Topic: Asynchronous iterations

Matthias Bolten discusses the scalability of multigrid solvers for linear systems arising from discretized partial differential equations. On modern supercomputers, heterogeneous CPUs and GPUs and the widening gap between computation, network, and memory speeds complicate parallelization. Classical multigrid analysis relies on tightly coupled multiplicative components, whereas additive and asynchronous variants relax this coupling. The talk compares approaches to improving high-performance multigrid scalability, including asynchronous execution.

Erik Boman discusses preconditioning for asynchronous linear solvers. Inner products create synchronization requirements in Krylov methods, while preconditioners can also improve iterations such as Richardson's method. The talk focuses on asynchronous incomplete factorizations and introduces ATS-ILU, an iterative incomplete LU method with synchronous and asynchronous versions that performs competitively with ParILU.

Edmond Chow examines how asynchronous updates improve parallel iterative computation. The first part covers asynchronous versions of classical first- and second-order linear iterations, Chebyshev methods, and multigrid, with attention to efficiency and fault tolerance. The second introduces reinforcement learning and asynchronous state-value estimation for finding optimal policies. When the state space is too large to enumerate, these updates focus computational effort on frequently visited regions.