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Multiresolution Shape Optimisation with Subdivision Surfaces

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Isogeometric Analysis and Applications 2014

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

Abstract

We review our recent work on multiresolution shape optimisation and present its application to elastic solids, electrostatic field equations and thin-shells. In the spirit of isogeometric analysis the geometry of the domain is described with subdivision surfaces and different resolutions of the same surface are used for optimisation and analysis. The analysis is performed using a sufficiently fine control mesh with a fixed resolution. During shape optimisation the geometry is updated starting with the coarsest control mesh and then moving on to increasingly finer control meshes. The transfer of data between the geometry and analysis representations is accomplished with subdivision refinement and coarsening operators. Moreover, we discretise elastic solids with the immersed finite element method, electrostatic field equations with the boundary element method and thin-shells with the subdivision finite element technique. In all three discretisation techniques there is no need to generate and maintain an analysis-suitable volume discretisation.

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Acknowledgements

The partial support of the EPSRC through grant # EP/G008531/1 and EC through the Marie Curie Actions (IAPP) program CASOPT project are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK

    Fehmi Cirak & Kosala Bandara

Authors
  1. Fehmi Cirak
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  2. Kosala Bandara
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Correspondence to Fehmi Cirak .

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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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Cirak, F., Bandara, K. (2015). Multiresolution Shape Optimisation with Subdivision Surfaces. 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_6

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