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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v5.i1.50
pages 39-46

Three-dimensional Bursting and Parallel Computing

S. Tabik
Depto. de Arquitectura de Computadores y Electrónica, Universidad de Almería, 04120 Almería, Spain
L. F. Romero
I-320-D, E. T. S. Ingenieros Industriales, Universidad de Málaga, 29013 Málaga, Spain
E. M. Garzon
Depto. de Arquitectura de Computadores y Electrónica, Universidad de Almería, 04120 Almería, Spain
Juan I. Ramos
Escuela de Ingenierias Industriales, Universidad de Malaga, Dr. Ortiz Ramos, s/n 29071 Malaga, Spain

ABSTRACT

This work presents a mathematical model and its parallel implementation via two parallel paradigms for the simulation of three-dimensional bursting phenomena. The mathematical model consists of four nonlinearly coupled partial differential equations and includes fast and slow subsystems. The differential equations have been discretized by means of a linearly implicit finite difference method in equally spaced grids. The resulting system of equations at each time level has been solved by means of an optimized preconditioned conjugate gradient method. The proposed mathematical model has been implemented via (i) a message passing paradigm based on the standard MPI and (ii) a shared address space paradigm based on SPMD OpenMP. The two implementations have been evaluated on three current parallel architectures, namely, a cluster of dual Xeon, a SGI Altix 3700 Bx2 system based on Itanium, and a Sun Fire E15K. It is shown that for the conditions reported here, the nonlinear dynamics of the three-dimensional bursting phenomena exhibits four different regimes, charachterized by asynchronous, synchronous, and then asynchronous oscillations before a quiescent state is reached. In addition, the fast system reaches steady state in much less time than the slow variables. It is also shown that both parallel pradigms lead to similar scalability on all considered platforms.


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