一种三维非定常线弹性问题的自适应并行算法

《一种三维非定常线弹性问题的自适应并行算法》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、Æ“è10530ÆÒ201510111165©aÒO241.82—?a¬ÆØ©˜«n‘š½~‚5¯Kg·A¿1Ž{Æž<ë7•P“¾S)BÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••õ‚†«•©){"˜lco›F˜«n‘š½~‚5¯Kg·A¿1Ž{Æž<ë7“6¶9…¡¾S)BÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••õ‚†«•©){Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2018{4{12AnAdaptiveParallelAlgorithmforSolvingThree-dimensionalUnstead

2、yLinearElasticityProblemCandidateTaoZhaoSupervisorAssociateProfessorChunshengFengCollegeSchoolofMathematicsandComputationalScienceProgramMathematicsSpecializationMultigridMethodandDomainDecompositionMethodDegreeMasterofScienceUniversityXiangtanUniversityDateApril12th,2018Á‡n‘š½~‚5.

3、2••3uNåÆ!(åÆÚ6Íܯõ+•.da¯K¯„¦)´‰Æ†ó§OŽïÄ9:.©阫n‘š½~‚5.,3.¼(Lagrangian)‚e‰Ñž˜••©Oæ^k•©Ú‚5k•lÑlÑÛ‚ª9ƒA¦)Ž{,ꊢL²T‚ªk•ؼê3lÑL2‰êeäkO(+h2)ÚØ.X,‰Ñž˜Ú•éþãlÑ‚ªXêÝ^‡êK•©Û,?OlÑÛ‚ªg·A¦)Ž{,ꊢL²T•{¦)Ç`u~^CG{ÚAMG-CG{.•,3MPI¿1‚¸¥,•þãg·AŽ{OуA¿1¦)Ž{;?˜Ú(ÜØÓ){ì¿1

4、Œ*Ð5,O˜«Äuž˜ºÝ'XÚ?§êg·A¿1Ž{9ƒA¦)¬,ꊢL²U?g·A¿1Ž{äk•Ð¦)Ç,XéuЩž•˜m¿©Ú••1Ú?§ê•64œ¹e,#g·A¿1Ž{¦)64ǃéU?cJ,30.66%.'…c:n‘š½~‚5.;g·AüÑ;“êõ‚{;¿1OŽIAbstractThethree-dimensionalunsteadylinearelasticmodeliswidelyusedinmanyelds,suchassolidmechanics,structuralmechanicsand uid-sol

5、idcoupling.Therapidsolutionofsuchproblemsisahotresearchtopicinscienceandengineeringcomputation.Inthiswork,forathree-dimensionalunsteadylinearelasticitymodel,IntheLagrangiangrid,afullydiscreteimplicitschemeswiththenitedierenceandthelinearniteelementmethodintime-spacedirectionsandth

6、ecorrespondingsolutionalgorithmaregiven.NumericalsimulationsshowthattheniteelementerrorfunctionofthisschemehasanerrororderofO(+h2)inthediscreteL2norm.Afterthat,ananalysisofin uenceofthetime-spacestepontheconditionnumberofthecoecientsmatrixofthediscreteschemeisgiven.Furthermore,the

7、algorithmofadaptivesolutionforfullydiscreteschemesisdesigned,NumericalexperimentsshowthatthemethodismoreecientthanthecommonlyusedCGmethodandAMG-CGmethod.Finally,aparallelalgorithmbasedontheadaptivealgorithmfore-mentionedisdesignedundertheMPIparallelprogrammingenvironment.Combinedwit

8、htheparallel