The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

Hinz, J.P. (Swiss Federal Institute of Technology)
Jaeschke, Andrzej (Lodz University of Technology)
Möller, M. (TU Delft Numerical Analysis)
Vuik, Cornelis (TU Delft Numerical Analysis)

2021

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases.

Adjoint-based optimization
Elliptic Grid Generation
Isogeometric Analysis
Parameterization techniques
Shape optimization

http://resolver.tudelft.nl/uuid:6201c932-49af-4302-9490-ca609d556473

https://doi.org/10.1016/j.cma.2021.113685

2021-08-27

0045-7825

Computer Methods in Applied Mechanics and Engineering, 378, 1-19

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2021 J.P. Hinz, Andrzej Jaeschke, M. Möller, Cornelis Vuik