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

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

Tielen, R.P.W.M. (TU Delft Numerical Analysis)
Möller, M. (TU Delft Numerical Analysis)
Göddeke, D. (University of Stuttgart)
Vuik, Cornelis (TU Delft Numerical Analysis)

2020

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.

ILUT smoother
Isogeometric analysis
Multigrid methods
p-multigrid

http://resolver.tudelft.nl/uuid:e95464d4-2023-4674-ac38-9861c6574a23

https://doi.org/10.1016/j.cma.2020.113347

0045-7825

Computer Methods in Applied Mechanics and Engineering, 372, 1-27

Institutional Repository

journal article

© 2020 R.P.W.M. Tielen, M. Möller, D. Göddeke, Cornelis Vuik