Shape Optimization by Pursuing Diffeomorphisms
- Hiptmair, Ralf 1Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
- Paganini, Alberto 1Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Published in:
- Computational Methods in Applied Mathematics. - Walter de Gruyter GmbH. - 2015, vol. 15, no. 3, p. 291-305
English
Abstract We consider PDE constrained shape optimization in
the framework of finite element discretization of
the underlying boundary value problem. We present an algorithm tailored to preserve and exploit
the approximation properties of the finite element method,
and that allows for arbitrarily high resolution of shapes. It
employs (i) B-spline based representations of the deformation diffeomorphism,
and (ii) superconvergent domain integral expressions for the shape gradient.
We provide numerical evidence of the performance of this method
both on prototypical well-posed and ill-posed shape optimization
problems.
the framework of finite element discretization of
the underlying boundary value problem. We present an algorithm tailored to preserve and exploit
the approximation properties of the finite element method,
and that allows for arbitrarily high resolution of shapes. It
employs (i) B-spline based representations of the deformation diffeomorphism,
and (ii) superconvergent domain integral expressions for the shape gradient.
We provide numerical evidence of the performance of this method
both on prototypical well-posed and ill-posed shape optimization
problems.
- Language
-
- English
- Open access status
- green
- Identifiers
-
- DOI 10.1515/cmam-2015-0013
- ISSN 1609-4840
- Persistent URL
- https://sonar.ch/global/documents/89138
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