带形无界域上依赖时间具有dirichlet边界条件薛定谔方程有限元方法

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1、‘/Ã.·þ·6žmäkDirichlet>.^‡Å½™·§k··{Æž<“6¶9…¡Û7U«gÇƶ¡êƆOŽ‰ÆÆÆï‰Ä;·’·OŽêƇ©·§êŠ·{nØ9ÙA^Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2011–4–20Analysisoffiniteelementschemeforthetime-dependentSchr¨odingerequationwithDirichletboundaryinanunboundedstripCandidateSupervi

2、sorandRankNianLuoProfessorJichengJinCollegeProgramMathematicsandComputationalScienceTheComputationalMathematicsSpecializationTheoryandApplicationsofNumericalMethodsforPDEsDegreeUniversityDateMasterofScienceXiangTanUniversityApr.20th,2011‰ÆØ©ŒÆM5(²

3、Ø©´<3“·eÕá?1ïĤïĤJ"Ø©¥AO±I5Ú^SN§Ø©Ø·¹?ÛÙ¦‡<½8N®²uL½>¤JŠ¬"é©ïĉÑ-‡z‡<Ú8N§þ®3©¥±²(·ªI²"<¿£(²{ÆJd<«ú"Šö¶µFϵÆØ©‡c¦^ÇFÖÆØ©Šö)Æk'3!¦^ÆØ©5½§Ó¿Æ3¿·I[k'Ü€½ÅxØ©E<‡Ú>f‡§#NØ©Ú/"<ljŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢§Œ±æ^K

4、¶µFϵFϵccFFÁ‡©ïĘ«‘/Ã.·þ·6žmäkDirichlet>.^‡Ž™·§k··{"Äk§·‚ÏLÚ<ó>.¿‰ÑT>.^‡§òÃ.·þÐ>Š¯K=z·˜‡k.·þÐ>Š¯K§,éT{z¯K©O3žmÚ˜mþ

5、^Crank-Nicolson‚ªÚV‚5½gk·%C?1lÑ"²Lî‚nØ©Û§y²·‚¤ElÑ‚ª´Ã^‡-½ÚÂñ§Óž§Âñ"·§‰Ñ˜‡êŠŽ~§`²·‚·{´k'…i:Ž™·§¶k·"·{¶<ó>.^‡¶Dirichlet>.^

6、‡"IAbstractThisthesisaddressesthefiniteelementmethodforthetime-dependentSchr¨odingerequationwithDirichletboundaryconditioninanunboundedstrip.Wefirstreducetheorig-inalproblemintoaninitial-boundaryvalueprobleminaboundeddomainbyintroducingatransparentboundarycondi

7、tion,thenfullydiscretizethisreducedproblembyapplyingCrank-Nicolsonschemeintimeandbilinearorquadraticfiniteelementapproximationinspace.Thisscheme,byarigorousanalysis,hasbeenprovedtobeunconditionallystableandconvergent,itsconvergenceorderhasalsobeenobtained.Fina

8、lly,wegiveanumericalexampletoverifytheaccuracyofthescheme.Keywords:schr¨odingerequation;finiteelementmethod;artificialboundarycondi-tion;Dirichletboundarycondition.II8¹1˜ÙÚó...................................................11ÙlÑk·‚ªE.......................

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