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

• Published in: Computer methods in applied mechanics and engineering Vol. 378; p. 113685
• Main Authors: Hinz, Jochen, Jaeschke, Andrzej, Möller, Matthias, Vuik, Cornelis
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2021; Elsevier BV
• Subjects: Adjoint-based optimization; Algorithms; Elliptic Grid Generation; Equations of state; Isogeometric Analysis; Iterative methods; Optimization; Parameterization; Parameterization techniques; Robustness (mathematics); Shape optimization; Elliptic Grid Generation; Isogeometric Analysis; Parameterization techniques; Shape optimization; Adjoint-based optimization
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.113685

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. •Discretizing the optimization problem with IGA enables treating both the domain parameterization problem and the state equation as additional PDE-constraints.•The gradient of the system is assembled fully symbolically using an adjoint formulation.•The algorithm employs automated local refinement with THB-splines.•The consistency of the scheme is tested by comparing the discrete solution to the exact minimizer of a problem with known solution.•We employ the methodology to designing a cooling element.