TY - INPR
A1 - Fußeder, Daniela
A1 - Simeon, Bernd
A1 - Vuong, Anh-Vu
T1 - A Framework for Shape Optimization in the Context of Isogeometric Analysis
N2 - 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.
KW - isogeometric analysis
KW - shape optimization
KW - adjoint approach
KW - weight optimization
KW - NURBS
Y1 - 2014
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3833
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-38330
ER -