## A PCG Implementation of an Elliptic Kernel in an Ocean Global Circulation Model Based on GPU Libraries

University of Naples "Federico II" – Dept. of Mathematics and Applications

arXiv:1210.1878 [math.NA] (5 Oct 2012)

@article{2012arXiv1210.1878C,

author={Cuomo}, S. and {De Michele}, P. and {Farina}, R. and {Chinnici}, M.},

title={"{A PCG Implementation of an Elliptic Kernel in an Ocean Global Circulation Model Based on GPU Libraries}"},

journal={ArXiv e-prints},

archivePrefix={"arXiv"},

eprint={1210.1878},

primaryClass={"math.NA"},

keywords={Mathematics – Numerical Analysis, 65Y5, 65Y10, 65F08, 65F35, 37N10},

year={2012},

month={oct},

adsurl={http://adsabs.harvard.edu/abs/2012arXiv1210.1878C},

adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

In this paper an inverse preconditioner for the numerical solution of an elliptic Laplace prob- lem of a global circulation ocean model is presented. The inverse preconditiong technique is adopted in order to efficiently compute the numerical solution of the elliptic kernel by using the Conjugate Gradient (CG) method. We show how the performance and the rate of convergence of the solver are linked to the discretized grid resolution and to the Laplace coefficients of the oceanic model. Finally, we describe an easy-to-implement version of the solver on the Graphical Processing Units (GPUs) by means of scientific computing libraries and we discuss its performance.

October 9, 2012 by hgpu