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 …

We consider optimal-scaling multigrid solvers for the linear systems that arise from the
discretization of problems with evolutionary behavior. Typically, solution algorithms for …

We present and analyze a new space-time parallel multigrid method for parabolic equations.
The method is based on arbitrarily high order discontinuous Galerkin discretizations in time …

The need for parallelism in the time dimension is being driven by changes in computer
architectures, where performance increases are now provided through greater concurrency …

We consider the comparison of multigrid methods for parabolic partial differential equations
that allow space–time concurrency. With current trends in computer architectures leading …

We discuss how “parallel-in-space & simultaneous-in-time” Newton-multigrid approaches
can be designed which improve the scaling behavior of the spatial parallelism by reducing …

Multigrid and related multilevel methods are the approaches of choice for solving linear
systems that result from discretization of a wide class of PDEs. A large gap, however, exists …

This paper investigates the efficiency, robustness, and scalability of approximate ideal
restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space …

For many applications, local time stepping offers an interesting and worthwhile alternative to
the by now well established global time step control. In fact, local time stepping can allow for …

In this paper, we present a multilevel space-time additive Schwarz method for solving linear
system of equations arising from the discretization of parabolic equations. With this method …