A parallel multigrid solver for multi-patch Isogeometric Analysis

TL;DR

This paper presents a parallel multigrid solver for multi-patch Isogeometric Analysis that scales efficiently in parallel environments, addressing the challenge of high spline degrees in large-scale PDE discretizations.

Contribution

The authors demonstrate that their previously developed multigrid solvers are parallelizable and maintain optimal performance with increasing spline degrees.

Findings

The solver scales well in parallel computing environments.

Multigrid methods outperform standard smoothers for high spline degrees.

The approach achieves optimal convergence rates in both grid size and spline degree.

Abstract

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.