DtN重構算法的有效性分析.pdf

1、浙江大學理學院碩士學位論文DtN重構算法的有效性分析姓名：沈皛雪申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：朱建新20090501AbstractThisarticlediscussesthevalidityofthenumericalmethodbasedonDirichlet—toNeumann(DtN)mapForacousticwaveguideswithacurvedinterfaceintwolayermedia，weprop

2、oseacoordinatetransformationtoflattentheinterfaceandchangetheHelmholtzequationintoasolvableformThenweusealargerangestepmethodtodiscretizetherangevariableandreducetheboundaryvalueproblemtoaninitialvalueproblembyDtNmapInnu

3、mericalsimulation，theprocessofdifferential，integral，inverseandeigenvalueproblemsmayinducecalculationerror，SOitisnecessarytoevaluatethevalidityWefoundthatforthewaveguidewithinternalinterfaceswhichchangeslowlytheresultsare

4、stableButiftheinterfacesimulatesasymmetricsteephillintheseabed，theamplitudeistoosmallduetotheinstabilityofRayleighiterationWbcanusetheresetmethodtosolvethisproblemthoughitmaytakemoretimeOurresearchdemonstratesthattheerro

5、rinnumericalsimulationisnotserious，thereasonofvibrationofwaveformisthattheinterfacechangestooquicklyInaddition，whenwetransformthecoordinatenearthepole，thedenominatoroftheintegrandintheiterativeprocessofthecootdinatetrans

6、formationmaybecomezeroAfterresearchingthecharacteroftheintergrand，wemakeuseofsymmetryoftheinterfacefunctiontoseparatetheintegralregionintoseveralparts，andtheintegralofthepartwhichcontmusthepoleisexactzeroSotheproblemisso