Scalability analysis of different parallel solvers for 3D fractional power diffusion problems. (31st January 2019)

• Record Type: Journal Article
• Authors: Čiegis, Raimondas; Starikovičius, Vadimas; Margenov, Svetozar; Kriauzienė, Rima
• Other Names: Wyrzykowski Roman guestEditor.; Szymanski Boleslaw guestEditor.; Pan Lei guestEditor.; Zhang Jun guestEditor.; Oliver Jonathan guestEditor.
• Is Part Of: Concurrency and computation. Volume 31:Number 19(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-01-31
• Subjects: convergence -- fractional diffusion -- fractional Laplacian -- multigrid -- parallel numerical algorithms -- parallel scalability; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.5163
• Languages: English
• ISSNs: 1532-0626

Abstract

Summary: In this paper, we develop and investigate the parallel numerical algorithms for three different state‐of‐the‐art numerical methods for solving the non‐local problems described by fractional powers of elliptic operators. These methods transform the non‐local problem into some local differential problems of elliptic or parabolic type. A two‐level parallelization approach is applied to construct the efficient parallel algorithms using the domain decomposition and master‐slave methods, to deal with the increase in computational complexity. We show and compare the serial and parallel solution times that are required to achieve similar accuracy of the solution using different algorithms. Results of extensive convergence tests are presented solving a three‐dimensional test problem with known decrease of the solution's convergence rate depending on the fractional power coefficient. We analyze and discuss the non‐trivial question, which parallel algorithm is recommended to achieve certain accuracy for the given fractional power coefficient.