1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Johannes Kepler University of Linz5 Johannes Kepler University of Linz
Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape optimization. It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. Their performance is illustrated through a few numerical examples.
Lecture Notes in Computer Science: 8th International Conference, Mmcs 2012, Oslo, Norway, June 28 – July 3, 2012, Revised Selected Papers, 2014
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Lecture Notes in Computer Science
8th International Conference on Mathematical Methods for Curves and Surfaces (MMCS 2012)Curves and Surfaces