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1、AbstractElement-freeGalerkin(EFG)methodnotonlyhastheadvantageofgettingridoftheshacklesofthegrid,buthasgoodstabilitycalculationandfastconvergenceandhighprecision,etc.Another,EFGmethodtopologyoptimizationcaneffectivelysolvethereconfigurablemeshandotherissues,whicharearousedb
2、yfiniteelementmethodtopologyoptimization.Moreimportantly,EFGmethodtopologyoptimizationcaneffectivelyeliminatecheckerboardphenomenon.Therefore,moreandmoreattentionofscholarshasbeenattractedbyEFGmethodanditstopologyoptimization.However,inlargescaleproblems,theresearchandappl
3、icationofEFGmethodanditstopologyoptimizationisseverelyconstrainedbythedrawbackthatEFGmethodhaslowcomputationefficiency.Atthesametime,GraphicProcessingUnit(GPU)hasbeenwidelyappliedinmanyfieldswiththerapiddevelopmentofparallelingcomputing.Therefore,accordingtotheshortcomingo
4、flowefficiencyandtime-consuming,thispapercarriesouttheGPUparallelcomputingresearchofEFGmethodanditstopologyoptimization.Themainresearchcontentsaresummarizedasfollows:Firstly,thethree-dimensionEFGstructureanalysismethodwasstudiedandapplied.Inthetwo-dimensional,weintroducedt
5、riangularelementtoinsteadoftheEFGtraditionalalgorithm’squadrilateralelements.Meanwhile,weintroducedtetrahedralelementtoinsteadofhexahedralelementinthethree-dimensional.Ontheotherhand,inordertoachievetheintegralcalculationofEFGmethod,theHammerintegralwasusedtoreplacetheGaus
6、sintegralwhichistheintegralmethodoftheEFGtraditionalalgorithm.Andtherelevantformulawasdetailedlyderived.Another,thefeasibilityofthealgorithmwasverifiedbytheanalysisofnumericalexamples.Secondly,theGPUparallelcomputingofEFGmethodwasinvestigated.Basedonthethoughtofinteracting
7、nodespairs,ajointassemblyschemeanditsGPUparallelalgorithmofthegeneralstiffnessmatrixandthegeneralpunishmentstiffnessmatrixandthepreprocessingmatrixwasraised.Moreover,anacceleratedalgorithmofEFGmethodwhichcouplesGPUandPreconditionedConjugateGradient(PCG)methodwaspresented.T
8、hederivationprocessofcorrelationformulaandtheflowchartofthisacceleratedalgorithmweregiven
