最佳差分方法研究及應用.pdf

1、成都理工大學碩士學位論文最佳差分方法研究及應用姓名：李江濤申請學位級別：碩士專業(yè)：計算機應用技術指導教師：周家紀20060501OptimalDifferenceMethodResearchandApplicationIntroductionoftheAuthor：LiJiangtao，wasbornonJanuary22，1978UndertheguidanceofProfZhouJiaji，shewasgraduatedfromCo

2、lIegeofComputerApplicationTecheniqueatChengduUniversityofTechnologyABSTRACTInthecomplexmedium，elasticwavesimulationisimportantandquiteactiveresearchdirectioninmechanics，mathematics，andgeophysicsThefinitedifferenceisaneff

3、ectivemethodinrealizingtheelasticwavetoforwardsimulationTheconventionalfinite—differencerequiresveryfinecomputationalgridswhenaccuracyofcomputationisimprovedThisproblemisavoidedwhenthederivativesarecomputedbymultir)licat

4、ionintheFourierdomain，butthismethodisrestrictedtocomputationalenvironmentsTherefore，thisthesishasstudiedtheoptimaldifferencemethod，andappliesitintheelasticwavetoforwardsimulationTheoptimal—differenceisafastdifferenceItin

5、troducestheoptimaldifferenceoperatorinthefinite—differencefoundationsTheoptimal—operatorisdesignedbyml‘m‘ml‘zl‘ngm。ecorrespondingpeakreiativeerroringroupvelocityThisthesisalsodiscussedtheapplicationofthismethodintheelast

6、icwavetoforwardsimulationThedifferenceiscarriedonthedisplacement—stresselastody—namicequationTheoperatorhalflengthtakesto46andeachwavelengthtakes3sampling，thentheprecisewavefieldcanbeobtainedIntheprocessofsolution，stagge

7、red—meshtechnologywhichissimilarwithVifieuxisusedThistechnologycalculatesthedifferentwavefieldquantityonthedifferentmeshpointHoweverbecausethemodelsizeislimited，itproducesthedisturbancewavefieldThisdisturbanceusestheHigd

8、onboundaryconditiontoabsorbitThiskindofboundaryconditioniscomposedofsomeoperator，andsimultaneouslysolvesfourverticesproblemsItismoreimportantthatidenticalformulacanapplytodifferentdimensionanddoesnotneedtomaketherevision

9、Theoptimal—differenceisstabletoallPoissonratio，soitdoesnotlimitedtomediummodelwhenthismethodisusedtosimulatethepropagationofelasticwaveandthespeedofcomputationisquickeronemagnitudethanconventionaldifferenceKeywords：finit