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Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers

  • Christoph Hofer
  • Ulrich Langer
  • Ioannis ToulopoulosEmail author
Original Research
  • 60 Downloads

Abstract

One challenging task in Isogeometric Analysis (IGA) is the segmentation of domains, which are represented via their boundaries, e.g. arising from a computer aided design model, into suitable blocks and the construction of their spline parametrizations. This yields a multipatch description of the domain. However, errors can occur during the computation of the associated control points when constructing the spline parametrizations of a patch. This leads to the derivation of non-matching interface parametrizations, i.e. gap and overlapping regions can appear between the patch interfaces. In this paper, we develop discontinuous Galerkin techniques in the context of IGA for solving elliptic diffusion problems on multipatch domains which can include gap and overlapping regions. This work is the continuation of two previous works, where we presented a complete discretization analysis for the case of having only gap regions. Here we focus on a unified presentation of the method for general gap and overlapping regions, and the development of efficient domain decomposition solvers based on tearing and interconnecting technology. In addition, we investigate the influence of the size of the gap/overlapping regions on the performance of the proposed solvers. Comparisons are shown and implementation issues are discussed on actual numerical examples.

Keywords

Elliptic diffusion problems Heterogeneous diffusion coefficients Isogeometric analysis Discontinuous Galerkin methods Multipatch domain representations Non-matching interface parametrizations IETI-DP domain decomposition solvers 

Mathematics Subject Classification

65M12 65M15 65M55 

Notes

Acknowledgements

This work was supported by the Austrian Science Fund (FWF) under the Grant NFN S117-03 and W1214-N15, Project DK4. The third author was further supported by the Project: COMET K2 XTribology, No. 849109; Project grantee: Excellence Center of Tribology.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2019

Authors and Affiliations

  • Christoph Hofer
    • 1
  • Ulrich Langer
    • 1
    • 2
  • Ioannis Toulopoulos
    • 2
    • 3
    Email author
  1. 1.Johannes Kepler University (JKU)LinzAustria
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  3. 3.AC2T Research GmbH, Austrian Excellence Center for TribologyWiener NeustadtAustria

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