A parallel multigrid solver for multi-patch Isogeometric Analysis
This work addresses the need for robust and parallelizable solvers for high-degree spline discretizations in Isogeometric Analysis, which is important for large-scale simulations.
The authors demonstrate that their previously proposed multigrid solvers for Isogeometric Analysis are parallelizable and scale well in a parallel environment, achieving optimal behavior in both grid size and spline degree.
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.