Parallel solvers for fractional power diffusion problems

Abstract

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.