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利用远场模式的完全与不完全数据反演声波阻尼区域 被引量：1

The reconstruction of scatterer for impedance boundary condition from the far field pattern
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摘要 提出一种方法,利用远场模式的完全数据与不完全数据反演声波阻尼区域,证明了方法的收敛性,并给出若干数值例子. The inverse scattering problem we are considering in this paper is to determine the acoustic wave impedance boundary. A method is presented which use complete and incomplete data of the far field pattern of the scattering wave to recover the impedance boundary. The convergence of our method is proven. In addition, we give several numerical examples, these examples show the practicality of our method.
作者 王枢 孟文辉
机构地区 西北大学数学系
出处 《纯粹数学与应用数学》 CSCD 北大核心 2006年第1期99-107,共9页 Pure and Applied Mathematics
关键词 反散射问题 反演 阻尼边界 inverse scattering problem, recover, impedance boundary
分类号 O175.29 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Colton D,Kress R.Integrel Equation Methods in Scattering Theory[M].New York:Wiley-Intescience Publication,1983.
  • 2Colton D,Monk P.A Novel Method for Solving The Inverse Scattering Problem for Time-harmonic Acoustic Waves in The Resonance Region Ⅱ[J].SIAM J.Appl.Math.,1986,46:505～523.
  • 3Colton D,Kress R.Inverse Acoustic and Electromagnetic Scattering Theory[M].Now York:Spring-Verlag,1992.
  • 4Ochs R L.The Limited Aperture Problem of Inverse Scattering:Dirichlet Boundary Condition[J].SIAM J.Appl.Math.,1987,47:1320～1341.
  • 5Colton D,Monk P.A Novel Method for Solving The Inverse Scattering Problem for Time-harmonic Acoustic Waves in The Resonance Region[J].SIAM J.Appl.Math.,1985,45:1039～1053.
  • 6王连堂,何志强.利用远场模式的不完全数据反演声波阻尼系数[J].计算数学,2003,25(2):245-256. 被引量：4
  • 7Gilberg D,Trudinger N S.Elliptic Partial Differential Equation of Second Order[M].New Youk:Springer-Verlag,1977.

二级参考文献7

  • 1D.Coltom and P.Monk, A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region, SIAM J. Appl. Math., 45(1985),1039-1053.
  • 2D.Coltom and P.Monk, A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region , SIAM J. Appl. Math., 46(1986),505-523.
  • 3D.Colton and R.Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Spring Verlag, 1992.
  • 4D.Colton and R.Kress, Integral Equation Method in scattering Theory, Wiley-Interscience Publication, New York, 1983.
  • 5D.Colton and A.Kirsch, Dense sets and far field patterns in acoustic wave propagation,SIAM J. Appl. Anal, 15(1984), 996-1006.
  • 6A.Kirsch, Generalized Boundary Value and Control Problems for the Helmholtz Equation,Habilitationschrift, Universitat Gottingen, Gottingen, West Germany, 1984.
  • 7王连堂.利用远场模式反演声波阻尼系数[J].计算数学,1999,21(1):89-98. 被引量：5

共引文献3

同被引文献8

  • 1Colton D, Monk P. A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region[J]. SIAM J. Appl. Math., 1985,45:1039-1053.
  • 2Colton D, Monk P. A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region Ⅱ[J]. SIAM J. Appl. Math.,1986,46:506-523.
  • 3Kitsch A, Kress R. An optimization method in inverse acoustic scattering[M]//Boundary Elements IX vol 3 Fluid Flow and Potential Applications. New York:Springer-Verlag Berlin Heidelberg, 1987,3.
  • 4Ochs R L. The limited aperture problem of inverse acoustic scattering: Dirichlet Bounary Contions[J]. SIAM J. Appl. Math., 1987,47:1320-1941.
  • 5Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory[M]. New York: Springer-Verlag, 1992.
  • 6Colton D, Kress R. Integral Equation Methods in Scattering Theory[M]. New York: Wiley-Interscience Publication, 1983.
  • 7王连堂.反演声波阻尼系数的一个逼近方法[J].计算数学,2000,22(3):265-274. 被引量：12
  • 8王连堂,何志强.利用远场模式的不完全数据反演声波阻尼系数[J].计算数学,2003,25(2):245-256. 被引量：4

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纯粹数学与应用数学
2006年 第1期

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