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International Conference on Mathematical Methods for Curves and Surfaces

MMCS 2012: Mathematical Methods for Curves and Surfaces pp 189–212Cite as

Planar Parametrization in Isogeometric Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Author information

Authors and Affiliations

  1. Dept. of Appl. Math. & Comp. Sci., Technical University of Denmark, Denmark

    Jens Gravesen & Anton Evgrafov

  2. Institute of Applied Geometry, Johannes Kepler University, Austria

    Dang-Manh Nguyen

  3. Applied Mathematics, SINTEF ICT, Norway

    Peter Nørtoft

Authors
  1. Jens Gravesen
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  2. Anton Evgrafov
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  3. Dang-Manh Nguyen
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  4. Peter Nørtoft
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Editor information

Editors and Affiliations

  1. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  2. DMA, University of Oslo, P.O.Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

  3. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  4. University of Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Gravesen, J., Evgrafov, A., Nguyen, DM., Nørtoft, P. (2014). Planar Parametrization in Isogeometric Analysis. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_11

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54381-4

  • Online ISBN: 978-3-642-54382-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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