A Framework for Shape Optimization in the Context of Isogeometric Analysis

  • We develop a framework for shape optimization problems under state equation con- straints where both state and control are discretized by B-splines or NURBS. In other words, we use isogeometric analysis (IGA) for solving the partial differential equation and a nodal approach to change domains where control points take the place of nodes and where thus a quite general class of functions for representing optimal shapes and their boundaries becomes available. The minimization problem is solved by a gradient descent method where the shape gradient will be defined in isogeometric terms. This gradient is obtained following two schemes, optimize first–discretize then and, reversely, discretize first–optimize then. We show that for isogeometric analysis, the two schemes yield the same discrete system. Moreover, we also formulate shape optimization with respect to NURBS in the optimize first ansatz which amounts to finding optimal control points and weights simultaneously. Numerical tests illustrate the theory.

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Author:Daniela Fußeder, Bernd Simeon, Anh-Vu Vuong
Document Type:Preprint
Language of publication:English
Date of Publication (online):2014/07/23
Year of first Publication:2014
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2014/07/24
Tag:NURBS; adjoint approach; isogeometric analysis; shape optimization; weight optimization
Page Number:24
Source:Computer Methods in Applied Mechanics and Engineering, Band 286, 1. April 2015, Seiten 313-331, http://www.sciencedirect.com/science/article/pii/S0045782514005076
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012