An adaptive parareal algorithm

The parareal in time algorithm

In this paper we present the current status of a method, first introduced in 2001 authored by J.-L. Lions, Y. Maday and G. Turinici that allows for parallization in time for the simulation of systems of Ordinary Differential Equations or time dependent partial differential equations. Following the same strategy as the one that is used in domain decomposition methods for solving elliptic problem...

Stability of the Parareal Algorithm

This paper represents one of the contributions at a minisymposium on the Parareal algorithm at this domain decomposition conference. The minisymposium was organized by Professor Yvon Maday, who is also one of the originators of the Parareal algorithm. The main objective is to be able to integrate a set of differential equations using domain decomposition techniques in time. We refer to the revi...

Adaptive Parareal for systems of ODEs

The parareal scheme (resp. PITA algorithm) proposed in [4] (resp. [1]) considers two levels of grids in time in order to split the domain in time-subdomains. A prediction of the solution is computed on the fine grid in parallel. Then at each end boundaries of time subdomains, the solution makes a jump with the previous initial boundary value (IBV) of the next time-subdomain . A correction of th...

Parareal Algorithm Implementation and Simulation in Julia

We present a full implementation of the parareal algorithm—an integration technique to solve di erential equations in parallel— in the Julia programming language for a fully general, rst-order, initial-value problem. Our implementation accepts both coarse and ne integrators as functional arguments. We use Euler’s method and another Runge-Kutta integration technique as the integrators in our exp...

Nonlinear Convergence Analysis for the Parareal Algorithm