Tuning Up TVD HOPMOC Method on Intel MIC Xeon Phi Architectures with Intel Parallel Studio Tools

Abstract

This paper focuses on the parallelization of TVD Method scheme for numerical time integration of evolutionary differential equations. The Hopmoc method for numerical integration of differential equations was developed aiming at benefiting from both the concept of integration along characteristic lines as well as from the spatially decomposed Hopscotch method. The set of grid points is initially decomposed into two subsets during the implementation of the integration step. Then, two updates are performed, one explicit and one implicit, on each variable in the course of the iterative process. Each update requires an integration semi step. This is carried out along characteristic lines in a Semi-Lagrangian scheme based on the Modified Method of Characteristics. This work analises two strategies to implement the parallel version of TVD Hopmoc based on the analysis performed by Intel Tools such Parallel and Threading Advisor. A naive solution is substituted by a chunk loop strategy in order to avoid fine-grain tasks inside main loops.