Sequential numerical methods for integrating initial value problems (IVPs) can be
prohibitively expensive when high numerical accuracy is required over the entire interval of …

Parareal is a well-studied algorithm for numerically integrating systems of time-dependent
differential equations by parallelizing the temporal domain. Given approximate initial values …

Parareal is a recent algorithm able to parallelize the time dimension in spite of its sequential
nature. It has been applied to several linear and nonlinear problems and, very recently, to a …

In this article, we present the Python framework pySDC for solving collocation problems with
spectral deferred correction (SDC) methods and their time-parallel variant PFASST, the …

This paper explores the application of the parareal algorithm to simulations of ELMs in ITER
plasma. The primary focus of this research is identifying the parameters that lead to optimum …

In silico investigation of skin permeation is an important but also computationally demanding
problem. To resolve all scales involved in full detail will not only require exascale computing …

Revisionist integral deferred correction methods are a family of parallel-in-time methods to
solve systems of initial values problems. The approach is able to bootstrap lower-order time …

Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent
differential equations by parallelizing the temporal domain. Among them, Parareal computes …

Parareal is a recent time parallelization algorithm based on a predictor–corrector
mechanism. Recently, it has been applied for the first time to a fully-developed plasma …

It is shown that numerical modelling of edge plasma physics may be successfully
parallelized in time. The parareal algorithm has been employed for this purpose and the …