简介:ThepreconditionedGauss-Seideltypeiterativemethodforsolvinglinearsystems,withtheproperchoiceofthepreconditioner,ispresented.ConvergenceofthepreconditionedmethodappliedtoZ-matricesisdiscussed.Alsotheoptimalparameterispresented.NumericalresultsshowthattheproperchoiceofthepreconditionercanleadtoeffectivebythepreconditionedGauss-Seideltypeiterativemethodsforsolvinglinearsystems.
简介:Non-singularfictitiousboundaryintegralequationsfororthotropicelasticplaneproblemswerededucedaccordingtoboundaryconditionsbythetechniquesofsingularpoints-outside-domain.Thentheunknownfictitiousloadfunctionsalongthefictitiousboundarywereexpressedintermsofbasicsplinefunctions,andtheboundary-segment-leastsquaresmethodwasproposedtoeliminatetheboundaryresiduesobtained.Bytheabovesteps,numericalsolutionstotheintegralequationscanbeachieved.Numericalexamplesaregiventoshowtheaccuracyandefficiencyoftheproposedmethod.
简介:Afinitedifferencemethodispresentedtosimulatetransversevibrationsofanaxiallymovingstring.Bydiscretizingthegoverningequationandtheequationofstress-strainrelationatdifferentfrictionalknots,twolinearsparsefinitedifferenceequationsystemsareobtained.Thetwoexplicitdifferenceschemescanbecalculatedalternatively,whichmakethecomputationmuchmoreefficient.Thenumericalmethodmakesthenonlinearmodeleasiertodealwithandoftruncationerrors,O(Δt~2+Δx~2).Italsoshowsquitegoodstabilityforsmallinitialvalues.Numericalexamplesarepresentedtodemonstratetheefficiencyandthestabilityofthealgorithm,anddynamicanalysisofaviscoelasticstringisgivenbyusingthenumericalresults.
简介:AVU-decompositionmethodforsolvingasecond-orderconeproblemispresentedinthispaper.Itisfirsttransformedintoanonlinearprogrammingproblem.Then,thestructureoftheClarkesubdifferentialcorrespondingtothepenaltyfunctionandsomeresultsofitsVU-decompositionaregiven.Underacertaincondition,atwicecontinuouslydifferentiabletrajectoryiscomputedtoproduceasecond-orderexpansionoftheobjectivefunction.Aconceptualalgorithmforsolvingthisproblemwithasuperlinearconvergencerateisgiven.
简介:Basedonthefundamentaldynamicequationsoffunctionallygradedmaterial(FGM)cylindricalshell,thispaperinvestigatesthesoundradiationofvibrationalFGMshellinwaterbymobilitymethod.ThismodeltakesintoaccounttheexteriorfluidloadingduetothesoundpressradiatedbytheFGMshell.TheFGMcylindricalshellwasexcitedbyaharmoniclineradialforceuniformlydistributingalongthegenerator.TheFGMshellequationsofmotion,theHelmholtzequationintheexteriorfluidmediumandth...
简介:TheresultsofplaneturbulentwakegivenbyChouPeiyuanareconsideredasthefirstorderap-proximationandputintotheequationsofturbulentfluctuation.Theequationsaresolvednumericallywithintherangeofmicro-scalebymeansofspectrummethod.Thedouble,tripleandquadruplefluctuatingvelocitycorrelationsareobtainedbycomputation.Theyareingoodagreementwithexperimentalresults.
简介:Themethodofnonlinearparabolizedstabilityequations(PSE)isappliedinthesimulationofvortexstructuresincompressiblemixinglayer.Thespatially-evolvingunstablewaves,whichdominatethevortexstructure,areinvestigatedthroughspatialmarchingmethod.Theinstantaneousflowfieldisobtainedbyaddingtheharmonicwavestobasicflow.TheresultsshowthatT-Swavesdonotkeepgrowingexponentiallyasthelinearevolution,theenergytransfertohighorderharmonicmodes,andthatfinallyallharmonicmodesgetsaturatedduetononlinearinteraction.Themeanflowdistortioninducedbythenonlinearinteractionbetweentheharmonicmodesandtheirconjugateharmonicones,makesgreatchangeoftheaverageflowandincreasesthethicknessofmixinglayer.PSEmethodscanwellcapturethetwo-andthree-dimensionallargescalenonlinearvortexstructuresinmixinglayerssuchasvortexroll-up,vortexpairing,andAvortex.
简介:Thispaperfirstanalyzesthefeaturesoftwoclassesofnumericalmethodsforglobalanalysisofnonlineardynamicalsystems,whichregardstatespacerespectivelyascontinuousanddiscreteones.Onbasisofthisunderstandingitthenpointsoutthatthepreviouslyproposedmethodofpointmappingundercellreference(PMUCR),haslaidaframeworkforthedevelopmentofatwoscalednumericalmethodsuitablefortheglobalanalysisofhighdimensionalnonlinearsystems,whichmaytaketheadvantagesofb...
简介:Inthispaper,anewmethodoftopologicalcleanupforquadrilateralmeshispresented.Themethodfirstselectsapatchofmesharoundanirregularnode.Itthenseeksthebestconnectionoftheselectedpatchaccordingtoitsirregularvalenceusinganewtopologicaloperation:smallpolygonreconnection(SPR).Byreplacingtheoriginalpatchwithanoptimalonethathaslessirregularvalence,meshqualitycanbeimproved.Threeapplicationsbasedontheproposedapproachareenumerated:(1)improvingthequalityofaquadrilateralmesh,(2)convertingatriangularmeshtoaquadrilateralone,and(3)adaptingatrianglegeneratortoaquadrilateralone.Thepresentedmethodishighlyeffectiveinallthreeapplications.
简介:Ageneralizedhyperbolicperturbationmethodispresentedforhomoclinicsolutionsofstronglynonlinearautonomousoscillators,inwhichtheperturbationprocedureisimprovedforthosesystemswhoseexacthomoclinicgeneratingsolutionscannotbeexplicitlyderived.Thegeneralizedhyperbolicfunctionsareemployedasthebasisfunctionsinthepresentproceduretoextendthevalidityofthehyperbolicperturbationmethod.Severalstronglynonlinearoscillatorswithquadratic,cubic,andquarticnonlinearityarestudiedindetailtoillustratetheefficiencyandaccuracyofthepresentmethod.
简介:Asetofparameterscalledrelativeorbitalelementsweredefinedtodescribetherelativemotionofthesatellitesintheformationflying.Withthehelpoftheseparameters,theeffectoftheperturbationsontherelativeorbittrajectoryandgeometricpropertiesofsatelliteformationcanbeeasilyanalyzed.First,therelativeorbitalelementsarederived,andpointedout:iftheeccentricityoftheleadingsatelliteisasmallvalue,therelativeorbittrajectoryisdeterminedbytheintersectionbetweenanellipticcylinderandaplaneintheleadingsatelliteorbitframereference;andtheparametersthatdescribetheellipticcylinderandtheplanecanbeusedtoobtaintherelativeorbittrajectoryandtherelativeorbitalelements.Second,byanalyzingtheeffectsofgravitationalperturbationsontherelativeorbitusingtherelativeorbitalelements,itisfoundthatthepropagationofarelativeorbitconsistsoftwoparts:oneisthedriftoftheellipticcylinder;andtheotheristherotationoftheplaneresultedfromtherotationofthenormaloftheplane.Meanwhile,theanalyticformulaeforthedriftandrotationratesofarelativetrajectoryundergravitationalperturbationsarepresented.Finally,therelativeorbittrajectoryandthecorrespondingchangeswereanalyzedwithrespecttotheJ2perturbation.
简介:ThestabilitydegreeofperiodicsolutionofnonlinearnonautonomoussystemwasdefinedbymeansoftheFloquettheory.Amethodevaluatingthestabilitydegreeofperiodicsolutionbasedontransientresponsewaspresentedbytheaidoftheconceptofdynamicsystemsorflows.Thecriticalvalueofasystemwasdeterminedbythecondition,i.e.,itsstabilitydegreeequalszero.Stableregionsofrotorsystemswithbalancedandunbalanceddisksupportedonlubricatedbearingswerecalculated.Thestudyshowsthatstableregiondecreaseswiththeincreaseofspeedforabalancedrotorsystemanddecreaseswiththeincreaseofunbalanceforanunbalancedrotorsystem.Stableregionsofperiodicsolutionsarelessthanthatofequilibriumpointsunderthesamesystematicconditions.
简介:Theexactanalyticmethodwasgivenby[1].Itcanbeusedforarbitraryvariablecoefficientdifferentialequationsandthesolutionobtainedcanhavethesecondorderconvergentprecision.Inthispaper,anewhighprecisionalgorithmisgivenbasedon[1],throughabendingproblemofvariablecross-sectionbeams.Itcanhavethefourthconvergentprecisionwithoutincreasingcomputationwork.Thepresentcomputationmethodisnotonlysimplebutalsofast.Thenumericalexamplesaregivenattheendofthispaperwhichindicatethatthehighconvergentprecisioncanbeobtainedusingonlyafewelements.Thecorrectnessofthetheoryinthispaperisconfirmed.
简介:纸论述改进没有元素的Galerkin(IEFG)为三维的波浪繁殖的方法。改进移动最少平方(IMLS)近似被采用构造形状函数,它与一个重量函数把一个直角的函数系统用作基础函数。与常规移动相比最少平方(MLS)近似,在IMLS的代数学的方程系统近似不是性恶的,并且没有导出反的矩阵,能直接被解决。因为比在MLS近似在IMLS有更少系数,更少节点比在没有元素的Galerkin方法在IEFG方法被选择。因此,IEFG方法有更高的计算速度。在IEFG方法,Galerkin弱形式被采用获得一个discretized系统方程,并且惩罚方法被使用强加必要边界条件。为二点的边界价值问题的传统的差别方法为时间discretization被选择。当波浪方程和边界起始的条件取决于时间,可伸缩的参数,节点的数字和时间,步长度为集中学习被考虑。
简介:Theformulaswhicharesuitabletobirefringentmediumwithsymmetricplanearederivedbymeansofphaseretardintegration.Wehaveadoptedthisconcepttotheaxisymmetricproblemsanddeducedsomeusefulformulasforthesecases.Asapracticalapplication,thestrainrateanalysisofflowinadivergingoraconvergingvesselisillustratedattheendofthispaper.