Multigrid methods on high performance computers
Presenter
May 6, 2026
Abstract
Multigrid methods are among the fastest iterative methods for the solution of linear systems arising from the discretization of partial differential equations. As such they are used in a wide range of applications, including ones requiring huge computations. As a result parallelization of multigrid methods is common and various scalable solvers exist. On modern supercomputers as any other computational method multigrid has to cope with heterogenity and a growing imbalance of network and memory speeds on the one hand and CPU's and GPU's compute speed on the other hand. Different techniques have been developed to cope with these challenges.
Multigrid methods are very well-analyzed and this analyses usually are based on the multiplicative nature and tight coupling of their different components. Nevertheless, additive multigrid has been considered relatively early in multigrid's history and various authors also studied asynchronous variants with less tight coupling in recent years.
In the talk multigrid methods on high performance computers and various approaches to increase scalability, including asynchrony will be discussed.