Blank, Luise and Meisinger, Johannes (2022) Optimal control of anisotropic Allen-Cahn equations. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 28: 71. ISSN 1292-8119, 1262-3377
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This paper aims at solving an optimal control problem governed by an anisotropic Allen-Cahn equation numerically. Therefor we first prove the Frechet differentiability of an in time discretized parabolic control problem under certain assumptions on the involved quasilinearity and formulate the first order necessary conditions. As a next step, since the anisotropies are in general not smooth enough, the convergence behavior of the optimal controls is studied for a sequence of (smooth) approximations of the former quasilinear term. In addition the simultaneous limit in the approximation and the time step size is considered. For a class covering a large variety of anisotropies we introduce a certain regularization and show the previously formulated requirements. Finally, a trust region Newton solver is applied to various anisotropies and configurations, and numerical evidence for mesh independent behavior and convergence with respect to regularization is presented.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; QUASI-STATIC PLASTICITY; PHASE-FIELD MODEL; REGULARIZATION; Allen-Cahn equation; anisotropy; quasilinear parabolic equation; optimal control; regularization; discretization; optimality conditions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Luise Blank |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 07:30 |
| Last Modified: | 07 Feb 2024 07:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56610 |
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