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10.1.1.25.2026 - L eve lSetM ethod s and F astM arch ingM...

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Unformatted text preview: L eve lSetM ethod s and F astM arch ingM ethod s Evo lv ingIn ter facesinC om pu tat iona lG eom etry , F lu idM echan ics ,C om pu terV is ion , andM ater ia lsSc ience J .A .Seth ian D ep t .o fM athem at ics U n ivers ityo fC a liforn ia B erke ley C am b r idgeU n ivers ityP ress , down loaded from : h ttp ://m ath .berke ley .edu/seth ian/ leve l set .h tm l. Evo lu t iono fTheoryandA lgor ithm sforIn ter faceP ropagat ion Theoryo fCu rveandSu rfaceEvo lu tion : C orners ,Shock s ,S ingu lar itiesandEn tropyC ond ition s ( C haps .,:Re f.[ , ] ) ? T rack ingIn terfaceM otionw ithSchem es fromH yperbo licC on servationLaw s ( C hap .:R e f.[ ] ) X X X X X X XX z X X X X X X XX z L eve lSetP erspective t + F jr j = In it ia lV a lueP rob lem ( C hap .:R e f.[ ] ) ? adap t iv ity ? NARROWBAND LEVELSETM ETHOD S ( C hap .:R e f. ) S tationaryP erspective jr T j F = B oundaryV a lueP rob lem (C hap .:R e f.[ ]) ? adap t iv ity ? FA STMARCH ING M ETHOD S ( C hap .:R e f.[ ] ) P P P P P P PP q) ADD IT IONALFORMULAT ION S U n structu redM esh L eve lSetM ethod s ( C hap .:R e f.[ ] ) C oup lingtoPhy sics : Ex ten sionV e loc ities ( C hap . :Re f. ) U n structu redM esh F astM arch ingM ethod s ( C hap . :R e f.[ ] ) ? APPL ICAT ION S G eom etry (Chap . ) G r idG eneration (Chap . ) Se ism icA na ly sis (Chap . ) C om pu tationa lG eom etry (Chap . ) C om pu terV ision (Chap s ,, ) O p tim a lityandC on tro l (Chap . ) F lu idM echan ics (Chap . ) C om bu stion (Chap . ) M ater ia lsSc iences (Chap . ) Sem iconductorM anu factu r ing (Chap . ) Th isbook isan in troduct iontoleve lsetm ethod sandF astM arch ing M ethod s ,wh icharepow erfu lnum er ica ltechn iquesforana lyz ingand com pu t ing in terfacem ot ion inahosto fsett ings .Theyre lyonafunda- m en ta lsh iftinhowonev iew sm ov ingboundar ies ,reth ink ingthenatu- ra lgeom etr icLagrang ianperspect iveandrep lac ing itw ithanEu ler ian part ia ld ierent ia lequat ionperspect ives .Theresu lt ingnum er ica ltech- n iquesareu sedtotrackth ree-d im en s iona lfron tsthatcandeve lopsharp cornersandchangetopo logyastheyevo lve . Thebookbeg in sw ithanoverv iewo fthetw otechn iques ,andthenp ro- v idesan in troduct iontothedynam icso fm ov ingcu rvesandsu rfaces . N ex t ,ec ientcom pu tat iona ltechn iquesforapp rox im at ingv iscos ityso- lu t ion stopart ia ld ierent ia lequat ion saredeve loped ,u s ingnum er ica l techno logy from hyperbo liccon servat ion law s .Th isbu ild safram ew ork forop t im a lim p lem en tat ion so fadap t ivetechn iquesforN arrowB and L eve lSetM ethod sandF astM arch ingM ethod s .Theen t irem ethodo l- ogy isthenredeve lopedontr iangu latedm eshes ,fo llow edbyaser ieso f ex ten s ion so fthebas icideas .A largeco llect iono fapp licat ion sisg iven , inc lud ingexam p lesfrom phy s ics ,chem istry , u idm echan ics ,com bu s- t ion ,im agep rocess ing ,m ater ia lssc ience ,fab r icat iono fm icroe lectron ic com ponen ts ,com pu terv is ion ,con tro ltheory ,com...
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