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Scalability analysis of different parallel solvers for 3D fractional power diffusion problems
Author(s) -
Čiegis Raimondas,
Starikovičius Vadimas,
Margenov Svetozar,
Kriauzienė Rima
Publication year - 2019
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.5163
Subject(s) - convergence (economics) , scalability , domain decomposition methods , computer science , rate of convergence , domain (mathematical analysis) , parallel algorithm , algorithm , mathematical optimization , mathematics , key (lock) , finite element method , mathematical analysis , physics , computer security , database , economics , thermodynamics , economic growth
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.