p-multigrid methods and their comparison to h-multigrid methods within Isogeometric Analysis

Journal Article (2020)
Author(s)

Roel Tielen (TU Delft - Numerical Analysis)

M. Moller (TU Delft - Numerical Analysis)

D. Göddeke (University of Stuttgart)

K. Vuik (TU Delft - Numerical Analysis)

Research Group
Numerical Analysis
Copyright
© 2020 R.P.W.M. Tielen, M. Möller, D. Göddeke, Cornelis Vuik
DOI related publication
https://doi.org/10.1016/j.cma.2020.113347
More Info
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Publication Year
2020
Language
English
Copyright
© 2020 R.P.W.M. Tielen, M. Möller, D. Göddeke, Cornelis Vuik
Research Group
Numerical Analysis
Volume number
372
Pages (from-to)
1-27
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Abstract

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the spline degree p instead of the mesh width h, and compare it to h-multigrid methods. Since the use of classical smoothers (e.g. Gauss–Seidel) results in a p-multigrid/h-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated as well. Numerical results and a spectral analysis indicate that the use of this smoother exhibits convergence rates essentially independent of h and p for both p-multigrid and h-multigrid methods. In particular, we compare both coarsening strategies (e.g. coarsening in h or p) adopting both smoothers for a variety of two and three dimensional benchmarks. Furthermore, the ILUT smoother is compared to a state-of-the-art smoother (Hofreither and Takacs 2017) using both coarsening strategies. Finally, the proposed p-multigrid method is used to solve linear systems resulting from THB-spline discretizations.