Solution of univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov methods. (March 2021)

• Record Type: Journal Article
• Authors: Garcia, T.; Spiteri, P.; Ziane-Khodja, L.; Couturier, R.
• Is Part Of: Advances in engineering software. Volume 153(2021)
• Publication Date: 2021-03
• Subjects: multisplitting methods -- synchronous parallel algorithms -- asynchronous parallel algorithms -- sparse non-linear systems -- Krylov methods -- pseudo - linear problem -- boundary value problem; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2020.102929
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: Solution of univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov methods. Behavior of the numerical parallel iterative algorithms is analyzed in each case. Two distinct applications are presented and solved by a mixed Newton - multisplitting method and by a relaxation method with projection. Implementation of algorithms is described. Numerical synchronous and asynchronous parallel simulation achieved on a grid are presented and compared. Abstract: The paper improves a preliminary experimental study on a cluster by adding both theoretical results and experimental tests on a grid platform. These algorithms solve univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov's methods. This paper also analyses these algorithms using contraction techniques. Two distinct applications, with discretized boundary value problems, are analyzed and simulated. First, a univalued convection-diffusion problem perturbed by an increasing diagonal operator is presented. Then, follows the description of a diffusion problem whose solution is constrained. This situation classically leads to the solution of a multivalued pseudo-linear problem in which the linear part is perturbed by an increasing diagonal multivalued operator. Parallel asynchronous and synchronous algorithms were implemented and tested on a grid platform composed of physically adjacent or geographically distant machines. In addition, the simulation results are detailed and show that the elapsed times obtained for the asynchronous algorithms are significantly less than those obtained for the synchronous algorithms.