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 …

This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …

The parareal algorithm is a method to solve time-dependent problems parallel in time: it
approximates parts of the solution later in time simultaneously to parts of the solution earlier …

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 …

We consider the solution of parabolic partial differential equations (PDEs). In standard time-
stepping techniques multigrid can be used as an iterative solver for the elliptic equations …

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 …

The time‐parallel framework for constructing parallel implicit time‐integration algorithms
(PITA) is revisited in the specific context of linear structural dynamics and near‐real‐time …

The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-
order collocation solution to an ODE by performing a series of correction sweeps using a low …

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

Multigrid schemes that solve parabolic distributed optimality systems discretized by finite
differences are investigated. Accuracy properties of finite difference approximation are …