2019/09/03 by Frédéric Magoulès, Frederic Magoules, Magoules, Frederic +2
Computer Science · Mathematics · #Acceleration #Algorithm #Applied mathematics #Asynchronous communication #Computer science #Convergence (economics) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Fourier transform #Fractional Fourier transform #Inverse Laplace transform #Laplace transform #Laplace transform applied to differential equations #Laplace–Stieltjes transform #Mathematical analysis #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Parallel #Polynomial and algebraic computation #Synchronization (alternating current) #Telecommunications #Two-sided Laplace transform #and Cluster Computing (cs.DC) #cs.DC #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1909.01473
arxiv created 2019/09/03 · openalex publication_date 2019/09/03 · arxiv updated 2019/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.