Lecture 06: The Impact of Computer Architectures on the Design of Algebraic Multigrid Methods

Algebraic multigrid (AMG) is a popular iterative solver and preconditioner for large sparse linear systems. When designed well, it is algorithmically scalable, enabling it to solve increasingly larger systems efficiently. While it consists of various highly parallel building blocks, the original method also consisted of various highly sequential components. A large amount of research has been performed over several decades to design new components that perform well on high performance computers. As a matter of fact, AMG has shown to scale well to more than a million processes. However, with single-core speeds plateauing, future increases in computing performance need to rely on more complicated, often heterogenous computer architectures, which provide new challenges for efficient implementations of AMG. To meet these challenges and yield fast and efficient performance, solvers need to exhibit extreme levels of parallelism, and minimize data movement. In this talk, we will give an overview on how AMG has been impacted by the various architectures of high-performance computers to date and discuss our current efforts to continue to achieve good performance on emerging computer architectures