用正則化方法求解聲波散射反問題和Abel積分方程.pdf

1、分類號：——密級：單位代碼：!Q92學號：2Q塑24箜西北大學碩士學位論文題目：旦墾型垡壺選盛豎壹遮鱟盟廛塑塑一壘叁壘曼!塑金壅猩作者：至壹垂指導教師至遣堂專業(yè)技術(shù)職務(wù)煎撞學科(專業(yè))鹽簋熬堂答辯日期學位授予日期二00六年五月壘窒!!!竺l叁塞塑塞2AbstractSincethe1960’s，theilwerseproblernsof“6Ⅱdingthecauseorinverseimage(input)fromknowⅡe行亂tor

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4、enceInthi8di8sertation，theauthordiscussesthenumercalsoluti徹forthedirectacousticscatteringproblemwiththeNeumannboundarycondition，andpaysmoreattentionstodlscussnumericalreco、憾rlngtheshapeoftheobstaclere百on，whichistheinvers

5、eprobIemofthedirectacousticscatteringproblemwiththeDiricllletorimpedanceboundaryconditionBesidestheabovediscussions，basedontheTikhonovregularizedmethod，theauthorput8forwardanothernumericalinver8ionalgorithmfornumericalso

6、lutionofaclas8ofAbelintegr81equation8Themain、vorksofthisdis8ertation8reasf0Ilows：1ThenumericaJa190rithmsofthedirectacousticscatteringproblemwiththeNeum明nboundaryconditionisstudiedThismethodtransformtheoriginalproblemtoth

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8、vethosenumericalmethodsbee矗bctive，andtheresultscanbeusedasvaliddatainthestudyoftheinver8eacousticscatteringproblem2Tikhonovregularizationnumericalmethodforreco垤訂ngthe8hapeofanobstaclefromtheinfbmationoftimeharmonicincide

9、ntacousticwave8ndfar最eldpatternofthe8catteredwavewithfhBquencyinthere80nanceregionisinVestigatedFirstU婦eindicatorfunctionwhichr印resentingthescatteringcharacteristic8isconstructedSecondbjbasedonthepropertyofthefunction，th

10、efundament“equationforsolvingtheinverseproblemisestablishedThen，七heshapeoftheobstacIeisdeterminedbynumericalsolutionThismethodrequiresnoapriorinformationofthetypeofboundaryconditionimposedontheobjectsanditsshapeNumeric“e

11、xperimentsshowthevaIidityandpr髓ticalityofthismethod3Aschemeoflinearsamplingmethodisdevelopedfortheinverseproblemwhiehrecoveringthesh印eofanobstaclefromtheinformationoftimeharmonicincidentacousticwavea】1dthefar矗eldpatterno