A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

Tielen, R.P.W.M. (TU Delft Numerical Analysis)
Möller, M. (TU Delft Numerical Analysis)
Vuik, Cornelis (TU Delft Delft Institute of Applied Mathematics)

Manni, C. (editor)
Speleers, H. (editor)

2022

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.

http://resolver.tudelft.nl/uuid:481d9da6-fbee-49cb-820b-04ab5f442e1e

https://doi.org/10.1007/978-3-030-92313-6_11

Springer

2023-02-13

Springer INdAM Series

Springer INdAM Series, 2281-518X, 49

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.

Institutional Repository

book chapter

© 2022 R.P.W.M. Tielen, M. Möller, Cornelis Vuik