简介:Inthispaper,standardandeconomicalcascadicmultigridmethodsareconsideredforsolvingthealgebraicsystemsresultingfromthemortarfiniteelementmethods.Bothcascadicmultigridmethodsdonotneedfullellipticregularity,sotheycanbeusedtotacklemoregeneralellipticproblems.Numericalexperimentsarereportedtosupportourtheory.
简介:CascadicmultigridtechniqueformortarWilsonfiniteelementmethodofhomogeneousboundaryvalueplanarlinearelasticityisdescribedandanalyzed.FirstthemortarWilsonfiniteelementmethodforplanarlinearelasticitywillbeanalyzed,andtheerrorestimateunderL2andH1normisoptimal.Thenacascadicmultigridmethodforthemortarfiniteelementdiscreteproblemisdescribed.Suitablegridtrans-feroperatorandsmootheraredevelopedwhichleadtoanoptimalcascadicmultigridmethod.Finally,thecomputationalresultsarepresented.
简介:Inthepresentpaperweextendthemethodpresentedby0.AxelssonandP.VassilevskicalledAMLPversion(i)ofrecursivelyconstructingpreconditionerforthestiffnessmatrixinthediscretizationofselfadjointsecondorderellipticboundaryvalueproblems.Inourextendedmethodthesystemstobeeliminatedoneachlevelcontainingthemajorblockmatricesofthegivenmatrixcanbesolvedapproximately,whiletheymustbesolvedexactlyintheoriginalmethod.
简介:Inthispaperweprovethattheasymptoticrateofconvergenceofthemod-ifiedGauss-Seidelmethodofanon-singularM-matrixisamonotonicfunctionforpreconditionparameters0≤αi≤1-2,(i=1,2,…,n-1).
简介:AimsandScope:NumericalMathematics:Theory,MethodsandApplications(NM-TMA)publisheshigh-qualityoriginalresearchpapersontheconstruction,analysisandapplicationofnumericalmethodsforsolvingscientificproblems.Importantresearchandexpositorypapersdevotedtothenumericalsolutionofmathematicalproblemsarisinginallareasofscience
简介:AimsandScope:NumericalMathematics:Theory,MethodsandApplications(NM-TMA)publisheshigh-qualityoriginalresearch
简介:AimsandScope:NumericalMathematics:Theory,MethodsandApplications(NM-TMA)publisheshigh-qualityoriginalresearchpapersontheconstruction,analysisandapplicationofnumericalmethodsforsolvingscientificproblems.Importantresearchandexpositorypapersdevotedtothenumericalsolutionofmathematicalproblemsarisinginallareasofscienceandtechnologyareexpected.ThejournaloriginatesfromthejournalNumericalMathematics:AJournalofChineseUniversities(EnglishEdition).
简介:Somewaysofmultilevelrelaxedpreconditioningmatricesforthestiffnessmatrixinthediscretizationofselfadjointsecondorderellipticboundaryvalueproblemsareproposed.Forreason-ableassumptionsoftherelaxedfactorω,smallerrelativeconditionnumbersaregiven.Theoptimalrelaxedfactorωisderived,too.
简介:InthispaperweprovethattheconvergencerateofthemodifiedGauss-Seidelmethodisamonotonicfunctionforsomepreconditionparameters.
简介:AconicNewtonmethodisattractivebecauseitconvergestoalocalminimizzerrapidlyfromanysufficientlygoodinitialguess.However,itmaybeexpensivetosolvetheconicNewtonequationateachiterate.InthispaperweconsideraninexactconicNewtonmethod,whichsolvesthecouicNewtonequationoldyapproximatelyandinsonmunspecifiedmanner.Furthermore,weshowthatsuchmethodislocallyconvergentandcharacterizestheorderofconvergenceintermsoftherateofconvergenceoftherelativeresiduals.
简介:Resolventmethodsarepresentedforgeneratingsystematicallyiterativenumericalalgorithmsforconstrainedproblemsinmechanics.Theabstractframeworkcorrespondstoageneralmixedfiniteelementsubdif-ferentialmodel,withdualandprimalevolutionversions,whichisshowntoapplytoproblemsoffluiddynamics,transportphenomenaandsolidmechanics,amongothers.Inthismanner,Uzawa’stypemethodsandpenalization-dualityschemes,aswellasmacro-hybridformulations,aregeneralizedtononnecessarilypotentialnanlinearmechanicalproblems.
简介:Aformulationofadifferentialequationasprojectionandfixedpointpi-Memalloivsapproximationsusinggeneralpiecnvisefunctions.Weproneexistenceanduniquenessoftheupproximatesolution*convergenceintheL2normandnodalsupercnnvergence.TheseresultsgeneralizethoseobtainedearlierbyHulmeforcontinuouspiecevjisepolynomialsandbyDelfour-Dubeaufordiscontinuouspieceuiisepolynomials.Adualityrelationshipforthetwotypesofapproximationsisalsogiven.
简介:Inthispaper,thesemi-discreteandfullydiscreteFourierspectralschemesfortheGinzburg-LandaucoupledwithBBMequationswithperiodicinitialvalueproblemareproposed,andtheconvergenceandstabilitiesfortheschemesareproved.
简介:Inthispaper,wesetupageneralframeworkofparallelmatrixmullisplittingrelaxationmethodsforsolvinglargescalesystemoflinearequations.Weinvestigatetheconvergencepropertiesofthisframeworkandgiveseveralsufficientconditionsensuringittoconvergeaswellasdiverge.Atlast,weconcludeanecessaryandsufficientconditionfortheconvergenceofthisframeworkwhenthecoefficientmatrixisanL-matrix.