NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (10): 1233-1244.

• 论文 • 上一篇

NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET

尤云祥, 缪国平

School of Naval Architecture and Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, P. R. China

收稿日期:2001-11-27 修回日期:2003-05-09 出版日期:2003-10-18 发布日期:2003-10-18
基金资助:
the Excellent Doctorial Paper Foundation of Education Ministry of China; the Shuguang Project of Shanghai Education Committee

NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET

YOU Yun-xiang, MIAO Guo-ping

School of Naval Architecture and Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, P. R. China

Received:2001-11-27 Revised:2003-05-09 Online:2003-10-18 Published:2003-10-18
Supported by:
the Excellent Doctorial Paper Foundation of Education Ministry of China; the Shuguang Project of Shanghai Education Committee

摘要/Abstract

摘要： A nonlinear optimization method was developed to solve the inverse problem of determining the shape of a hard target from the knowlegde of the far-field pattern of the acoustic scattering wave,it was achieved by solving independently an ill-posed linear system and a well-posed minimization problem.Such a separate numerical treatment for the ill-posedness and nonlinearity of the inverse problem makes the numerical implementation of the proposed method very easy and fast since there only involves the solution of a small scale minimization problem with one unknown function in the nonlinear optimization step for determining the shape of the sound-hard obstacle.Another particular feature of the method is that it can reproduce the shape of an unknown hard target efficiently from the knowledge of only one Fourier coefficient of the far-field pattern.Moreover,a two-step adaptive iteration algorithm was presented to implement numerically the nonlinear optimization scheme.Numerical experiments for several two-dimensional sound-hard scatterers having a variety of shapes provide an independent verification of the effectiveness and practicality of the inversion scheme.

Abstract: A nonlinear optimization method was developed to solve the inverse problem of determining the shape of a hard target from the knowlegde of the far-field pattern of the acoustic scattering wave,it was achieved by solving independently an ill-posed linear system and a well-posed minimization problem.Such a separate numerical treatment for the ill-posedness and nonlinearity of the inverse problem makes the numerical implementation of the proposed method very easy and fast since there only involves the solution of a small scale minimization problem with one unknown function in the nonlinear optimization step for determining the shape of the sound-hard obstacle.Another particular feature of the method is that it can reproduce the shape of an unknown hard target efficiently from the knowledge of only one Fourier coefficient of the far-field pattern.Moreover,a two-step adaptive iteration algorithm was presented to implement numerically the nonlinear optimization scheme.Numerical experiments for several two-dimensional sound-hard scatterers having a variety of shapes provide an independent verification of the effectiveness and practicality of the inversion scheme.

中图分类号:

O175

尤云祥;缪国平. NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1233-1244.

YOU Yun-xiang;MIAO Guo-ping. NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1233-1244.

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NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET

NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET

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