Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods

@article{Hofer2017InexactDI,
  title={Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods},
  author={Christoph Hofer and Ulrich Langer and Stefan Takacs},
  journal={arXiv: Numerical Analysis},
  year={2017}
}
In this paper, we investigate inexact variants of dual-primal isogeometric tearing and interconnecting methods for solving large-scale systems of linear equations arising from Galerkin isogeometric discretizations of elliptic boundary value problems. The considered methods are extensions of standard finite element tearing and interconnecting methods to isogeometric analysis. The algorithms are implemented by means of energy minimizing primal subspaces. We discuss the replacement of local sparse… 
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5 Citations
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Methods Citations
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5 Citations

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Citation Type

Inexact IETI-DP for conforming isogeometric multi-patch discretizations
TLDR
The sparse LU factorizations are replaced by fast diagonalization based preconditioners to get a faster IETI-DP method while maintaining the same explicit condition number bound.
Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations
  • S. Takacs
  • Computer Science
    Mathematical Models and Methods in Applied Sciences
  • 2018
TLDR
The approximation error estimates and the multigrid solver are extended to this multi-patch case and allow to solve the linear system arising 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.
A Parallel Multigrid Solver for Multi-Patch Isogeometric Analysis
  • C. Hofer, S. Takacs
  • Computer Science
    Lecture Notes in Computational Science and Engineering
  • 2019
TLDR
The authors show that the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree and that they scale well in a parallel environment.
Overlapping Schwarz methods for isogeometric analysis based on generalized B-splines
A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers

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