mesh generation for implicit goemetires

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1、MeshGenerationforImplicitGeometriesbyPer-OlofPerssonM.S.EngineeringPhysics,LundInstituteofTechnology,1997SubmittedtotheDepartmentofMathematicsinpartialfulfillmentoftherequirementsforthedegreeofDoctorofPhilosophyattheMASSACHUSETTSINSTITUTEOFTECHNOLOGYFebruary2005c2005Per

2、-OlofPersson.Allrightsreserved.TheauthorherebygrantstoMITpermissiontoreproduceanddistributepubliclypaperandelectroniccopiesofthisthesisdocumentinwholeorinpart.Author..............................................................DepartmentofMathematicsDecember8,2004Certi

3、fiedby..........................................................AlanEdelmanProfessorofAppliedMathematicsThesisSupervisorCertifiedby..........................................................GilbertStrangProfessorofMathematicsThesisSupervisorAcceptedby.....................

4、....................................RodolfoRubenRosalesChairman,CommitteeonAppliedMathematicsAcceptedby.........................................................PavelEtingofChairman,DepartmentCommitteeonGraduateStudents2MeshGenerationforImplicitGeometriesbyPer-OlofPerss

5、onSubmittedtotheDepartmentofMathematicsonDecember8,2004,inpartialfulfillmentoftherequirementsforthedegreeofDoctorofPhilosophyAbstractWepresentnewtechniquesforgenerationofunstructuredmeshesforgeometriesspec-ifiedbyimplicitfunctions.Aninitialmeshisiterativelyimprovedbysolv

6、ingforaforceequilibriumintheelementedges,andtheboundarynodesareprojectedusingtheimplicitgeometrydefinition.Ouralgorithmgeneralizestoanydimensionandittypicallyproducesmeshesofveryhighquality.WeshowasimplifiedversionofthemethodinjustonepageofMATLABcode,andwedescribehowtoim

7、proveandextendourimplementation.Priortogeneratingthemeshwecomputeameshsizefunctiontospecifythedesiredsizeoftheelements.Wehavedevelopedalgorithmsforautomaticgenerationofsizefunctions,adaptedtothecurvatureandthefeaturesizeofthegeometry.Weproposeanewmethodforlimitingthegr

8、adientsinthesizefunctionbysolvinganon-linearpartialdifferentialequation.Weshowthatthesolutiontoourgradientlimitingequa