Garcke, Harald and Huettl, Paul and Kahle, Christian and Knopf, Patrik and Laux, Tim (2023) PHASE-FIELD METHODS FOR SPECTRAL SHAPE AND TOPOLOGY OPTIMIZATION. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 29: 10. ISSN 1292-8119, 1262-3377
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We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to represent the shapes over which we minimize. The idea behind this method is to modify the Laplace operator by introducing phase-field dependent coefficients in order to extend the eigenvalue problem on a fixed design domain containing all admissible shapes. The resulting shape and topology optimization problem can then be formulated as an optimal control problem with PDE constraints in which the phase-field function acts as the control. For this optimal control problem, we establish first-order necessary optimality conditions and we rigorously derive its sharp interface limit. Eventually, we present and discuss several numerical simulations for our optimization problem.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EIGENVALUES; PERIMETER; MINIMIZERS; REGULARITY; DIRICHLET; DERIVATIVES; FUNCTIONALS; EXISTENCE; RESPECT; Eigenvalue optimization; shape optimization; topology optimization; PDE constrained optimization; phase-field approach; first order condition; sharp interface limit; Gamma-limit; finite element approximation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Feb 2024 12:42 |
| Last Modified: | 28 Feb 2024 12:42 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59516 |
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