The strip method for shape derivatives

A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape d...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2022-04, Vol.123 (7), p.1606-1626
Main Authors: Hardesty, Sean, Antil, Harbir, Kouri, Drew P., Ridzal, Denis
Format: Article
Language:English
Subjects:
boundary method
Coupling
Finite element method
finite elements
Quadratures
Shape optimization
Strip
strip method
volume method
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Summary:A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches to computing shape derivatives. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. As an added benefit, its computational complexity is comparable to that of the boundary method, that is, it is faster than the volume method. We illustrate the benefits of the strip method with numerical examples.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6908