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

Abstract

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. It 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 heavier work load. With our balancing scheme, a gain of approximately 45% in execution time is achieved, in certain cases.