Load Balancing for the Numerical Solution of the Navier-Stokes Equations

In this paper we simulate the performance of a load balancing scheme. In particular, we study the application of the Extrapolated Diffusion(EDF) method for the efficient parallelization of a simple ’atmospheric’ model, which involves the numerical solution of the steady state Navier-Stokes(NS) equations in the horizontal plane and random load values, corresponding to the ”physics” computations, in the vertical plane. For the numerical solution of NS equations we use the local Modified Successive Overrelaxation (LMSOR) method with local parameters thus avoiding the additional cost caused by the global communication of the involved parameter ω in the classical SOR method. We have implemented an efficient domain decomposition technique by using a larger number of processors in the areas of the domain with havier work load. Our results show that in certain cases we have a gain up to approximately 50% in execution time when our load balancing scheme is applied.