Optimized explicit finite-difference schemes for spatial derivatives using maximum norm

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1、JournalofComputationalPhysics250(2013)511–526ContentslistsavailableatSciVerseScienceDirectJournalofComputationalPhysicsjournalhomepage:www.elsevier.com/locate/jcpOptimizedexplicitfinite-differenceschemesforspatialqderivativesusingmaximumnormJin-HaiZhang⇑,Zh

2、en-XingYaoInstituteofGeologyandGeophysics,ChineseAcademyofSciences,Beijing,ChinaarticleinfoabstractArticlehistory:Conventionalexplicitfinite-differencemethodshavedifficultiesinhandlinghigh-fre-Received1September2012quencycomponentsduetostrongnumericaldispers

3、ions.OnecanreducethenumericalReceivedinrevisedform27February2013dispersionsbyoptimizingtheconstantcoefficientsofthefinite-differenceoperator.Differ-Accepted21April2013entfromtraditionaloptimizedschemesthatusethe2-normandtheleastsquares,wepro-Availableonline1

4、0May2013posetoconstructtheobjectivefunctionsusingthemaximumnormandsolvetheobjectivefunctionsusingthesimulatedannealingalgorithm.Boththeoreticalanalysesandnumeri-Keywords:calexperimentsshowthatouroptimizedschemeissuperiortotraditionaloptimizedOptimizedschem

5、eschemeswithregardtothefollowingthreeaspects.First,itprovidesuswithmuchmoreExplicitfinite-differenceflexibilitywhendesigningtheobjectivefunctions;thuswecanusevariouspossibleformsNumericaldispersionMaximumnormandcontentstomaketheobjectivefunctionsmorereasonab

6、le.Second,itallowsfortighterSimulatedannealingalgorithmerrorlimitation,whichisshowntobenecessarytoavoidrapiderroraccumulationsforsimulationsonlarge-scalemodelswithlongtraveltimes.Finally,itispowerfultoobtaintheoptimizedcoefficientsthataremuchclosertothetheo

7、reticallimits,whichmeansgreatersavingsincomputationaleffortsandmemorydemand.Ó2013TheAuthors.PublishedbyElsevierInc.Allrightsreserved.1.IntroductionTheexplicitfinite-difference(FD)schemeisoneofthemostpopularapproachesusedinvariousnumericalsimulations,because

8、itissimpleinitsnumericalimplementationandispowerfulinhandlingcomplexmedia.However,theconventionalexplicitFDmethodhasseriousnumericalartifactsinthepresenceofhigh-frequencycomponentsand/orcoarsegrids.Thisproble