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Properties of Spline Spaces Over Structured Hierarchical Box Partitions

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Isogeometric Analysis and Applications 2018 (IGAA 2018)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 133))

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Abstract

Given a spline space spanned by Truncated Hierarchical B-splines (THB), it is always possible to construct a spline space spanned by Locally Refined B-splines (LRB) that contains the THB-space. Starting from configurations where the two spline spaces are equal, we address what happens to the properties of the LRB-space when it is modified by local one-directional refinement at convex corners of, and along edges between dyadic refinement regions. We show that such local modifications can reduce the number of B-splines over each element to the minimum prescribed by the polynomial bi-degree, and that such local refinements can be used for improving the condition numbers of mass and stiffness matrices.

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References

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Acknowledgements

This project has received funding from the The Research Council of Norway under grant agreement No 270922.

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Authors and Affiliations

  1. SINTEF, Oslo, Norway

    Ivar Stangeby & Tor Dokken

Authors
  1. Ivar Stangeby
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  2. Tor Dokken
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Corresponding author

Correspondence to Tor Dokken .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Harald van Brummelen

  2. Department of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Cornelis Vuik

  3. Department of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Matthias Möller

  4. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Clemens Verhoosel

  5. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Bernd Simeon

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

    Bert Jüttler

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Stangeby, I., Dokken, T. (2021). Properties of Spline Spaces Over Structured Hierarchical Box Partitions. In: van Brummelen, H., Vuik, C., Möller, M., Verhoosel, C., Simeon, B., Jüttler, B. (eds) Isogeometric Analysis and Applications 2018. IGAA 2018. Lecture Notes in Computational Science and Engineering, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-030-49836-8_9

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