The decomposition method for an interior inverse scattering problem with a Neumann boundary condition

ZHANG Huan; LIU Lihan

doi:10.13471/j.cnki.acta.snus.2020.05.02.2020A016

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The decomposition method for an interior inverse scattering problem with a Neumann boundary condition

Research articles | 更新时间：2023-11-01

- The decomposition method for an interior inverse scattering problem with a Neumann boundary condition
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 60, Issue 4, Pages: 170-176(2021)
- 作者机构：
  
  重庆师范大学数学科学学院，重庆 401331
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020.05.02.2020A016
  CLC： O175
- Published：25 July 2021，
  
  Published Online：05 November 2020，
  
  Received：02 May 2020，
  
  Accepted：09 June 2020
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张欢,刘立汉.基于分裂法的内部Neumann反散射问题[J].中山大学学报(自然科学版),2021,60(04):170-176.

ZHANG Huan,LIU Lihan.The decomposition method for an interior inverse scattering problem with a Neumann boundary condition[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(04):170-176.
张欢,刘立汉.基于分裂法的内部Neumann反散射问题[J].中山大学学报(自然科学版),2021,60(04):170-176. DOI： 10.13471/j.cnki.acta.snus.2020.05.02.2020A016.

ZHANG Huan,LIU Lihan.The decomposition method for an interior inverse scattering problem with a Neumann boundary condition[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(04):170-176. DOI： 10.13471/j.cnki.acta.snus.2020.05.02.2020A016.

摘要

通过分裂法研究了具有Neumann边界条件的内部声波反散射问题。首先，证明了在Neumann边界条件下散射体的位置、形状可由腔体内部的点源测量数据唯一确定。然后，用分裂法的思想来反演未知散射体的边界及其形状。最后，给出了2个数值例子来验证该方法的可行性和有效性。

Abstract

An internal acoustic inverse scattering problem with a Neumann boundary condition is studied by using the decomposition method. First， it is proved that the position and shape of a scatterer can be uniquely determined by the measurement data of the point source inside the cavity with the Neumann boundary condition. Then， the boundary of the unknown scatter and its shape is reconstructed by using the idea of the decomposition method. Finally， two numerical examples are given to verify the feasibility and effectiveness of the method.

关键词

内部反散射Neumann边界条件分裂法

Keywords

interior inverse scattering problemNeumann boundary conditionthe decomposition method

references

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Related Author

Huan ZHANG

Lihan LIU

LIU Lihan

CUI Xiaoying

CAI Jingqiu

Related Institution

School of Mathematical Sciences, Chongqing Normal University

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