Hybrid MPI/OpenMP/OpenACC Implementations for the Solution of Convection-Diffusion Equations with the HOPMOC Method

The need for fast solution of large scientific and industrial problems has long motivated the quest for improvements both in software as well as in hardware, since the inception of computing tools. In this context, vectorization, parallelization of tasks have been important strategies for the improvement of hardware efficiency during the last decades. Operator splitting techniques for the numerical solution of partial differential equations are also an attempt towards the same goal, on the software side. This work presents two parallel implementations of the Hopmoc method to solve parabolic equations with convective dominance on a cluster with multiple multicore nodes or GPUs. The Hopmoc method is based both on the modified method of characteristics and the Hopscotch method. It is implemented through an explicit-implicit operator splitting technique. Hopmoc has been studied on distributed memory machines under MPI. In this work Hopmoc is implemented on clusters of multiple cores or GPUs in one single programming model. Previous results had shown that Hopmoc is a scalable parallel procedure with respect to distributed memory machines. New numerical results of the technique presented herein show performance improvements of up to 300 times when compared with the sequential version.