• Corpus ID: 238634183

Inexact IETI-DP for conforming isogeometric multi-patch discretizations

@article{Schneckenleitner2021InexactIF,
  title={Inexact IETI-DP for conforming isogeometric multi-patch discretizations},
  author={Rainer Schneckenleitner and Stefan Takacs},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.06087}
}
In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have proven a condition number estimate for a IETI-DP method using sparse LU factorizations for the subdomain problems that is explicit, among other parameters, in the grid size and the spline degree. In the present paper, we replace the sparse LU factorizations by… 
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SHOWING 1-8 OF 8 REFERENCES
Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods
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…
Dual-primal isogeometric tearing and interconnecting solvers for multipatch continuous and discontinuous Galerkin IgA equations: DP-IETI solvers for multipatch cG and dG IgA equations
We present results regarding fast and robust solvers for equations arising from continuous and discontinuous Galerkin discretization of heterogeneous diffusion problems in the context of Isogeometric…
Isogeometric Preconditioners Based on Fast Solvers for the Sylvester Equation
TLDR
It is shown that a preconditioning strategy which is based on the solution of a Sylvester-like equation at each step of an iterative solver is robust with respect to both mesh size and spline degree, although it may suffer from the presence of complicated geometry or coefficients.
Inexact FETI-DP methods
Inexact FETI-DP domain decomposition methods are considered. Preconditioners based on formulations of FETI-DP as a saddle point problem are used which allow for an inexact solution of the coarse…
IETI – Isogeometric Tearing and Interconnecting
Highlights ► A new IsogEometric Tearing and Interconnecting (IETI) method is proposed. ► Exact geometry representation of IGA and solver design of FETI methods are combined. ► Coupling conditions for…
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method
The FETI method and its two-level extension (FETI-2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative solution of second-order solid mechanics and…
Condition number bounds for IETI-DP methods that are explicit in h and p
TLDR
This work derives condition number bounds that show the expected behavior in the grid size h and that are quasi-linear in the spline degree p and provides a convergence analysis that covers several choices of the primal degrees of freedom: the vertex values, the edge averages, and the combination of both.