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限制加性许瓦兹预条件的变形及其在二维三温能量方程中的应用

ArtideID:1001.246X(2008)06-0649-10

AVariantRestrictedAdditiveSchwarzPreconditionerandApplicationinTwo..dimensional

Three--temperatureEnergyEquations

CAOYanhual,2,LiuXingpin92,GU

Tongxian92

(I・NorthChinaElectricPowerUniversity,Department旷胁舶∞Ⅲ妇and只协妇。&咖增102206,China;

2・LCP,InstituteoIAp#如aPhysicsand

Computatwna/Mathema*/cx.Be/舛ng100088,Chi∞)

AbstI僦:we

presentaVariantrestrictedAdditiVe

Schwa=preconditionerandapplyPartial—Ne咖n-K响v.SchW妣如ri‰to

sol7。∞rdin唧algebraicequationsoftwo。dimensional

three-temperaturesystems.IterationandCPUtimefor咖ve瑁ence册decreased.Numericalresultsshowefficiencyofthemethod.

Keywor凼:paralleIimplementation;proe。nditi。∞r;itemtivesolution;additiveSchwarz

method;energyeqIIati咖CLCnumber:0242Domunentcode:A

0IntrOduction

IncompleteLU(ILU)preconditioners,combinedwithKrylovsubspaceacceleration,yieldtechniques

tnatprovldeagoodcomprommebetweenrobustnessand

efficiencyinsolvinggenerallargesparselinearequations¨“1・Preconditioninggeneralsparselinearsystemsremainsbyfarthebiggestchallengein

obtaininggoodperformanceforiterativesolutionmethodsonhigh.performance

computers.Oftenti埘【es.

parallelimplementationsofengineeringandscientific

applicationsutilizepreconditioningtechniquessuchasanadditiveSchwarzprocedure.Theprocedurewasintroducedinsolvingsymmetricpositivedeftnite

ellipticproblems,andWaSlaterextendedtomany

nonsymmetricandnonellipticsvstems_[3一纠.InRef・[6],CaiandSarkisintroducedapreconditionerbased0nane%ctivevaIi锄tofSchw啦procedure,calledrestrictedadditiveSchwarz(RAS)method,forcaseswithoved印pedsubdomai璐.It

reduceshalfofthecommunication

costanditerationnumber

comparedwithastand盯dadditiveSchw卸眩

method・However,itsconvergencerate,intermsofthenumberof

iteration,deg.enerate8asnumberofprocessorislargeduetolackofcommunicationbetweensubdomains.

InthispaperweproposeachangeofRAS.Thenewvarianttakes

advantageofmore

iIlfb瑚tionin

adjacentprocessorstomakethepreconditioner“moreaccurate”.Itdecreases

iter{札ioncoumandCPU

time・Thusweobtainfaster

convergencerate.However,local

communicationforprecondili叻ingincreases・Sincelocalcommunicationisusuallyinexpensive,thisshortcomingisc啪pensatedbydecreasingiterationcounts.

Intwo—dimensionalsimulationofastrophysicsandinertialconfinementfusion(ICF),itoffenneedslta,ceiveddate:2007—06—21:Reviseddate:2007—12—09

Foundationitem:sIIpportedbytheNationalNaturalScienceFoundation0fChina(granted

No.10571017,10701015,60373015and605330'20)aIld

NationalBasicResearch

n理弹mofChina(grantedNo.2005CB2213(X)).

Biography:CaoYanhua(1976一),male,Hunan,PhD,majorin伽删Ⅲtali∞lalⅫ_lbem鲥∞.

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