A level set formulation for Willmore flow | Zendy

Martin Rumpf | Zendy; Marc Droske | Zendy

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A level set formulation for Willmore flow

Author(s) -

Martin Rumpf,

Marc Droske

Publication year - 2004

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/105

Subject(s) - level set (data structures) , mathematics , discretization , set (abstract data type) , metric (unit) , flow (mathematics) , balanced flow , function (biology) , willmore energy , mathematical analysis , level set method , geometry , mean curvature flow , computer science , curvature , mean curvature , operations management , segmentation , artificial intelligence , evolutionary biology , economics , image segmentation , biology , programming language

A level set formulation of Willmore flow is derived using the gradient flow per- spective. Starting from single embedded surfaces and the corresponding gradient flow, the metric is generalized to sets of level set surfaces using the identification of normal velocities and variations of the level set function in time via the level set equation. The approach in particular allows to identify the natural dependent quantities of the derived variational formulation. Furthermore, spatial and tempo- ral discretization are discussed and some numerical simulations are presented.

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