# Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric Analysis

## TL;DR

This paper extends multigrid solvers for Isogeometric Analysis to handle both conforming and non-conforming multi-patch discretizations, demonstrating improved efficiency when combined with Gauss-Seidel smoothing.

## Contribution

It introduces multigrid solvers for non-conforming multi-patch Isogeometric Analysis and shows enhanced performance with combined smoothing techniques.

## Key findings

- Multigrid solvers effectively handle non-conforming discretizations.
- Combining the proposed smoother with Gauss-Seidel improves convergence.
- Extended multigrid methods outperform previous conforming-only approaches.

## Abstract

Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global parameterization of the computational domain. In non-trivial cases, the domain is decomposed into patches having separate parameterizations and separate discretization spaces. If the discretization spaces agree on the interfaces between the patches, the coupling can be done in a conforming way. Otherwise, non-conforming discretizations (utilizing discontinuous Galerkin approaches) are required. The author and his coworkers have previously introduced multigrid solvers for Isogeometric Analysis for the conforming case. In the present paper, these results are extended to the non-conforming case. Moreover, it is shown that the multigrid solves get even more powerful if the proposed smoother is combined with a (standard) Gauss-Seidel smoother.