## Abstract

Isogeometric Analysis (IgA) can be considered as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. The development of efficient solvers for discretizations arising in IgA is a challenging task, as most (standard) iterative solvers have a detoriating performance for increasing values of the approximation order p of the basis functions. Recently, p-multigrid methods have been developed as an alternative solution strategy. With p-multigrid methods, a multigrid hierarchy is constructed based on the approximation order p instead of the mesh width h (i.e. h-multigrid). The coarse grid correction is then obtained at level p = 1, where B-spline basis functions coincide with standard Lagrangian P_{1} basis functions, enabling the use of well known solution strategies developed for the Finite Element Method to solve the residual equation. Different projection schemes can be adopted to go from the high-order level to level p = 1. In this paper, we compare a direct projection to level p = 1 with a projection between each level 1 ≤ k ≤ p in terms of iteration numbers and CPU times. Numerical results, including a spectral analysis, show that a direct projection leads to the most efficient method for both single patch and multipatch geometries.

Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference |

Editors | Fred J. Vermolen, Cornelis Vuik |

Place of Publication | Cham |

Publisher | Springer Science |

Pages | 1001-1009 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-030-55874-1 |

ISBN (Print) | 978-3-030-55873-4 |

DOIs | |

Publication status | Published - 2021 |

Event | European Numerical Mathematics and Advanced Applications Conference 2019 - Hotel Zuiderduin , Egmond aan Zee, Netherlands Duration: 30 Sep 2019 → 4 Oct 2019 https://www.enumath2019.eu/ |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 139 |

ISSN (Print) | 1439-7358 |

ISSN (Electronic) | 2197-7100 |

### Conference

Conference | European Numerical Mathematics and Advanced Applications Conference 2019 |
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Abbreviated title | ENUMATH 2019 |

Country/Territory | Netherlands |

City | Egmond aan Zee |

Period | 30/09/19 → 4/10/19 |

Internet address |

### 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-careOtherwise 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.