The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications
Jochen Hinz (École Polytechnique Fédérale de Lausanne)
Andrzej Jaeschke (Lodz University of Technology)
Matthias Möller (TU Delft - Numerical Analysis)
Cornelis Vuik (TU Delft - Numerical Analysis)
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Abstract
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.