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1、COMBINEDLAPLACIANANDOPTIMIZATION-BASEDSMOOTHINGFORQUADRATICMIXEDSURFACEMESHES1ZhijianChen,JosephR.Tristano,WaKwok1Ansys,inc.,275TechnologyDrive,Canonsburg,PA15317,U.S.A.{james.chen,joe.tristano,wa.kwok}@ansys.comABSTRACTQuadraticelementsplacestringentrequir
2、ementsonasurfacemeshsmoother.Oneofthebiggestchallengesisthatagoodlinearelementmaybecomeinvalidwhenmid-sidenodesareintroduced.Tohelpalleviatethisproblem,anewobjectivefunctionforoptimization-basedsmoothingisproposedfortriangularandquadrilateralelements,linear
3、orquadratic.Unlikethecurrentpopularapproaches,thisobjectivefunctionmakesitpossibleforasmoothingalgorithmtountangleandsmoothinasingleprocess.Thisobjectivefunctionhashigherordercontinuousderivativesandonlyoneminimum,ifany,thatmakeitsuitableforoptimizationtech
4、niques.Eventhoughoptimization-basedsmoothingobtainsmuchhigherqualityresultscomparedtootheralgorithms,suchasconstrainedLaplaciansmoothing,itisalsoslowerthanthesealgorithms.Thatsaid,wealsopresentaneffectivewaytolimitthenumberofcallstooptimization-basedsmoothi
5、ngsuchthatthehighestqualitymeshisobtainedintheleastamountoftime.Keywords:optimization-basedsmoothing,constrained-Laplaciansmoothing,smoothingobjectivefunction,surfacemeshbettermesh,iftheobjectivefunctionisproperlyformulated.1.INTRODUCTIONOptimization-baseds
6、moothingvariesbasedon:thetypeofmeshbeingsmoothed,theoptimizationmethodused,andthedistortionmetricselectedtoconstructtheobjectivefunction.MeshqualityisakeyfactorinFEManalysis.Therearenumerouswaystoachieveahighqualitymesh[1],suchasOneofthekeystothesuccessofan
7、optimization-basedcontrollingthediscretizationsize,controllingtheedgesmoothingalgorithmistodefineanappropriateobjectivevalenceofmeshnodesandcontrollingthedistortionofthefunction.Aninappropriateobjectivefunctioncanwastetimeindividualelementshapes.Meshsmoothi
8、ng(relaxation)[2],intheoptimizationalgorithmalongwithcausingtheimprovesqualitybyadjustingnodelocationstoreducethealgorithmtofailtoimprovethemeshquality.Mostefficientdistortionoftheelementshapeswithoutc
