[HSC15]A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation

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1、Computers&Fluids110(2015)96–107ContentslistsavailableatScienceDirectComputers&Fluidsjournalhomepage:www.elsevier.com/locate/compfluidAparalleladaptivenonlineareliminationpreconditionedinexactNewtonmethodfortransonicfullpotentialequationa,⇑abFeng-NanHwang,Yi-ChengSu,Xiao-ChuanCaiaDepartmentofMat

2、hematics,NationalCentralUniversity,Jhongli32001,TaiwanbDepartmentofComputerScience,UniversityofColorado,Boulder,CO80309,USAarticleinfoabstractArticlehistory:Weproposeandstudyaright-preconditionedinexactNewtonmethodforthenumericalsolutionoflargeReceived1November2013sparsenonlinearsystemofequati

3、ons.ThetargetapplicationsarenonlinearproblemswhosederivativesAccepted2April2014havesomelocaldiscontinuitiessuchthatthetraditionalinexactNewtonmethodsuffersfromslowornoAvailableonline18April2014convergenceevenwithglobalizationtechniques.Theproposedadaptivenonlineareliminationprecondi-tionedinex

4、actNewtonmethodconsistsofthreemajoringredients:asubspacecorrection,aglobalKeywords:update,andanadaptivepartitioningstrategy.ThekeyideaistoremovethelocalhighnonlinearitybeforeTransonicflowperformingtheglobalNewtonupdate.ThepartitionusedtodefinethesubspacenonlinearproblemisAdaptivenonlinearelimina

5、tionchosenadaptivelybasedontheinformationderivedfromtheintermediateNewtonsolution.SomeInexactNewtonLocalhighnonlinearitynumericalexperimentsarepresentedtodemonstratetherobustnessandefficiencyofthealgorithmcom-DensityupwindingfinitedifferenceparedtotheclassicalinexactNewtonmethod.Someparallelperf

6、ormanceresultsobtainedonaclusterofShockwavePCsarereported.Ó2014ElsevierLtd.Allrightsreserved.1.Introductionmodifythevariableofthenonlinearsystem.Forexample,Hwangetal.[13]employsanonlinearelimination(NE)technique[14]asTheclassofinexactNewtonmethod(IN)[8,15]ispopularforarightpreconditionerforaqu

7、asione-dimensionalshockedductsolvinglargesparsenonlinearsystemofequationsarisingfromdis-flowcalculation.ThekeyideaofNEistoimplicitlyremovethesecretizationofpartialdifferentialequations(PDEs).INisquiterobustcomponentsthatcausetroubleforIN