Performance Evaluation of MPI/OpenMP Algorithm for 3D Time Dependent Problems

We consider the 3D time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, approached in terms of velocity and pressure. In a parallel algorithm, based on a novel direction splitting approach, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. In order to achieve good parallel performance, the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one-dimensional second order elliptic boundary value problems in each spatial direction. The parallel code was developed using MPI and OpenMP and tested on modern computer systems. The performed tests illustrate the parallel efficiency, and the scalability, of the direction-splitting based algorithm.