Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations

Abstract

In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system arizing from the discretization of a partial differential equation in Isogeometric Analysis in a single-patch setting with convergence rates that are provably robust both in the grid size and the spline degree. In real-world problems, the computational domain cannot be nicely represented by just one patch. In computer aided design, such domains are typically represented as a union of multiple patches. In the present paper, we extend the approximation error estimates and the multigrid solver to this multi-patch case.

References in corpus (1)

• Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods

Cited by in corpus (10)

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• Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis
• A p-multigrid method enhanced with an ILUT smoother and its comparison to h-multigrid methods within Isogeometric Analysis
• Robust multigrid solvers for the biharmonic problem in isogeometric analysis
• A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers
• Condition number bounds for IETI-DP methods that are explicit in h and p
• Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
• Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric Analysis
• A parallel multigrid solver for multi-patch Isogeometric Analysis
• A quasi-robust discretization error estimate for discontinuous Galerkin Isogeometric Analysis