Modeling of Distributions of Polymer Properties Using Parallel Computing in Matlab. II: Bivariate Distributions

PINTOS, ESTEBAN; ASTEASUAIN, MARIANO

Cancún, México

Congreso; XV Simposio Latinoamericano de Polímeros - XIII Congreso Iberoamericano de Polímeros (SLAP 2016); 2016

Sociedad Polimérica de México

The polymer chain microstructure (molecular weight distribution, copolymer composition distribution, branching distribution, etc.) has a strong influence on the processing and end-use properties of the material. In many cases, a proper characterization of polymer samples requires simultaneous information on distributions of several properties. However, the development of mathematical models able to predict multivariate distributions leads to highly complex problems for which seldom solution approaches have been developed. In particular, large systems of differential-algebraic equations (DAE) are usually encountered. Therefore, model efficiency in terms of CPU time and memory requirements becomes a very significant issue.In previous works we developed a technique for modeling bivariate distributions based on the 2D probability generating function (2D pgf) transformation. A key step of this technique is the inversion of the 2D pgf transform. Three inversion methods are available: the 2D IFG, the 2D Papoulis and the 2D Pap-IFG methods. The structure of the DAE of the 2D pgf models make them suitable for parallel computation. In this work, the performance of the 2D pgf technique with each of these methods using parallel computation is compared. Models were implemented in MATLAB® R2014a with MATLAB Parallel Computing ToolboxTM for parallelization of the model execution. Models were solved in a standard desktop computer equipped with an Intel® Core? i7-2600 processor (four workers) running at 3.4 GHz and 12 GB of RAM memory.