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An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An Improved Hybrid Method for Inverse Obstacle Scattering Problems
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摘要 An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method. An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.
作者 LIU JUAN MA FU-MING
机构地区 College of Information Science and Technology School of Mathematics
出处 《Communications in Mathematical Research》 CSCD 2011年第3期215-226,共12页 数学研究通讯（英文版）
基金 The Major State Research Development Program(2005CB321701) of China
关键词 hybrid method inverse obstacle scattering one incident direction unknown scatterer hybrid method, inverse obstacle scattering, one incident direction, unknown scatterer
分类号 O241.81 [理学—计算数学] TS104.5 [轻工技术与工程—纺织工程]
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参考文献15

  • 1Kress, R., Uniqueness and numerical methods in inverse obstacle scattering, J. Phys. Conf. Ser., 73(2007), 012003.
  • 2Kirsch, A. and Kress, R., On an integral equation of the first kind in inverse acoustic scattering, Inverse Problems, in: Cannon and Hornung eds., Internat. Schriftenreihe Numer. Math., vol. 77, Birkhiuser, Basel, 1986, pp. 93-102.
  • 3Kirsch, A. and Kress, R., A numerical method for an inverse scattering problem, in: Engl and Groetsch ed., Inverse and ill-posed problems, pp. 279-290, Notes Rep. Math. Sci. Engrg., Vol. 4, Academic Press, Orlando, 1987.
  • 4Kirsch, A. and Kress, R., An optimization method in inverse acoustic scattering in: Brebbia et al. ed., Fluid Flow and Potential Applications, pp. 3-18, Boundary Elements IX, Vol.3, Springer-Verlag, Berlin Heidelberg, New York, 1987.
  • 5Hettlich, F., Frchet derivatives in inverse obstacle scattering, Inverse Problems, 11(1995), 371-382.
  • 6Potthast, R., Frchet differentiability of the solution to the acoustic Neumann scattering prob- lem with respect to the domain, J. Inverse Ill-posed Probl., 4(1996), 67-84.
  • 7Serranho, P., A hybrid method for inverse scattering for shape and impedance, Inverse Prob- lems, 22(2006), 663-680.
  • 8Kress, R. and Serranho, P., A hybrid method for sound-hard obstle reconstruction, J. Corn- put. Appl. Math., 204(2007), 418-427.
  • 9Serranho, P., A hybrid method for inverse obstacle scattering problems, PhD. Thesis, Georg- August-Universitat, Germany, Gottingen, 2007.
  • 10Ivanyshyn, 0., Shape reconstruction of acoustic obstacles from the modulus of the far field pattern, Inverse Probl. Imaging, 1(2007), 609-622.
Communications in Mathematical Research
2011年 第3期

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