A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

Roel Tielen; Matthias Möller; Kees Vuik

doi:10.1007/978-3-030-92313-6_11

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 volume › Chapter › Scientific

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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.

Original language	English
Title of host publication	Springer INdAM Series
Editors	C. Manni, H. Speleers
Publisher	Springer
Pages	259-278
Number of pages	20
DOIs	https://doi.org/10.1007/978-3-030-92313-6_11
Publication status	Published - 2022

Publication series

Name	Springer INdAM Series
Volume	49
ISSN (Print)	2281-518X
ISSN (Electronic)	2281-5198

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.

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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.",

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PY - 2022

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N2 - 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.

AB - 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.

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A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

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