2023年全國(guó)碩士研究生考試考研英語一試題真題(含答案詳解+作文范文)_第1頁
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1、70Sj7!洳≥:≥~碩士學(xué)位⑧論文論文題目:一類橢圓型偏微分方程反問題的無網(wǎng)格方法姓名金邦梯學(xué)科(郇Ip)計(jì)算數(shù)學(xué)指導(dǎo)教師鄭耀教授所在學(xué)院理學(xué)院提交日期2005年3月摘要MeshlessMethodsforSomeInverseProblemsAssoeiatedwithEllipticPartialDifferentialEquationsAbstractInverseproblemsariseinmanyengineeringan

2、dscientificcontexts,andtheyarenowplayingacentralrolethereInpracticalapplications,theproblemunderinvestigationisoftengovernedbypartialdifferentialequationsHencethesolutionofpracticalinverseproblemsoftenleadstosolvinginver

3、seproblemsassociatedwithpartialdifferentialequationsThisthesisfocusesontheclassofinverseproblemsthatcanbeformulatedasCauchyproblemswithellipticpartialdifferentialequationswhicharenotoriousfortheir川posednessInparticularwe

4、willinvestigatetheCauchyproblemassociatedwiththeLaplaceequationforthesteady—statebeatconduction,nondestructivetesting洲D(zhuǎn)T)andgeophysics,theHelmholtzequationsforacousticanalysis,electromagneticfield,vibrationofmembranesand

5、otherstructures,andheatconductioninafin,andtheNaviersysteminlinearelasticityInthethesis,severalnovelnumericalschemesbasedonmeshlessmethodsaleproposedforthesolutionoftheinverseproblemsassociatedwithellipticpartialdifferen

6、tialequationsThesemeshlessmethodscanbeformulatedinthegeneralframeworkofradialbasisfunctioncollocationtechniquesPreliminarynumericalresultsfortheLaplaceequationandNaviersystemarepresented,andtrickyissuesassociatedwiththes

7、emethods,suchastheill—conditioningwiththeinterpolationmatrixandeffectofshapeparameterareinvestigatedItisfoundthatusingregularizationmethods,suchasthetruncatedsingularvaluedecompositionandTitdaonovregularization,tosolveth

8、eresultingsystemoflinearequationsnotonlymitigatesthe川conditioningwiththematrixequation,butalsoalleviatesthedifficultywithdetermininganappropriateshapeparameterintheradialbasisfunctionsItisconcludedthattheradialbasisfunct

9、ioncollocationtechniquescoupledwithregularizationmethodscouldbecompetitivealternativestoexistingmethodsfortheseproblems[[owever,forspecificequations,suchastheLaplaceequation,theHelmholtzequationandtheNaviersystem,wecanim

10、provethecomputationalefficiencysignificantlybyemployingdifferentialoperatorgearedradialbasisfunctions、Tobemorespecific,wemayemploythefundamentalandgeneralsolutionstothedifferentialoperatorsastheradialbasisfunctions,which

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