简介：Basedonelementarygrouptheory,theblockpivotmethodsforsolv-ingtwo-dimensionalelasticfrictionalcontactproblemsarepresentedinthispaper.Itisprovedthatthealgorithmsconvergewithinafinitenumberofstepswhenthefrictioncoefficientis'relativesmall'.Unlikemostmathematicalprogrammingmeth-odsforcontactproblems,theblockpivotmethodspermitmultipleexchangesofbasicandnonbasicvariables.

简介：Analgorithmforsolvingaclassofsmoothconvexprogrammingisgiven.Usingsmoothexactmultiplierpenaltyfunction,asmoothconvexprogrammingisminimizedtoaminimizingstronglyconvexfunctiononthecompactsetwasreduced.ThenthestronglyconvexfunctionwithaNewtonmethodonthegivencompactsetwasminimized.

简介：Aneuralnetwork(NN)isapowerfultoolforapproximatingboundedcontinuousfunctionsinmachinelearning.TheNNprovidesaframeworkfornumericallysolvingordinarydifferentialequations(ODEs)andpartialdifferentialequations(PDEs)combinedwiththeautomaticdifferentiation(AD)technique.Inthiswork,weexploretheuseofNNforthefunctionapproximationandproposeauniversalsolverforODEsandPDEs.ThesolveristestedforinitialvalueproblemsandboundaryvalueproblemsofODEs,andtheresultsexhibithighaccuracyfornotonlytheunknownfunctionsbutalsotheirderivatives.ThesamestrategycanbeusedtoconstructaPDEsolverbasedoncollocationpointsinsteadofamesh,whichistestedwiththeBurgersequationandtheheatequation(i.e.,theLaplaceequation).

简介：ThepreconditionedGauss-Seideltypeiterativemethodforsolvinglinearsystems,withtheproperchoiceofthepreconditioner,ispresented.ConvergenceofthepreconditionedmethodappliedtoZ-matricesisdiscussed.Alsotheoptimalparameterispresented.NumericalresultsshowthattheproperchoiceofthepreconditionercanleadtoeffectivebythepreconditionedGauss-Seideltypeiterativemethodsforsolvinglinearsystems.

简介：Themainobjectiveforthisresearchwastheanalyticalexplorationofthedynamicsofplanarsatelliterotationduringthemotionofanellipticalorbitaroundaplanet.First,werevisittheresultsofJ.Wisdometal.(1984),inwhich,bytheelegantchangeofvariables(consideringthetrueanomalyfastheindependentvariable),thegoverningequationofsatelliterotationtakestheformofanAbelordinarydifferentialequation(ODE)ofthesecondkind,asortofgeneralizationoftheRiccatiODE.WenotethatduetothespecialcharacterofsolutionsofaRiccati-typeODE,thereexiststhepossibilityofsuddenjumpinginthemagnitudeofthesolutionatsomemomentoftime.Inthephysicalsense,thisjumpingoftheRiccati-typesolutionsofthegoverningODEcouldbeassociatedwiththeeffectofsuddenacceleration/decelerationinthesatelliterotationaroundthechosenprincipleaxisatadefinitemomentofparametrictime.Thismeansthatthereexistsnotonlyachaoticsatelliterotationregime(aspertheresultsofJ.Wisdometal.(1984)),butakindofgradientcatastrophe(Arnold,1992)couldoccurduringthesatelliterotationprocess.Weespeciallynotethatifagradientcatastrophecouldoccur,thisdoesnotmeanthatitmustoccur:suchapossibilitydependsontheinitialconditions.Inaddition,weobtainedasymptoticalsolutionsthatmanifestaquasi-periodiccharacterevenwiththestrongsimplifyngassumptionse→0,p=1,whichreducethegoverningequationofJ.Wisdometal.(1984)toakindofBeletskii'sequation.

简介：TheresultsofplaneturbulentwakegivenbyChouPeiyuanareconsideredasthefirstorderap-proximationandputintotheequationsofturbulentfluctuation.Theequationsaresolvednumericallywithintherangeofmicro-scalebymeansofspectrummethod.Thedouble,tripleandquadruplefluctuatingvelocitycorrelationsareobtainedbycomputation.Theyareingoodagreementwithexperimentalresults.

简介：Inthispaper,howtocomputetheeigenfrequenciesofthestructurescomposedofaseriesofinclinedcablesisshown.Thephysicsofaninclinedcablecanbecomplicated,sosolvingthedifferentialequationsevenapproximatelyisdifficult.However,ratherthansolvingthesystemof4first-orderequationsgoverningthedynamicsofeachcable,thegoverningequationsareinsteadconvertedtoasetofequationsthattheexteriormatrixsatisfies.Therefore,theexteriormatrixmethod(EMM)isusedwithoutsolvingtheoriginalgoverningequations.Eventhoughthisproducesasystemof6first-orderequations,thesimpleasymptotictechniquestofindthefirstthreetermsoftheperturbativesolutioncanbeused.Thesolutionscanthenbeassembledtoproducea6×6exteriormatrixforacablesection.Thematricesforeachcableinthestructurearemultipliedtogether,alongwiththeexteriormatricesforeachjoint.Therootsoftheproductgiveustheeigenfrequenciesofthesystem.

简介：TheevolutionequationsofmomentsfortheBrowniancoagulationofnanoparticlesinbothcontinuumandfreemoleculeregimesareanalyticallystudied.TheseequationsarederivedusingaTaylor-expansiontechnique.Theself-preservingsizedistributionisinvestigatedusinganewlydefineddimensionlessparameter,andtheasymptoticvaluesforthisparameteraretheoreticallydetermined.Thedimensionlesstimerequiredforaninitialsizedistributiontoachieveself-preservationisalsoderivedinbothregimes.Oncethesizedistributionbecomesself-preserving,thetimeevolutionofthezerothandsecondmomentscanbetheoreticallyobtained,anditisfoundthatthesecondmomentvarieslinearlywithtimeinthecontinuumregime.Equivalentequations,ratherthantheoriginalonesfromwhichtheyarederived,canbeemployedtoimprovetheaccuracyoftheresultsandreducethecomputationalcostforBrowniancoagulationinthecontinuumregimeaswellasthefreemoleculeregime.

简介：Inthispaper,afullythird-orderaccurateprojectionmethodforsolvingtheincompressibleNavier-Stokesequationsisproposed.Toconstructthescheme,acontinuousprojectionprocedureisfirstlypresented.Wethenderiveasufficientconditionforthecontinuousprojectionequationstobetemporallythird-orderaccurateapproximationsoftheoriginalNavier-Stokesequationsbymeansofthelocaltruncation-error-analysistechnique.Thecontinuousprojectionequationsarediscretizedtemporallyandspatiallytothird-orderaccuracyonthestaggeredgrids,resultinginafullythird-orderdiscreteprojectionscheme.Thepossibilitytodesignhigher-orderprojectionmethodsisthusdemonstratedinthepresentpaper.Aheuristicstabilityanalysisisperformedonthisprojectionmethodshowingtheprobabilityofitsbeingstable.Thestabilityofthepresentschemeisfurtherverifiedthroughnumericaltests.Thethird-orderaccuracyofthepresentprojectionmethodisvalidatedbyseveralnumericaltestcases.

简介：Aself-adaptiveprecisealgorithminthetimedomainwasemployedtosolve2-Dnonlinearcoupledheatandmoisturetransferproblems.Byexpandingvariablesatadiscretizedtimeinterval,thevariationsofvariablescanbedescribedmoreprecisely,andanonlinearcoupledinitialandboundaryvalueproblemwasconvertedintoaseriesofrecurrentlinearboundaryvalueproblemswhicharesolvedbyFEtechnique.Inthecomputation,noadditionalassumptionandthenonlineariterationarerequired,andacriterionforself-adaptivecomputationisproposedtomaintainsufficientcomputingaccuracyforthechangesizesoftimesteps.Inthenumericalcomparison,thevariationsofmaterialpropertieswithtemperature,moisturecontent,andbothtemperatureandmoisturecontentaretakenintoaccount,respectively.Satisfactoryresultshavebeenobtained,indicatingthattheproposedapproachiscapableofdealingwithcomplexnonlinearproblems.

简介：Fastsolvinglarge-scalelinearequationsinthefiniteelementanalysisisaclassicalsubjectincomputationalmechanics.Itisakeytechniqueincomputeraidedengineering(CAE)andcomputeraidedmanufacturing(CAM).Thispaperpresentsahigh-efciencyimprovedsymmetricsuccessiveover-relaxation(ISSOR)preconditionedconjugategradient(PCG)method,whichmaintainstheconvergenceandinherentparallelismconsistentwiththeoriginalform.Ideally,thecomputationcanbereducednearlyby50%ascomparedwiththeoriginalalgorithm.Itissuitableforhigh-performancecomputingwithitsinherentbasichigh-efciencyoperations.Bycomparingwiththenumericalresults,itisshownthattheproposedmethodhasthebestperformance.