A Parallel-in-Time-and-Space HPC Framework for a Class of Fractional Evolution Equations

摘要

We develop a high performance computing (HPC) framework for efficient simulations of a class of fractional-order partial differential equations (FPDE), using high-order in time and space parallel algorithms. HPC systems provide a large number of processing cores with limitations on the amount of memory available per core. Such limitations impose severe constraints for resolving fine spatial structures that require large degrees of freedom (DoF). In this article, using several message passing interface (MPI) communicators, we develop and demonstrate an efficient hybrid framework that combines parallel in time and space tasks that facilitate careful balance between parallel performance within the memory constraint to simulate the FPDE model. We demonstrate the approach for a 3D fractional PDE using several million spatial DoF.