Asynchronous Time-Parallel Method based on Laplace Transform

TL;DR

This paper introduces an asynchronous Laplace transform method for quasilinear problems that reduces synchronization delays in parallel computations, leading to improved efficiency and convergence.

Contribution

The paper presents a novel asynchronous Laplace transform approach based on the Gaver-Stehfest algorithm, enhancing parallel efficiency for time-dependent problems.

Findings

Demonstrates convergence of the proposed method

Shows improved parallel efficiency over classical algorithms

Reveals interesting properties through experiments

Abstract

Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor, which leads to a lot of wasted time. In this paper, we propose an original asynchronous Laplace transform method formalized for quasilinear problems based on the well-known Gaver-Stehfest algorithm. Parallel experiments show the convergence of our new method, as well as several interesting properties compared with the classical algorithms.