Parallel solution of the discretised and linearised G-heat equation. (2018)

• Record Type: Journal Article
• Authors: Spiteri, Pierre; Ouaoua, Amar; Chau, Ming; Boutabia, HacÁ¨ne
• Is Part Of: International journal of high performance computing and networking. Volume 11:Number 1(2018)
• Page Start: 66
• Page End: 82
• Publication Date: 2018
• Subjects: G-heat equation -- relaxation methods -- parallel computing -- asynchronous iteration -- financial application; High performance computing -- Periodicals; Computer networks -- Periodicals; High performance computing; Periodicals; 004.05
• Languages: English
• ISSNs: 1740-0562

Abstract

The present study deals with the numerical solution of the G-heat equation. Since the G-heat equation is defined in an unbounded domain, we firstly state that the solution of the G-heat equation defined in a bounded domain converges to the solution of the G-heat equation when the measure of the domain tends to infinity. Moreover, after time discretisation by an implicit time marching scheme, we define a method of linearisation of each stationary problem, which leads to the solution of a large scale algebraic system. A unified approach analysis of the convergence of the sequential and parallel relaxation methods is given. Finally, we present the results of numerical experiments.