力时的力学分析[J].宁波大学学报（理工版）,1997,10(4):42-48.
-
8刘洋,程立,汪家春,王启超,袁忠才,时家明.发光等离子体对6GHz高功率微波的防护性能研究[J].发光学报,2016,37(10):1292-1298. 被引量：3
-
9汪能军.核心单筒式悬挂结构中四面开洞核心筒体的扭转振动[J].宁波大学学报（理工版）,1998,11(2):50-56.
-
10王芳芳,张业荣.Relevance vector machine technique for the inverse scattering problem[J].Chinese Physics B,2012,21(5):19-24. 被引量：5
