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Higher-order moving mesh methods for PDE-constrained shape optimization

Abstract:
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of PDE-constraints. This shape optimization method is based on discretized deformation diffeomorphisms and allows for arbitrarily high resolution of shapes with arbitrary smoothness. Numerical experiments show that it allows the solution of PDE-constrained shape optimization problems to high accuracy.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1137/17M1133956

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
ORCID:
0000-0003-3309-7657
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Farrell, PE More by this author
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Scientific Computing Journal website
Volume:
40
Issue:
4
Pages:
A2356–A2382
Publication date:
2018-08-02
Acceptance date:
2018-05-07
DOI:
EISSN:
1095-7197
ISSN:
1064-8275
Pubs id:
pubs:700446
URN:
uri:0f23fcdf-8b39-4904-820d-5fc48bd1b452
UUID:
uuid:0f23fcdf-8b39-4904-820d-5fc48bd1b452
Local pid:
pubs:700446

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