Title: The performance model for a parallel SOR algorithm using the red-black scheme

Authors: Italo Epicoco; Silvia Mocavero; Giovanni Aloisio

Addresses: Department of Engineering for Innovation, University of Salento, via per monteroni – 73100 Lecce, Italy; Scientific Computing and Operation Division, Euro-Mediterranean Center on Climate Change, via per monteroni – 73100 Lecce, Italy. ' Scientific Computing and Operation Division, Euro-Mediterranean Center on Climate Change, via per monteroni – 73100 Lecce, Italy. ' Department of Engineering for Innovation, University of Salento, via per monteroni – 73100 Lecce, Italy; Scientific Computing and Operation Division, Euro-Mediterranean Center on Climate Change, via per monteroni – 73100 Lecce, Italy

Abstract: The successive over relaxation (SOR) is a variant of the iterative Gauss-Seidel method for solving a linear system of equations Ax = b. The SOR algorithm is used within the Nucleus for European Modelling of the Ocean (NEMO) model for solving the elliptical equation for the barotropic stream function. The NEMO performance analysis shows that the SOR algorithm introduces a significant communication overhead. Its parallel implementation is based on the red-black method and foresees a communication step at each iteration. An enhanced parallel version of the algorithm has been developed by acting on the size of the overlap region to reduce the frequency of communications. The overlap size must be carefully tuned for reducing the communication overhead without increasing the computing time. This work describes an analytical performance model of the SOR algorithm that can be used for establishing the optimal size of the overlap region.

Keywords: SOR algorithm; successive over relaxation; NEMO model; climate models; performance modelling; high performance computing; red-black scheme; elliptical equations; barotropic stream function; climate change; ocean circulation.

DOI: 10.1504/IJHPSA.2012.050989

International Journal of High Performance Systems Architecture, 2012 Vol.4 No.2, pp.101 - 109

Received: 03 Aug 2012
Accepted: 07 Sep 2012

Published online: 02 Sep 2014 *

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