Parallelization of multidimensional hyperbolic partial differential equation on détente instantanée contrôlée dehydration process

Abstract

The purpose of this research is to propose some new modified mathematical models to enhance the previous model in simulating, visualizing and predicting the heat and mass transfer in dehydration process using instant controlled pressure drop (DIC) technique. The main contribution of this research is the mathematical models which are formulated from the regression model (Haddad et al., 2007) to multidimensional hyperbolic partial differential equation (HPDE) involving dependent parameters; moisture content, temperature, and pressure, and independent parameters; time and dimension of region. The HPDE model is performed in multidimensional; one, two and three dimensions using finite difference method with central difference formula is used to discretize the mathematical models. The implementation of numerical methods such as Alternating Group Explicit with Brian (AGEB) and Douglas-Rachford (AGED) variances, Red Black Gauss Seidel (RBGS) and Jacobi (JB) method to solve the system of linear equation is another contribution of this research. The sequential algorithm is developed by using Matlab R2011a software. The numerical results are analyzed based on execution time, number of iterations, maximum error, root mean square error, and computational complexity. The grid generation process involved a fine grained large sparse data by minimizing the size of interval, increasing the dimension of the model and level of time steps. Another contribution is the implementation of the parallel algorithm to increase the speedup of computation and to reduce computational complexity problem. The parallelization of the mathematical model is run on Matlab Distributed Computing Server with Linux operating system. The parallel performance evaluation of multidimensional simulation in terms of execution time, speedup, efficiency, effectiveness, temporal performance, granularity, computational complexity and communication cost are analyzed for the performance of parallel algorithm. As a conclusion, the thesis proved that the multidimensional HPDE is able to be parallelized and PAGEB method is the alternative solution for the large sparse simulation. Based on the numerical results and parallel performance evaluations, the parallel algorithm is able to reduce the execution time and computational complexity compared to the sequential algorithm.