# Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods

## TL;DR

This paper explores inexact dual-primal isogeometric tearing and interconnecting methods, replacing direct solvers with iterative multigrid solvers to efficiently solve large-scale elliptic PDE discretizations.

## Contribution

It introduces inexact variants of the methods, integrating iterative solvers into the framework, and evaluates their performance through numerical experiments.

## Key findings

- Inexact methods with iterative solvers perform comparably to exact methods.
- Multigrid solvers significantly reduce computational time.
- Numerical results demonstrate the efficiency of the proposed inexact approaches.

## Abstract

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 direct solvers by iterative methods, particularly, multigrid solvers. We investigate the incorporation of these iterative solvers into different formulations of the algorithm. Finally, we present numerical examples comparing the performance of these inexact versions.