@Article{cmes.2007.020.001,
AUTHOR = {J. M. F.  Trindade, J. C. F.  Pereira},
TITLE = {On the Efficiency of the Parallel-in-Time Finite Volume Calculation of the Unsteady Navier-Stokes Equations},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {20},
YEAR = {2007},
NUMBER = {1},
PAGES = {1--10},
URL = {http://www.techscience.com/CMES/v20n1/25015},
ISSN = {1526-1506},
ABSTRACT = {In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative method. A simple performance model is proposed to estimate the efficiency of the parallel calculations as a function of the most relevant parameters that contribute to the computing time required to perform a parallel-in-time calculation. Among them, we have analyzed the influence of the number of processors, the number of iterations in the parallel-in-time algorithm and the influence of the coarse to fine time-grid step size ratio. The good agreement between the obtained parallel efficiency and the values estimated by the proposed performance model allows to conclude that parallel-in-time efficiency is quantitatively different from the parallel efficiency of the space domain decomposition, regarding the number of processors available for a fixed problem dimension. A significant speed-up is possible when the temporal scale of the problem is large and enough processors are available.},
DOI = {10.3970/cmes.2007.020.001}
}