二維聲波反散射問題的數(shù)值方法與Nystrom方法的應(yīng)用.pdf

1、西北大學(xué)碩士學(xué)位論文二維聲波反散射問題的數(shù)值方法與Nystrom方法的應(yīng)用姓名：常立曄申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王連堂20090610Abstract(英文摘要1AbstractInverseproblemsresearchoriginatedinthefundamentalpapersofTikhonovinthe1960’SInverseproblemshaveverybroadapplicationprospect

2、s，widelyappearinvariousfieldsofthenaturalsciencesandpracticalengineeringandtechnologysuchassubsurfaceprospecting，nondestructivematerialtesting，medicalCT，seismologysonarandSOon勱einverseacousticscatteringproblemisanimporta

3、ntbranchoftheresearchoftheinverseproblemsOverthepasttwodecades，fromtheorytomethod，theinverseacousticscatteringproblemresearchhasbeenmadegreatprogressandanumberofeffectivenumericalmethodshavebeenproposedButbecauseoftheill

4、posednessandcomplexityofinverseproblems，thereisstillsomeobstaclebetweentheresearchandactualapplicationsoftheinverseacousticscatteringproblemsInthispaper，inverseacousticscatteringproblemshavebeenstudiedandsomesatisfactory

5、conclusionsarereachedAtthesametime，theNystrSmmethodusingtosolvethedirectscatteringproblemhasbeenappliedtootheraspects，practicalexamplesaregivenThispaperisdividedintosixparts：Thefirstchapterisintroduction，thecurrentstatus

6、ofresearchintheinverseproblemsandinverseacousticscatteringproblemsisreportedThesecondchapterisTheExteriorProblemofHelmholtzEquationthebasesofinverseproblem，thedirectscatteringproblemissolvedbylayerpotentialtheoryforDiric

7、hletboundarythischapterintroducespotentialtheoryandtheNystrSmmethodThethirdchapterisAMethodoftheInverseObstacleScatteringProblem，thischapterrecovertheDirichletboundarybyTaylorexpansionoftotalfieldonspecialboundaryThefort

8、hchapterisAcousticRadiationProblemof2DCavityitusessinglelayerpotentialtoapproachtoexteriorsoundpressure，thenturnsittothesolutiontothesecondkindboundaryintegralequationsbyjumprelationsofthepotentialtheoryandsolvesitbyNyst