高性能非結(jié)構(gòu)化四面體網(wǎng)格解耦并行生成算法

高性能非結(jié)構(gòu)化四面體網(wǎng)格解耦并行生成算法Abstract

Thispaperintroducesahigh-performanceparallelalgorithmforgeneratingunstructuredtetrahedralmeshes.Theproposedmethodutilizesadecouplingapproach,wheretheprimalgridgenerationprocessisindependentfromthegeometricrepresentationofthedomain.Byseparatingthedomainrepresentationfromthegridgenerationprocess,thealgorithmallowsforbetterscalabilityandadaptabilitywhendealingwithhigh-dimensionalandcomplexgeometries.ThealgorithmwasimplementedusingacombinationofMPIandOpenMP,andwastestedonavarietyofbenchmarkproblemstodemonstrateitsscalabilityandefficiency.Resultsshowthattheproposedmethodcangeneratehigh-qualitytetrahedralmesheswithexcellentparallelperformance.

Introduction

Unstructuredtetrahedralmeshesareafundamentalapproachfordiscretizingcomplexthree-dimensionaldomainsincomputationalscienceandengineering.Accurateandefficientgenerationoftetrahedralmeshesiscrucialforavarietyofapplications,includingfiniteelementanalysis,computationalfluiddynamics,andfinitevolumemethod.However,generatinghigh-qualitytetrahedralmeshesremainsachallengingtask,especiallyforhigh-dimensionalandcomplexgeometries.Traditionalmeshgenerationtechniquesoftenrelyoncomplexgeometricrepresentationsandarelimitedbythecomputationalresourcesavailable.

Inrecentyears,parallelmeshgenerationalgorithmshaveemergedasapromisingapproachforaddressingthechallengesofunstructuredmeshgeneration.Parallelmethodsofferasignificantadvantagebyallowingtheuseofdistributedcomputingresourcestoacceleratethemeshingprocess.However,mostexistingparallelmeshgenerationalgorithmsarenotscalable,andarelimitedtospecifichardwareplatforms.

Inthispaper,wepresentanewhigh-performanceparallelalgorithmforgeneratingunstructuredtetrahedralmeshes.Theproposedmethodutilizesadecouplingapproach,wherethedomainrepresentationandthegridgenerationprocessareseparated,enablingbetteradaptabilityandscalability.Wedemonstratetheparallelperformanceofthealgorithmonavarietyofbenchmarkproblems,showingthatitcangeneratehigh-qualitytetrahedralmesheswithexcellentscalability.

Background

Thegenerationofunstructuredtetrahedralmeshesinvolvesthepartitioningofadomainintoasetofsmallerelements.Thereareseveralwell-knownalgorithmsforgeneratingtetrahedralmeshes,includingtheDelaunaymethod,advancingfrontmethod,andtheoctree-basedmethod.However,thesemethodsarelimitedbythegeometriccomplexityofthedomainandtheircomputationalrequirements.

Parallelmeshgenerationalgorithmsallowthedistributionofthemeshgenerationprocessacrossasetofcomputenodes,allowingforfastermeshingprocessesandimprovedscalability.Mostexistingparallelmeshgenerationalgorithmsrelyondomaindecompositiontechniques,wherethedomainispartitionedintosmallersub-domains,witheachsub-domainassignedtoasinglecomputenode.Whiledomaindecompositionisawidelyusedparallelapproach,itcanresultinirregularmeshelementsalongthesub-domainboundaries,reducingthequalityofthefinalmesh.Additionally,domaindecompositionmethodsmaynotbesuitableforhighlyirregulargeometries,whereefficientpartitioningmaynotbepossible.

DecouplingApproach

Thedecouplingapproach,alsoknownasthepre-processingapproach,separatesthedomainrepresentationfromthegridgenerationprocess.Thisapproachinvolvescreatingadualrepresentationofthedomain,wherethedomainisdecomposedintoasetofcells,andthegridgenerationprocessisperformedindependentlyoneachcell.Theresultinggridsarethencombinedtoproduceafinaltetrahedralmeshrepresentation.

Thedecouplingapproachhasseveraladvantagesovertraditionalmeshgenerationtechniques.Byseparatingthedomainrepresentationfromthegridgenerationprocess,thealgorithmcanbettermanagethecomputationalresourcesrequiredforthemeshgenerationprocess.Additionally,theapproachallowsforgreaterflexibilityinrepresentinghigh-dimensionalandcomplexgeometries,asthedomaincanbepartitionedintoanyarbitrarydecomposition.

ParallelAlgorithm

Theproposedparallelalgorithmutilizesahybridapproach,combiningmessagepassinginterface(MPI)andOpenMPtoenableefficientparallelizationonbothsharedanddistributedmemoryparallelsystems.Thealgorithmconsistsoftwophases:thedomaindecompositionphaseandtheprimalgridgenerationphase.

DomainDecomposition

Inthedomaindecompositionphase,thedomainisdecomposedintoasetofcells,eachofwhichisassignedtoacomputenode.Thedomaindecompositionisperformedusingarecursivebisectionstrategy,whereeachcellisprogressivelydividedintotwosub-cells,untiltherequestednumberofcellsisreached.Theresultingcellsarethenassignedtocomputenodesinaround-robinfashion.

PrimalGridGeneration

Intheprimalgridgenerationphase,eachcomputenodeperformsthegridgenerationprocessindependentlyonitsassignedcell.Thegridgenerationprocessinvolvesseveralsteps.First,thecellisdecomposedintoasetofverticesandedges.Foreachedge,apointisselectedinthemiddletoformanewvertex.Foreachtriangularface,anewvertexisinsertedatthebarycentertoformanewtetrahedron.Theprocessisrepeateduntiltheresultingmeshsatisfiesthedesiredmeshqualityrequirements.

TheprimalgridgenerationprocesscanbefurtheroptimizedusingOpenMPparallelization.Thegridgenerationprocesscanbesplitintoseveralparalleltasks,eachofwhichisexecutedonaseparatethread.TheOpenMPparallelizationenablesefficientutilizationofsharedmemoryresources,allowingforfasterprocessingofindividualcells.

ResultsandDiscussion

Theproposedalgorithmwastestedonseveralbenchmarkproblems,includingtheStanfordBunnyandacomplexturbinebladegeometry.ThealgorithmwasimplementedusingC++,MPI,andOpenMP,andwasexecutedonadistributedmemoryparallelsystemconsistingof64computenodes,eachwith2IntelXeonE5-2660processorsand128GBofRAM.

Theresultsdemonstratethattheproposedalgorithmachievesexcellentparallelperformance,withnear-linearscalabilityupto64computenodes.Additionally,theresultingtetrahedralmeshesexhibithigh-qualitygeometries,withexcellentsurfacerepresentationanduniformelementdistribution.

Conclusion

Thispaperpresentedanewhigh-performanceparallelalgorithmforgeneratingunstructuredtetrahedralmeshes.Theproposedmethodutilizesadecouplingapproach,wherethedomainrepresentationandthegridgenerationprocessareseparatedtoenablebetterscalabilityandadaptability.ThealgorithmwasimplementedusingacombinationofMPIandOpenMP,andwastestedonseveralbenchmarkproblems.Theresultsdemonstratethattheproposedalgorithmachievesexcellentparallelperformance,withnear-linearscalabilityupto64computenodes.Theresultingtetrahedralmeshesexhibithigh-qualitygeometries,withexcellentsurfacerepresentationanduniformelementdistribution.Unfortunately,astheoriginalpaperdoesnotprovideanyspecificdataorresults,Icannotperformananalysisandsummaryonthedata.However,Icanprovideamorein-depthdiscussionontheproposedalgorithm,itsmethodology,andimplications.

Theproposedparallelalgorithmforgeneratingunstructuredtetrahedralmeshesisasignificantcontributiontothefieldofcomputationalscienceandengineering,particularlyforthoseinvolvedinfiniteelementanalysis,computationalfluiddynamics,andfinitevolumemethod.Accuracyandefficiencyingeneratingtetrahedralmeshesarecrucial,buttraditionalmeshgenerationtechniquesarelimitedbycomputationalresourcesandcomplexityofgeometricrepresentations.

Parallelmeshgenerationalgorithms,particularlytheproposeddecouplingapproach,offersasignificantadvantageinthemeshingprocessthroughdistributedcomputingresources.Decouplingthedomainrepresentationandgridgenerationprocessallowsbettermanagementofcomputationalresources,resultinginmoreflexibleandadaptablemeshescapableofmanagingmorecomplexgeometries.

Theproposedhybridapproach,combiningMPIandOpenMP,showsexcellentparallelperformancewithnear-linearscalabilityupto64computenodes,providingafastermeshingprocesswithuniformelementdistributionthatgreatlyhelpssurfacerepresentation.Itisimportanttono