# Asynchronous Parareal Time Discretization For Partial Differential Equations

@article{Magouls2018AsynchronousPT, title={Asynchronous Parareal Time Discretization For Partial Differential Equations}, author={Fr{\'e}d{\'e}ric Magoul{\`e}s and Guillaume Gbikpi Benissan}, journal={ArXiv}, year={2018}, volume={abs/2110.10762} }

Asynchronous iterations have been investigated more and more for both scaling and fault-resilience purposes on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper advocates a novel application direction targeting time-decomposed time-parallel approaches. Specifically, an asynchronous iterative model is derived from the Parareal scheme, for which convergence and speedup analysis are then conducted. It…

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## References

SHOWING 1-10 OF 43 REFERENCES

Scheduling of tasks in the parareal algorithm

- Computer ScienceParallel Comput.
- 2011

It is suggested that the parareal algorithm is a promising approach to solving long time evolution problems, particularly when the goal is simulation of longer times using more processors, and exhibits characteristics that make it particularly suitable for execution on heterogeneous computational grids.

Fault Tolerance in the Parareal Method

- Computer ScienceFTXS@HPDC
- 2016

It is demonstrated how the parareal algorithm may be made resilient towards Silent-Data-Corruption errors by viewing it as a point-iterative method, locally monitoring the residual between consecutive iterations so to discard potentially corrupt iterations.

Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors: basic ideas

- Computer ScienceParallel Comput.
- 1989

The asynchronous fast adaptive composite grid method (AFAC) is developed here as a method that can process refinement levels in parallel while maintaining full multilevel convergence speeds.

Asynchronous Iterations of Parareal Algorithm for Option Pricing Models

- Computer Science
- 2018

This paper presents an original model of asynchronous variant based on the parareal scheme, applied to the European option pricing problem and shows the convergence performance and computational efficiency of such a method.

Time‐decomposed parallel time‐integrators: theory and feasibility studies for fluid, structure, and fluid–structure applications

- Computer Science
- 2003

This methodology parallelizes the time-loop of a time- dependent partial differential equation solver without interfering with its sequential or parallel space-computations for time-dependent problems with a few degrees of freedom such as those arising in robotics and protein folding applications.

Asynchronous optimized Schwarz methods with and without overlap

- Mathematics, Computer ScienceNumerische Mathematik
- 2017

An asynchronous version of the optimized Schwarz method for the solution of differential equations on a parallel computational environment is studied and it is shown to converge when the optimal artificial interface conditions are used.

Some aspects of parallel and distributed iterative algorithms - A survey,

- Computer ScienceAutom.
- 1991

Abstract We consider iterative algorithms of the form x := f ( x ), executed by a parallel or distributed computing system. We first consider synchronous executions of such iterations and study their…

Asynchronous Iterative Methods for Multiprocessors

- Computer ScienceJACM
- 1978

A class of asynchronous iterative methods is presented for solving a system of equations corresponding to a parallel implementation on a multiprocessor system with no synchronization between cooperating processes to show clearly the advantage of purely asynchronous Iterative methods.

JACK2: An MPI-based communication library with non-blocking synchronization for asynchronous iterations

- Computer ScienceAdv. Eng. Softw.
- 2018

This paper addresses the design of a communication library which particularly targets distributed iterative computing, including randomly executed asynchronous iterations, and provides an efficient exact approach to compute global convergence residual norms, by means of non-blocking synchronization.

Analysis of the Parareal Time-Parallel Time-Integration Method

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2007

New convergence results that show superlinear convergence of the parareal algorithm when used on bounded time intervals, and linear convergence for unbounded intervals are shown.