A Direct Projection to Low-Order Level for p-Multigrid Methods in Isogeometric Analysis

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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 P1 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 languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
Place of PublicationCham
PublisherSpringer
Pages1001-1009
Number of pages9
ISBN (Electronic)978-3-030-55874-1
ISBN (Print)978-3-030-55873-4
DOIs
Publication statusPublished - 2021
EventEuropean Numerical Mathematics and Advanced Applications Conference 2019 - Hotel Zuiderduin , Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019
https://www.enumath2019.eu/

Publication series

NameLecture Notes in Computational Science and Engineering
Volume139
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceEuropean Numerical Mathematics and Advanced Applications Conference 2019
Abbreviated titleENUMATH 2019
CountryNetherlands
CityEgmond aan Zee
Period30/09/194/10/19
Internet address

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