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1、JOURNALOFCOMPUTATIONALPHYSICS135,280±292(1997)ARTICLENO.CP975706AFastAlgorithmforParticleSimulations*L.GreengardandV.RokhlinDepartmentofComputerScience,YaleUniversity,NewHaven,Connecticut06520ReceivedJune10,1986;revisedFebruary5,1987WerestrictourattentioninthispapertothecasewhereA
2、nalgorithmispresentedfortherapidevaluationofthepotentialthepotential(orforce)atapointisasumofpairwiseandforce®eldsinsystemsinvolvinglargenumbersofparticlesinteractions.Morespeci®cally,weconsiderpotentialsofwhoseinteractionsareCoulombicorgravitationalinnature.ForatheformsystemofNpa
3、rticles,anamountofworkoftheorderO(N2)hastraditionallybeenrequiredtoevaluateallpairwiseinteractions,un-lesssomeapproximationortruncationmethodisused.Thealgo-F5Ffar1(Fnear1Fexternal),rithmofthepresentpaperrequiresanamountofworkproportionaltoNtoevaluateallinteractionstowithinroundoff
4、error,makingitwhereF(whenpresent)isarapidlydecayingpotentialnearconsiderablymorepracticalforlarge-scaleproblemsencounteredin(e.g.,VanderWaals),Fexternal(whenpresent)isindepen-plasmaphysics,¯uiddynamics,moleculardynamics,andcelestialmechanics.Q1987AcademicPressdentofthenumberofpart
5、icles,andFfar,thefar-®eldpotential,isCoulombicorgravitational.Suchmodelsde-scribeclassicalcelestialmechanicsandmanyproblemsin1.INTRODUCTIONplasmaphysicsandmoleculardynamics.Inthevortexmethodforincompressible¯uid¯owcalculations[4],anThestudyofphysicalsystemsbymeansofparticlesimu-im
6、portantandexpensiveportionofthecomputationhaslationsiswellestablishedinanumberof®eldsandisthesameformalstructure(thestreamfunctionandthebecomingincreasinglyimportantinothers.Themostclassi-vorticityarerelatedbyPoisson'sequation).calexampleisprobablycelestialmechanics,butmuchre-Inas
7、ystemofNparticles,thecalculationofFnearre-centworkhasbeendoneinformulatingandstudyingparti-quiresanamountofworkproportionaltoN,asdoestheclemodelsinplasmaphysics,¯uiddynamics,andmolecularcalculationofFexternal.ThedecayoftheCoulombicordynamics[5].gravitationalpotential,however,issuf
8、®cientlyslowthatTherearetwomajorc
