The D'Yakonov fully explicit variant of the iterative decomposition method

Armadillo generation distributed system with geranium Cadcam cluster for solving 2D telegraphic problem

“…We also note the various constant improvements in speedup and efficiency performance analysis carried out in [44] using the overlapping domain decomposition method, while Sun and Gustafson proposed a generalized speedup formula as the ratio of the parallel to sequential speed. In our experiment we were able to show this conformity to be true of the formula to our problems using the various parallel strategies application on the abovementioned problem in contrast to the analytical approach in [1,12,13,25,38]. As in relation to the performance strategies implementation, a thorough study of speedup models together with their advantages is implemented in [8,10,30,39] and shows the same conformity to our implementation.…”

“…Several approaches to dealing with solving the telegraphic equation problems numerically for determining stability had been carried out by using different approaches in [12,13,21]. Our approach as compared with what was done in [1,12,13,38] was that we applied the difference scheme of alternating methods to schedule the n-independent tridiagonal systems on a distributed system of two clusters using MPI and PVM to determine speedup and efficiency in contrast to their own analytical approach to show that convergence is true using our parallel strategies. In [9,11] are shown speedup and efficiency applications but in comparison, our results generated using Armadillo cluster and geranium Cadcam cluster on the telegraphic problem give better conformity to linearity for speedup and closeness to unity for efficiency.…”

“…We call Equation (38) domain decomposition (DD) efficiency, which includes the increase of CPU time induced by grid overlap at interfaces and the CPU time variation generated by DD techniques. The second term N 0 /N 1 in the right-hand side of Equation (37) represents the increase in the number of iterations required by the parallel method to achieve a specified accuracy compared with the serial method.…”

Parallelization of 2-D IADE-DY Scheme on Geranium Cadcam Cluster for Heat Equation

“…This work is distinct while promoting flexibility, and applies standard parallel concepts. Several approaches to solving heat equation have been carried out in [6,25,26,27] and [13,29,32]. We have applied the 2-D IADE-DY scheme by simulation to schedule the n tri-diagonal system of equations with the above method used to show improvement on speedup, effectiveness, and efficiency.…”

Parallel Implementation of 2-D Telegraphic Equation on MPI/PVM Cluster

“…The ADI method in [27] has been used to solve heat equation in 2-D. Several approaches to solve the telegraphic equation problems numerically have been carried out in [1,12,13,23,26,31]. Our approach compared to [1,13,26,33] is the application of the difference schemes on a distributed system of MPI/PVM cluster to evaluating the effects of the algorithms on different mesh sizes with the use of the domain decomposition parallel implementation. We determine the various speedups and efficiency through domain decomposition method.…”