Modelos de paralelização de aplicações científicas estruturadas em árvores: geração de estimativas iniciais utilizando algoritmo de subdivisão

Abstract

Parallel computing has been widely used in various fields of knowledge to solve highly complex problems, which typically require high processing time when you solved sequentially. The iterative solution of systems of nonlinear equations is considered one of these problems for a large number of applications, particularly when the system has many dimensions, which justifies their parallelization. The development of models of parallelization for the iterative solution of systems of nonlinear equations based on n-ary trees is the focus of this study, this research is linked to the problem of generation of initial estimates used in computer simulation of reactive distillation columns. We developed four models of parallelization, one after another, with the following model created from improvements in the previous model. The implementation of the parallel model is written in the C programming language, using the MPI library from an enhanced version of the algorithm, which is optimized memory usage, by a more e cient method of programming logic. In experiments conducted in a cluster, we used data from actual cases known in literature and the results prove the correctness of the models implemented. All models have provided advantages over the original application in diferent situations analyzed here, but the results were more significant for the models 03 and 04, when run on the real case of largest size, reaching values close to linear speedup, with peaks of order of 3.94, 7.74 and 13.77 for 4, 8 and 16 nodes, respectively.