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Optimal control for reinitialization in finite element level set methods
Author(s) -
Basting Christopher,
Kuzmin Dmitri,
Shadid John N.
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4348
Subject(s) - level set method , level set (data structures) , finite element method , mathematical optimization , eikonal equation , mathematics , optimal control , residual , term (time) , constraint (computer aided design) , flexibility (engineering) , convection–diffusion equation , set (abstract data type) , computer science , mathematical analysis , algorithm , engineering , geometry , physics , statistics , structural engineering , segmentation , quantum mechanics , artificial intelligence , image segmentation , programming language
Summary A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first‐order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE‐based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd.