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 …

In writing this book, I set out to create an accessible introduction to fast multipole methods
(FMMs) and techniques based on integral equation formulations. These are powerful tools …

High-performance computing trends towards many-core systems are expected to continue
over the next decade. As a result, parallel-in-time methods, mathematical formulations which …

In this paper we propose a novel way to integrate time-evolving partial differential equations
that contain nonlinear advection and stiff linear operators, combining exponential integration …

This paper presents, discusses and analyses a massively parallel-in-time solver for linear
oscillatory partial differential equations, which is a key numerical component for evolving …

A numerical method for variable coefficient elliptic PDEs on three dimensional domains is
described. The method is designed for problems with smooth solutions, and is based on a …

Rational exponential integrators (REXI) are a class of numerical methods that are well suited
for the time integration of linear partial differential equations with imaginary eigenvalues …

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine
propagator within a parallel iteration. It allows for large-scale parallelism that leads to …

A framework for exponential time discretization of the multilayer rotating shallow water
equations is developed in combination with a mimetic discretization in space. The method is …

A numerical method for variable coefficient elliptic problems on two dimensional domains is
described. The method is based on high-order spectral approximations and is designed for …