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NUMERICAL METHOD FOR THE SHAPE RECONSTRUCTION OF A HARD TARGET
作者姓名:尤云祥  缪国平
作者单位:School of Naval Architecture and Ocean Engineering,Shanghai Jiaotong University,School of Naval Architecture and Ocean Engineering,Shanghai Jiaotong University Shanghai 200030,P.R.China,Shanghai 200030,P.R.China
基金项目:theExcellentDoctorialPaperFoundationofEducationMinistryofChina,theShuguangProjectofShanghaiEducationCommittee
摘    要:IntroductionAninverseproblemofconsiderableimportanceinvariousfieldsofengineeringtechnology ,suchasnondestructivetesting ,medicalimaging ,remotesensingandseismicimaging ,istodeterminetheshapeofascatteringobjectfromitsfar_fieldeffectsontheacousticscatteringwaves.However,thiskindofproblemisparticularlydifficulttosolvesinceitisbothnonlinearandill_posed1].Fortunately ,therehavebeenseveralmethodsdevelopedforsolvingnumericallytheinverseproblemduringthelastdecade .Ofparticularimportancearenonlinearop…

收稿时间:27 November 2001

Numerical method for the shape reconstruction of a hard target
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.
Authors:You Yun-xiang  Miao Guo-ping
Institution:School of Naval Architecture and Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, P.R. China
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.
Keywords:acoustic scattering  inverse problem  far-field pattern
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