Multilevel Parallelization: Grid Methods for Solving Direct and Inverse Problems

In this paper we present grid methods which we have developed for solving direct and inverse problems, and their realization with different levels of optimization. We have focused on solving systems of hyperbolic equations using finite difference and finite volume numerical methods on multicore architectures. Several levels of parallelism have been applied: geometric decomposition of the calculative domain, workload distribution over threads within OpenMP directives, and vectorization. The run-time efficiency of these methods has been investigated. These developments have been tested using the astrophysics code AstroPhi on a hybrid cluster Polytechnic RSC PetaStream (consisting of Intel Xeon Phi accelerators) and a geophysics (seismic wave) code on an Intel Core i7-3930K multicore processor. We present the results of the calculations and study MPI run-time energy efficiency