%0 Journal Article
%A Tabik, S.
%A Romero, L. F.
%A Garzon, E. M.
%A Ramos, Juan I.
%D 2007
%I Begell House
%N 1
%P 39-46
%R 10.1615/IntJMultCompEng.v5.i1.50
%T Three-dimensional Bursting and Parallel Computing
%U http://dl.begellhouse.com/journals/61fd1b191cf7e96f,62eaf5c935d4bac7,00a8b6131ecb4f17.html
%V 5
%X 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.
%8 2007-07-01