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1、Fastphononicband-structurecalculationsthroughaGPUacceleratedmixed-variationalformulationAnkitSrivastava∗DepartmentofMechanical,Materials,andAerospaceEngineeringIllinoisInstituteofTechnology,Chicago,IL,60616USA(Dated:July31,2018)InthispaperwepresentaGraphicalProcessingUnit(gp
2、u)acceleratedmixedvariationalfor-mulationforfastphononicband-structurecalculationofarbitrarilycomplexunitcellsandreportspeedgainsofahundredfoldoverunoptimizedserialcpucomputations.Totheauthor’sknowl-edgethisisthefirstapplicationofgpucomputingtoanon-FE/FDTDbandstructurealgorit
3、hm.Theformulationispresentedinaformwhichisapplicableto1-,2-,and3-Dcases.However,inthispaperweconcentrateonoptimizingtheformulationwithintheparadigmofgpucomputing,presentingresultsfor2-Dunitcells.Themixed-variationalformulationhasbeenproventoshowfasterconvergencethanvariation
4、alprinciplesbasedpurelyonthedisplacementfield.Additionallytheintegralnatureofthemethodallowsforitsapplicationtounitcellsofarbitrarycomplexity.However,theapplicationofthisformulationwaslimitedtofairlysimpleunitcellsuntilrecentlywhenitsscopewasextendedtodealwithallBravaislattic
5、esandcomplexmicro-structures.Inthispaperwedescribetheapplicationoftheformulationwithintheframeworkofgpucomputingwithalongtermviewtowardshighlyefficientandmassivelydistributedband-structurealgorithmssuitablefortacklingoptimizationandinverseproblems.Wereportthatthecurrentformula
6、tionbecomesI/Oboundasopposedtocomputeboundindicatingthepotentialforyetfastercomputa-tionsthroughoptimizeddatatransferbetweenthehost(cpu)andthedevice(gpu).Wereportthattheaccurateband-structureevaluationovertheboundaryoftheIrreducibleBrillouinZone(IBZ)forthefirst18phononicbranc
7、hesofacomplex2-Dunitcell(with1132differentphases)canbeachievedinlessthan20secondsonaregulardesktop.Forasimplerunitcell,thefirstfewphononicbranchesarecalculatedinlessthan2.5secondsonthesamesystem.Theschemepresentedinthispaper,therefore,representsconsiderablesavingsinthecomputat
8、ionalcostsofphononic(andphotonic,throughextensionstothecurrentmethod)band-s
