Title
A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis
Author
Tielen, R.P.W.M. (TU Delft Numerical Analysis)
Möller, M. (TU Delft Numerical Analysis) 
Vuik, Cornelis (TU Delft Delft Institute of Applied Mathematics)
Contributor
Manni, C. (editor)
Speleers, H. (editor)
Department
Delft Institute of Applied Mathematics
Date
2022
Abstract
Since its introduction in [20], Isogeometric Analysis (IgA) has established itself as a viable alternative to the Finite Element Method (FEM). Solving the resulting linear systems of equations efficiently remains, however, challenging when high-order B-spline basis functions of order p> 1 are adopted for approximation. The use of Incomplete LU (ILU) type factorizations, like ILU(k) or ILUT, as a preconditioner within a Krylov method or as a smoother within a multigrid method is very effective, but costly [37]. In this paper, we investigate the use of a block ILUT smoother within a p-multigrid method, where the coarse grid correction is obtained at p= 1, and compare it to a global ILUT smoother in case of multipatch geometries. A spectral analysis indicates that the use of the block ILUT smoother improves the overall convergence rate of the resulting p-multigrid method. Numerical results, obtained for a variety of two dimensional benchmark problems, illustrate the potential of this block ILUT smoother for multipatch geometries.
To reference this document use:
http://resolver.tudelft.nl/uuid:481d9da6-fbee-49cb-820b-04ab5f442e1e
DOI
https://doi.org/10.1007/978-3-030-92313-6_11
Publisher
Springer
Embargo date
2023-02-13
Source
Springer INdAM Series
Series
Springer INdAM Series, 2281-518X, 49
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.
Part of collection
Institutional Repository
Document type
book chapter
Rights
© 2022 R.P.W.M. Tielen, M. Möller, Cornelis Vuik