Planar Parametrization in Isogeometric Analysis

  • Jens Gravesen
  • Anton Evgrafov
  • Dang-Manh Nguyen
  • Peter Nørtoft
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8177)

Abstract

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.

Keywords

Isogeometric analysis shape optimization parametrization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jens Gravesen
    • 1
  • Anton Evgrafov
    • 1
  • Dang-Manh Nguyen
    • 2
  • Peter Nørtoft
    • 3
  1. 1.Dept. of Appl. Math. & Comp. Sci.Technical University of DenmarkDenmark
  2. 2.Institute of Applied GeometryJohannes Kepler UniversityAustria
  3. 3.Applied MathematicsSINTEF ICTNorway

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