Performance analysis of parallel alternating directions algorithm for time dependent problems

Abstract

We consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. In a parallel algorithm, based on a new 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. The scheme used in the algorithm is composed of: pressure prediction, velocity update, penalty step, and pressure correction. 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 tested on modern computer systems. The performed numerical tests illustrate the parallel efficiency, and the scalability, of the direction-splitting based algorithm. © 2012 Springer-Verlag.