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Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

de Prenter, Frits and Verhoosel, Clemens V. and van Brummelen, Harald and Evans, John and Messe, Christian and Benzaken, Joseph and Maute, Kurt (2019) Multigrid solvers for immersed finite element methods and immersed isogeometric analysis. Computational Mechanics. Springer. DOI: 10.1007/s00466-019-01796-y ISSN 0178-7675

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Abstract

Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates. This preconditioning technique is applicable to higher-order discretizations, and enables solving large-scale immersed systems at a computational cost that scales linearly with the number of degrees of freedom. The performance of the preconditioner is demonstrated for conventional Lagrange basis functions and for isogeometric discretizations with both uniform B-splines and locally refined approximations based on truncated hierarchical B-splines.

Item URL in elib:https://elib.dlr.de/132603/
Document Type:Article
Title:Multigrid solvers for immersed finite element methods and immersed isogeometric analysis
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
de Prenter, FritsDepartment of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The NetherlandsUNSPECIFIED
Verhoosel, Clemens V.c.v.verhoosel (at) tue.nlUNSPECIFIED
van Brummelen, Haralde.h.v.brummelen (at) tue.nlUNSPECIFIED
Evans, Johnjohn.a.evans (at) colorado.eduUNSPECIFIED
Messe, ChristianChristian.Messe (at) dlr.deUNSPECIFIED
Benzaken, Josephjoseph.benzaken (at) disneyanimation.comUNSPECIFIED
Maute, Kurtkurt.maute (at) colorado.eduUNSPECIFIED
Date:10 November 2019
Journal or Publication Title:Computational Mechanics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
DOI :10.1007/s00466-019-01796-y
Publisher:Springer
ISSN:0178-7675
Status:Published
Keywords:FEA, IGA, Multigrid, B-Splines
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transport
DLR - Research area:Raumfahrt
DLR - Program:R RP - Raumtransport
DLR - Research theme (Project):R - Raumfahrzeugsysteme - Numerische Verfahren und Simulation
Location: Bremen
Institutes and Institutions:Institute of Space Systems > Space Launcher Systems Analysis
Deposited By: Messe, Christian
Deposited On:13 Dec 2019 09:36
Last Modified:13 Dec 2019 09:36

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