麥克斯韋方程的保結(jié)構(gòu)算法.pdf

1、南京師范大學(xué)碩士學(xué)位論文麥克斯韋方程的保結(jié)構(gòu)算法姓名：蔡加祥申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：王雨順20070511擒瓔ABSTRACTSinceMaxwellestablishedelectromagnetismwaveequationswhichdescribedtheevolutionsofelectromagneticfieldsinspaceandtimein1837，Maxwell’Sequationshavebee

2、ndevelopedformorethan100yearsTheyhavebeenappliedtoawiderangeofdifferentphysicalsituationsDuetotheactualenvironmentiscomplex，onlysomeclassicalproblemshaveexactsolutionsweoftendescribecharacteristicofelectromagneticwavebyn

3、umericalsolutionsIn1980s，F(xiàn)engKangproposedsymplecticalgorithms，whichwerestableandeffectiveinlongtimecomputationRecentlyBridgesandMarsdenhaveex—tendedthesymplecticalgorithms，andthenproposedtheconceptofthemulti—symplecticHa

4、miltonsystemandthecorrespondingmultisymplecticschemesAsthedevelopmentofthetheories，manyresearchershavecomputedfamousequationswithmultisympleeticalgorithms，suchasnonlinearwaveequation，nonlinearschrrdingerequation，Korteweg

5、—deVriesequation，Zakharov—Kuznetsovequa—tion，Kadomtsev—PetviashviliequationNumericalresultsindicatemultisymplecticalgorithmisusefulAtpresent，thereisnoattemptofapplyingmultisymplecticalgorithmtoMaxwell’SequationsMotivatio

6、nofthethesisisdevelopingthemuRisymplecticthe—oryandthemultisymplecticalgorithmofMaxwell’SequationsWetestwhetherthemultisympleeticalgorithmiseffectiveBasedontheBridges’multisymplecticform，wederivethreemultisymplecticschem

7、esforMaxwell’SequationsWederiveauewmultisymplecticschemewhichisprovedtobeselfadjointintimedirectionforMaxwell’SequationsThemulti—symplecticityofcompositionschemesbasedonthenewselfadjointschemeisalsodiscussedBytheinvestig

8、a—tionofthemultisymplecticPreissmanscheme，wederiveanew102一pointschemewhichcouplestwotimelevelsbyeliminatingtheauxiliaryvariablesforMaxwell’SequationsFurthermore，thenewderived102一pointschemeisprovedtopreservethediscretelo