Efficient p-Multigrid Based Solvers for Isogeometric Analysis on Multipatch Geometries

Conference Paper (2021)
Author(s)

Roel Tielen (TU Delft - Numerical Analysis)

Matthias Moller (TU Delft - Numerical Analysis)

K. Vuik (TU Delft - Numerical Analysis)

Research Group
Numerical Analysis
Copyright
© 2021 R.P.W.M. Tielen, M. Möller, Cornelis Vuik
DOI related publication
https://doi.org/10.1007/978-3-030-49836-8_10
More Info
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Publication Year
2021
Language
English
Copyright
© 2021 R.P.W.M. Tielen, M. Möller, Cornelis Vuik
Research Group
Numerical Analysis
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
Pages (from-to)
209-225
ISBN (print)
978-3-030-49835-1
ISBN (electronic)
978-3-030-49836-8
Reuse Rights

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Abstract

Isogeometric Analysis can be considered as the natural extension of the Finite Element Method (FEM) to higher-order spline based discretizations simplifying the treatment of complex geometries with curved boundaries. Finding a solution of the resulting linear systems of equations efficiently remains, however, a challenging task. Recently, p-multigrid methods have been considered [18], in which a multigrid hierarchy is constructed based on different approximation orders p instead of mesh widths h as it would be the case in classical h-multigrid schemes [8]. The use of an Incomplete LU-factorization as a smoother within the p-multigrid method has shown to lead to convergence rates independent of both h and p for single patch geometries [19]. In this paper, the focus lies on the application of the aforementioned p-multigrid method on multipatch geometries having a C0-continuous coupling between the patches. The use of ILUT as a smoother within p-multigrid methods leads to convergence rates that are essentially independent of h and p, but depend mildly on the number of patches.

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