Asynchronous time-parallel method based on Laplace transform

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.

Keywords:

• Laplace transform
• Gaver–Stehfest algorithm
• asynchronous iterations
• parallel computing
• quasilinear equation
• option pricing

2010 Mathematics Subject Classifications:

• 65Y05
• 65F10
• 68W10

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Frédéric Magoulès http://orcid.org/0000-0002-1198-7539

Qinmeng Zou http://orcid.org/0000-0001-7752-8100

Additional information

Funding

This work was funded by the project ADOM (Méthodes de décomposition de domaine asynchrones) of the French National Research Agency Agence Nationale de la Recherche (ANR).