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

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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.

Original languageEnglish
Article number113347
Pages (from-to)1-27
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Volume372
DOIs
Publication statusPublished - 2020

Keywords

  • ILUT smoother
  • Isogeometric analysis
  • Multigrid methods
  • p-multigrid

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