This review article serves to summarize the many advances in time-parallel computations
since the excellent review article by Gander,“50 years of Time Parallel Integration”(Gander …

Parallel‐in‐time methods, such as multigrid reduction‐in‐time (MGRIT) and Parareal,
provide an attractive option for increasing concurrency when simulating time‐dependent …

McDonald, Pestana and Wathen (SIAM J. Sci. Comput. 40 (2), pp. A2012-A1033, 2018)
present a method for preconditioning of time-dependent PDEs via approximation by a …

This paper presents a multilevel convergence framework for multigrid-reduction-in-time
(MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori …

Parallel‐in‐time algorithms have been successfully employed for reducing time‐to‐solution
of a variety of partial differential equations, especially for diffusive (parabolic‐type) …

This article presents a two-grid approach for developing a black-box iterative solver for a
large class of real-life problems in continuum mechanics (heat and mass transfer, fluid …

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of
intense development over recent decades, particularly for diffusion-dominated problems. It …

This paper describes a space-time parallel algorithm with space-time adaptive mesh
refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in …

Efficient parallel‐in‐time methods for hyperbolic partial differential equation problems
remain scarce. Here we investigate an approach based on circulant preconditioned …

In this article, we introduce the Python framework PyMGRIT, which implements the multigrid-
reduction-in-time (MGRIT) algorithm for solving (non-) linear systems arising from the …