简介:InthispaperwestudythecomputationalperformanceofvariantsofanalgebraicadditiveSchwarzpreconditionerfortheSchurcomplementforthesolutionoflargesparselinearsystems.Inearlierworks,thelocalSchurcomplementswerecomputedexactlyusingasparsedirectsolver.Therobustnessofthepreconditionercomesatthepriceofthismemoryandtimeintensivecomputationthatisthemainbottleneckoftheapproachfortacklinghugeproblems.InthisworkweinvestigatetheuseofsparseapproximationofthedenselocalSchurcomplements.TheseapproximationsarecomputedusingapartialincompleteLUfactorization.Suchanumericalcalculationisthecoreofthemulti-levelincompletefactorizationsuchastheoneimplementedinpARMS.Thenumericalandcomputingperformanceofthenewnumericalschemeisillustratedonasetoflarge3Dconvection-diffusionproblems;preliminaryexperimentsonlinearsystemsarisingfromstructuralmechanicsarealsoreported.
简介:GeneralizedSteiriertriplesystems,GS(2,3,n,g),areequivalenttomaximumconstantweightcodesoveranalphabetofsizeg+1withdistance3andweight3inwhicheachcodewordhaslengthn.ThenecessaryconditionsfortheexistenceofaGS(2,3,n,g)are(n-1)g≡0(mod2),n(n-1)g2≡0(mod6),andn≥g+2.Thesenecessaryconditionsareshowntobesufficientbyseveralauthorsfor2≤g≤11.Inthispaper,threenewresultsareobtained.First,itisshownthatforanygiveng,g≡0(mod6)andg≥12,ifthereexistsaGS(2.3.n.g)foralln,g+2≤n≤7g+13.thenthenecessaryconditionsarealsosufficient.Next,itisalsoshownthatforanygiveng,g≡3(mod6)andg≥15,ifthereexistsaGS(2,3,n,g)foralln,n≡1(mod2)andg+2≤n≤7g+6,thenthenecessaryconditionsarealsosufficient.Finally,asanapplication,itisprovedthatthenecessaryconditionsfortheexistenceofaGS(2,3,n,g)arealsosufficientforg=12,15.
简介:TheauthorobtainsaWeierstrassrepresentationforsurfaceswithprescribednormalGaussmapandGausscurvatureinH3.AdifferentialequationaboutthehyperbolicGaussmapisalsoobtained,whichcharacterizestherelationamongthehyperbolicGaussmap,thenormalGaussmapandGausscurvature.TheauthordiscussestheharmonicityofthenormalGaussmapandthehyperbolicGaussmapfromsurfacewithconstantGausscurvatureinH3toS2withcertainalteredconformalmetric.Finally,theauthorconsidersthesurfacewhosenormalGaussmapisconformalandderivesacompletelynonlineardifferentialequationofsecondorderwhichgraphmustsatisfy.
简介:The3-stageClosnetworkC(n,m,r)isconsideredasthemostbasicandpopularmultistageinterconnectionnetworkwhichhasbeenwidelyemployedfordatacommunicationsandparallelcomputingsystems.Quitealotofeortshasbeenputontheresearchofthe3-stageClosnetwork.Unfortunately,verylittleisknownforthemultiratemulticastClosnetworkwhichisthemostcomplicatedcase.Firstlyasucientconditionfor1-ratemulticastnetworkstobeSNBisgiven,fromwhicharesultfor2-ratemulticastnetworkstobeWSNBcaneasilybegotten.Furthermore,byusingareservation-schemerouting,morespecificresultfor2-ratemulticastnetworkstobeWSNBcanbeobtainedforthecaseofoneofthemexceeding1/2.