The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications
Numerical Analysis
2020-01-30 v1 Numerical Analysis
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.
Cite
@article{arxiv.2001.10921,
title = {The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications},
author = {Jochen Hinz and Andrzej Jaeschke and Matthias Möller and Cornelis Vuik},
journal= {arXiv preprint arXiv:2001.10921},
year = {2020}
}