A unified analysis framework for iterative parallel-in-time algorithms

Understand

Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization.

• Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG).
• These methods have been described using different notations, and the convergence estimates that are available are difficult to compare.
• We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions.