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arXiv · 2001.10921

The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications

Jochen Hinz·Andrzej Jaeschke·Matthias Möller·Cornelis Vuik
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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.

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Jochen Hinz, Andrzej Jaeschke, Matthias Möller, Cornelis Vuik. 2020-01-29. The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications. https://arxiv.org/abs/2001.10921

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