Generalization of parallel performance for multidimensional finite difference method of PDE problem.

Partial differential equation (PDE) has been used widely in the development of the mathematical model to predict, design and perform optimal strategy for process control. The PDE model is performed in multidimensional; one, two and three and it is discretized using finite difference method (FDM) with central difference formula. To solve the system of linear equations, numerical methods such as Alternating Group Explicit with Brian (AGEB) and Douglas-Rachford (AGED) variances, as well as the Jacobi (JB) method, are used. The grid decomposition 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. In order to improve execution time, the implementation of the parallel algorithm on Matlab Distributed Computing Server (MDCS) is significant. Furthermore, the parallel algorithm helps to increase the speedup of computation and to reduce the computational complexity problem. Inappropriate directive selection and unnecessary data distribution can lead to load imbalances, unnecessary communication, or the process going into idle state. Thus, data partitioning for multidimensional problem is critical for optimal performance. Both AGE method has the potential for parallelization because it is based on domain decomposition which is independent between processors. The computational complexity of the AGEB and AGED methods per iteration is found to be greater than that of the JB method. The computational time for JB is supposedly shorter than for AGED and AGEB, but this is contradicted by the fact that the number of iterations for JB is greater than for AGED and AGEB. [ABSTRACT FROM AUTHOR]