# 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…

## 9 Citations

### Convergence Theory for IETI-DP Solvers for Discontinuous Galerkin Isogeometric Analysis that is Explicit in ℎ and 𝑝

- Computer Science, MathematicsComput. Methods Appl. Math.
- 2022

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

- Computer ScienceArXiv
- 2021

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

- Mathematics, Computer ScienceArXiv
- 2021

This paper considers dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis and provides numerical experiments that indicate that similar results may hold for three dimensional domains.

### A IETI-DP method for discontinuous Galerkin discretizations in Isogeometric Analysis with inexact local solvers

- Computer ScienceArXiv
- 2022

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

- Computer Science, MathematicsArXiv
- 2022

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

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2022

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

- Computer Science, MathematicsArXiv
- 2021

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

- Computer ScienceArXiv
- 2021

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

- Computer Science, Mathematics
- 2020

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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