a parallel multigrid solver for semiconductor device equationsnew

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1、APARALLELMULTIGRIDSOLVERFORSEMICONDUCTORDEVICEEQUATIONSX.Han,D.M.Barry,andMJ.HowesDepartmentofElectronicandElectricalEngineering,UniversityofLeeds,LS29JT,UKEmail:een5xh@leeds.ac.uk,dmbandmjh@elec-eng.leeds.ac.ukAbstractThispaperpresentsaparallelmultigridalgorithmforsolvingsemicon

2、ductordeviceequationsintwo-dimensionsanditsimplementationonaMIMDparallelmachinewithdistributedmemory.ThenumericalexperimentsofaGaAsMESFETdevicesimulationdemonstratethecombinedhighefficiencyofthedomaindecompositionmethodandthemultigridmethod.Theparallelmultigridmethodusing16proces

3、sorsisupto60timesfasterdianasingle-griditerativesolverusingaprocessor.I.INTRODUCTIONSemiconductordevicesimulationsareanimportanttoolforbothphysicistsanddevicedesignengineerstoanalysephysicalphenomenainsidesemiconductordevicesandtopredicttheperformanceofnewdevicespriortofabricatio

4、n.ThesephysicalmodelsrequirethesolutionsofthePoissonequationforelectricalpotentialandthecurrentcontinuityequationsforelectronandholeconcentrations.Morecomplexmodelswillalsosolvefortheenergyandtemperaturedistributions.Numericaltechniquesmustbeusedtosolvetheseequationswhichrequiree

5、xtensivecomputingpower.Theincreasingcomplexityofbothdevicesandphysicalmodelshavechallengedtheavailablecomputingresources.Manyattemptshavebeenmadetodesignfastsimulations.Multigrid(MG)methodsofferafastandrobustiterativemethodforsolvingPDEsandhavefoundapplicationsinsemiconductordevi

6、cesimulation[1-3].Thesimulationofsemiconductordevicespossessesaninherentparallelismwhichrequiresmanyrepeatedoperationsondifferentgridpoints.Itisclearthatbyexploitingdieparallelismofthenumericalalgorithmsleadstogoodspeedupsofthesimulation.ThedirectsolutionmethodhasbeenusedonMIMDpa

7、rallelcomputersfordevicesimulation[4],howeverthisdoesnotshowgoodefficiencyinthecaseofnormalgridsizes.TheJocobi-SOR,Frankeliterativemethods[5]andconjugategradientiterativemethods[6]havebeenimplementedonSIMDConnectionMachines.Thisapproachislimitedwhenmodellingtheirregularstructures

8、ofmoderndevices.Transputernetworkshaveal