简介：WehavesuccessfullyportedanarbitraryhighorderdiscontinuousGalerkinmethodforsolvingthethreedimensionalisotropicelasticwaveequationonunstructuredtetrahedralmeshestomultipleGraphicProcessingUnits(GPUs)usingtheComputeUnifiedDeviceArchitecture(CUDA)ofNVIDIAandMessagePassingInterface(MPI)andobtainedaspeedupfactorofabout28.3forthesingle-precisionversionofourcodesandaspeedupfactorofabout14.9forthedouble-precisionversion.TheGPUusedinthecomparisonsisNVIDIATeslaC2070Fermi,andtheCPUusedisIntelXeonW5660.Toeffectivelyoverlapinter-processcommunicationwithcomputation,weseparatetheelementsoneachsubdomainintoinnerandouterelementsandcompletethecomputationonouterelementsandfilltheMPIbufferfirst.WhiletheMPImessagestravelacrossthenetwork,theGPUperformscomputationoninnerelements,andallothercalculationsthatdonotuseinformationofouterelementsfromneighboringsubdomains.Asignificantportionofthespeedupalsocomesfromacustomizedmatrix–matrixmultiplicationkernel,whichisusedextensivelythroughoutourprogram.PreliminaryperformanceanalysisonourparallelGPUcodesshowsfavorablestrongandweakscalabilities.

简介：Anewefficientmeshlessmethodbasedontheelement-freeGalerkinmethodisproposedtoanalyzethestaticdeformationofthinandthickplatestructuresinthispaper.Usingthenew3Dshell-likekinematicsinanalogytothesolid-shellconceptofthefiniteelementmethod,discretizationiscarriedoutbythenodeslocatedontheupperandlowersurfacesofthestructures.Theapproximationofallunknownfieldvariablesiscarriedoutbyusingthemovingleastsquares(MLS)approximationschemeinthein-planedirections,whilethelinearinterpolationisappliedthroughthethicknessdirection.Thus,differentboundaryconditionsaredefinedonlyusingdisplacementsandpenaltymethodisusedtoenforcetheessentialboundaryconditions.TheconstrainedGalerkinweakform,whichincorporatesonlydisplacementdegreesoffreedom(d.o.f.s),isderived.Amodified3Dconstitutiverelationshipisadoptedinordertoavoidoreliminatesomeself-lockingeffects.Thenumericefficiencyoftheproposedmeshlessformulationisillustratedbythenumericexamples.