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. Our model 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. Our results show that in certain cases we have a gain as much as approximately 45% in
execution time when our load balancing scheme is applied.