A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

Roel Tielen*, Matthias Möller, Kees Vuik

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific

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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.

Original languageEnglish
Title of host publicationSpringer INdAM Series
EditorsC. Manni, H. Speleers
Number of pages20
Publication statusPublished - 2022

Publication series

NameSpringer INdAM Series
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

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