  In this paper, we propose a hybrid parallel programming approach for a
numerical solution of a two-dimensional acoustic wave equation using an
implicit difference scheme for a single computer. The calculations are carried
out in an implicit finite difference scheme. First, we transform the
differential equation into an implicit finite-difference equation and then
using the ADI method, we split the equation into two sub-equations. Using the
cyclic reduction algorithm, we calculate an approximate solution. Finally, we
change this algorithm to parallelize on GPU, GPU+OpenMP, and Hybrid
(GPU+OpenMP+MPI) computing platforms.
  The special focus is on improving the performance of the parallel algorithms
to calculate the acceleration based on the execution time. We show that the
code that runs on the hybrid approach gives the expected results by comparing
our results to those obtained by running the same simulation on a classical
processor core, CUDA, and CUDA+OpenMP implementations.

Computational Physics;Numerical Analysis;Analysis of PDEs;Numerical Analysis