PHASE-FIELD METHODS FOR SPECTRAL SHAPE AND TOPOLOGY OPTIMIZATION

被引：4

作者：

Garcke, Harald ^{[1
]}

Huettl, Paul ^{[1
]}

Kahle, Christian ^{[2
]}

Knopf, Patrik ^{[1
]}

Laux, Tim ^{[3
]}

机构：

[1] Univ Regensburg, Fak Math, D-93053 Regensburg, Germany

[2] Univ Koblenz, Math Inst, D-56070 Koblenz, Germany

[3] Univ Bonn, Hausdorff Ctr Math, D-53115 Bonn, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷

关键词：

Eigenvalue optimization; shape optimization; topology optimization; PDE constrained optimization; phase-field approach; first order condition; sharp interface limit; Gamma-limit; finite element approximation; EIGENVALUES; PERIMETER; MINIMIZERS; REGULARITY; DIRICHLET; DERIVATIVES; FUNCTIONALS; EXISTENCE; RESPECT;

D O I：

10.1051/cocv/2022090

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：3269 / 3290

页数：57

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