"Load balancing using Hilbert spacefilling curves for parallel shallow water simulations"
Chaplygin A.V., Diansky N.A., and Gusev A.V. 
This paper presents a method of load balancing using Hilbert spacefilling curves applied to a parallel algorithm for solving shallow water equations. We consider the system of shallow water equations in the form presented in the ocean general circulation sigmamodel INMOM (Institute of Numerical Mathematics Ocean Model). This system of equations is one of the basic blocks of the model. Due to land points in the computational grid, the load balancing is an especially urgent task. The method of load balancing using Hilbert spacefilling curves is chosen as one of such methods. The paper demonstrates the greater efficiency of this method in comparison with the uniform partitioning without load balancing. It is shown that this method is a good alternative to the METIS standard library. Moreover, the optimality of the implemented partition for the shallow water equations exactly corresponds to the optimality for the INMOM threedimensional sigmamodel due to the same number of vertical levels in the entire computational domain. Keywords: shallow water equations, domain decomposition method, parallel computing, load balancing, Hilbert spacefilling curves.

