Preconditioning immersed isogeometric finite element methods with application to flow problems

Journal article (2019)

Authors

Frits de Prenter Eindhoven University of Technology
C. V. Verhoosel Eindhoven University of Technology
E. H. van Brummelen Eindhoven University of Technology
Affiliation
External organisation
Preconditioning Condition number Navier–Stokes Immersed finite element method Fictitious domain method Iterative solver
More Info
expand_more

Published Date

2019

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Affiliation

External organisation

Abstract

Immersed finite element methods generally suffer from conditioning problems when cut elements intersect the physical domain only on a small fraction of their volume. We present a dedicated Additive-Schwarz preconditioner that targets the underlying mechanism causing the ill-conditioning of these methods. This preconditioner is applicable to problems that are not symmetric positive definite and to mixed problems. We provide a motivation for the construction of the Additive-Schwarz preconditioner, and present a detailed numerical investigation into the effectiveness of the preconditioner for a range of mesh sizes, isogeometric discretization orders, and partial differential equations, among which the Navier–Stokes equations.