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Algorithmic Aspects of Isogeometric Shape Optimization

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Isogeometric Analysis and Applications 2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 107))

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Abstract

Shape optimization is concerned about finding optimal designs under the aspect of some cost criteria often involving the solution of a partial differential equation (PDE) over the afore said unknown shape. In general, industrial cases involve a geometric model from Computer Aided Design (CAD). However, solving PDEs requires an analysis suitable working model, typically a Finite Element (FEM) triangulation. Hence, some of the geometric properties known from the CAD model may be lost during this format change. Therefore, we employ isogeometric analysis (IGA) instead, which has a tighter connection between geometry, simulation and shape optimization. In this paper, we present a self-contained treatment of gradient based shape optimization method with isogeometric analysis, focusing on algorithmic and practical aspects like computation of shape gradients in an IGA formulation and updating B-spline and NURBS geometries.

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Acknowledgements

We thank Utz Wever from Siemens AG, Corporate Technology, for many helpful discussions on the subject.

This work was supported by the European Union within the Project 284981 “TERRIFIC” (7th Framework Program).

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Authors and Affiliations

  1. Technische Universität Kaiserslautern, Paul-Ehrlich-Str. Geb. 31, 67633, Kaiserslautern, Germany

    Daniela Fußeder & Bernd Simeon

Authors
  1. Daniela Fußeder
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  2. Bernd Simeon
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Corresponding author

Correspondence to Daniela Fußeder .

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Editors and Affiliations

  1. Johannes Kepler Universität Linz Institut für Angewandte Geometrie, Linz, Austria

    Bert Jüttler

  2. Technische Universität Kaiserslautern Fachbereich Mathematik, Kaiserslautern, Germany

    Bernd Simeon

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Fußeder, D., Simeon, B. (2015). Algorithmic Aspects of Isogeometric Shape Optimization. In: Jüttler, B., Simeon, B. (eds) Isogeometric Analysis and Applications 2014. Lecture Notes in Computational Science and Engineering, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-23315-4_8

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