Optimal control for reinitialization in finite element level set methods
نویسندگان
چکیده
A new optimal control 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. 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 approach is evaluated numerically in three different examples and compared to other PDE-based reinitialization techniques.
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