A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

Book chapter (2022)

Authors

R.P.W.M. Tielen Numerical Analysis - EEMCS
M. Möller Numerical Analysis - EEMCS
Cornelis Vuik Delft Institute of Applied Mathematics
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2022 R.P.W.M. Tielen, M. Möller, Cornelis Vuik
DOI
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https://doi.org/10.1007/978-3-030-92313-6_11
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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.