Preconditioning immersed isogeometric finite element methods with application to flow problems

摘要

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. (C) 2019 Elsevier B.V. All rights reserved.