About: Comparison study for level set and direct Lagrangean methods for computing Willmore flow of closed planar curves

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The main goal of this paper is to present results of comparison study for the level set and direct Lagrangian methods for computing evolution of the Willmore flow of embedded planar curves. To perform such a study we construct new numerical approximation schemes for both Lagrangian as well as level set methods based on semi-implicit in time and finite/complementary volume in space discretizations. The Lagrangian scheme is stabilized in tangential direction by the asymptotically uniform grid point redistribution. Both methods are experimentally second order accurate. Moreover, we show precise coincidence of both approaches in case of various elastic curve evolutions provided that solving the linear systems in semi-implicit level set method is done in a precise way, redistancing is performed occasionally and the influence of boundary conditions on the level set function is eliminated. The main goal of this paper is to present results of comparison study for the level set and direct Lagrangian methods for computing evolution of the Willmore flow of embedded planar curves. To perform such a study we construct new numerical approximation schemes for both Lagrangian as well as level set methods based on semi-implicit in time and finite/complementary volume in space discretizations. The Lagrangian scheme is stabilized in tangential direction by the asymptotically uniform grid point redistribution. Both methods are experimentally second order accurate. Moreover, we show precise coincidence of both approaches in case of various elastic curve evolutions provided that solving the linear systems in semi-implicit level set method is done in a precise way, redistancing is performed occasionally and the influence of boundary conditions on the level set function is eliminated. (en)
Title	Comparison study for level set and direct Lagrangean methods for computing Willmore flow of closed planar curves Comparison study for level set and direct Lagrangean methods for computing Willmore flow of closed planar curves (en)
skos:prefLabel	Comparison study for level set and direct Lagrangean methods for computing Willmore flow of closed planar curves Comparison study for level set and direct Lagrangean methods for computing Willmore flow of closed planar curves (en)
skos:notation	RIV/68407700:21340/09:00141335!RIV10-MSM-21340___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC06052), Z(MSM6840770010)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Oberhuber, Tomáš Beneš, Michal
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	307827
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/09:00141335
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Elastic curve; Willmore flow; Level set method; Lagrangian method; Tangential redistribution; Semi-implicit scheme; Complementary volume method (en)
http://linked.open.../riv/klicoveSlovo	Willmore flow Level set method Complementary volume method Elastic curve Lagrangian method Semi-implicit scheme Tangential redistribution
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[8E41AA5CAA23]
http://linked.open...i/riv/nazevZdroje	Computing and Visualization in Science
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	The Nečas Center for Mathematical Modeling
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	12
http://linked.open...iv/tvurceVysledku	Beneš, Michal Oberhuber, Tomáš
http://linked.open...n/vavai/riv/zamer	Aplikovaná matematika v technických a fyzikálních vědách
issn	1432-9360
number of pages	11 (xsd:int)
http://localhost/t...ganizacniJednotka	21340

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