Parallel solvers for fractional power diffusion problems. (20th June 2017)

• Record Type: Journal Article
• Authors: Čiegis, Raimondas; Starikovičius, Vadimas; Margenov, Svetozar; Kriauzienė, Rima
• Other Names: Carretero Jesus guestEditor.; Garcia‐Blas Javier guestEditor.; Nakano Koji guestEditor.; Mueller Peter guestEditor.; Grosu Daniel guestEditor.; Zheng Sheng guestEditor.; Xu Li guestEditor.; Xu Zheng guestEditor.; Yen Neil guestEditor.; Sugumaran Vijayan guestEditor.
• Is Part Of: Concurrency and computation. Volume 29:Number 24(2017)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-06-20
• Subjects: fractional diffusion -- fractional Laplacian -- multigrid -- parallel efficiency and scalability -- parallel numerical algorithms; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.4216
• Languages: English
• ISSNs: 1532-0626

Abstract

Summary: Mathematical models with fractional‐order differential operators are computationally expensive due to the non‐local nature of these operators. In this work, we construct and investigate parallel solvers for problems described by fractional powers of elliptic operators, like fractional diffusion. Three state‐of‐the‐art approaches are used to transform the non‐local fractional‐order differential problem into local partial differential equation problems formulated in a space of higher dimension. Numerical schemes and parallel algorithms are developed for all three approaches. The resulting parallel algorithms have very different properties. We investigate the weak and strong scalability of the developed parallel algorithms and compare their parallel performance.