Condition number bounds for IETI-DP methods that are explicit in h and p

@article{Schneckenleitner2019ConditionNB,
  title={Condition number bounds for IETI-DP methods that are explicit in h and p},
  author={Rainer Schneckenleitner and Stefan Takacs},
  journal={ArXiv},
  year={2019},
  volume={abs/1912.07909}
}
We study the convergence behavior of Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for solving large-scale algebraic systems arising from multi-patch Isogeometric Analysis. We focus on the Poisson problem on two dimensional computational domains. We provide a convergence analysis that covers several choices of the primal degrees of freedom: the vertex values, the edge averages, and the combination of both. We derive condition number bounds that show the expected… 
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A convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisson problem, where the patches are coupled using discontinuous Galerkin is developed.

Inexact IETI-DP for conforming isogeometric multi-patch discretizations

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.

IETI-DP for conforming multi-patch Isogeometric Analysis in three dimensions

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A convergence theory is presented that shows that the condition number of the preconditioned system only grows poly-logarithmically with the grid size, and that the convergence of the overall solver only mildly depends on the spline degree.

Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis

It is shown how stability results for single-patch domains can be carried over to multi- patch domains, and how stability strongly depends on the shape of the geometry.

IETI-DP methods for discontinuous Galerkin multi-patch Isogeometric Analysis with T-junctions

Dual-Primal Isogeometric Tearing and Interconnecting methods for the Stokes problem

This work uses Dual-Primal Isogeometric Tearing and Interconnecting methods to test out two different scaled Dirichlet preconditioners with different choices of primal degrees of freedom for a fast solver for linear systems obtained by discretizing the Stokes problem with multi-patch I sogeometric Analysis.

Towards a IETI-DP solver on non-matching multi-patch domains

This paper presents a generalization of isogeometric tearing and interconnecting solvers that means that the patches can meet in T-junctions, which increases the flexibility of the geometric model significantly.

Convergence theory for IETI-DP solvers for discontinuous Galerkin Isogeometric Analysis that is explicit in h and p

A convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisson problem, where the patches are coupled using discontinuous Galerkin.

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