A Distributed Memory Parallel Fourth-Order IADEMF Algorithm

The fourth-order finite difference Iterative Alternating Decomposition Explicit Method of Mitchell and Fairweather (IADEMF4) sequential algorithm has demonstrated its ability to perform with high accuracy and efficiency for the solution of a one-dimensional heat equation with Dirichlet boundary conditions. This paper develops the parallelization of the IADEMF4, by applying the Red-Black (RB) ordering technique. The proposed IADEMF4-RB is implemented on multiprocessor distributed memory architecture based on Parallel Virtual Machine (PVM) environment with Linux operating system. Numerical results show that the IADEMF4-RB accelerates the convergence rate and largely improves the serial time of the IADEMF4. In terms of parallel performance evaluations, the IADEMF4-RB significantly outperforms its counterpart of the second-order (IADEMF2-RB), as well as the benchmarked fourth-order classical iterative RB methods, namely, the Gauss-Seidel (GS4-RB) and the Successive Over-relaxation (SOR4-RB) methods.

@article{Mansor2019,
  title     = {A Distributed Memory Parallel Fourth-Order IADEMF Algorithm},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {10},
  number    = {9},
  year      = {2019},
  publisher = {The Science and Information Organization},
  author    = {Noreliza Abu Mansor and Norma Alias and Kamal Zulkifle and Mohammad Khatim Hasan},
  doi       = {10.14569/IJACSA.2019.0100979},
  url       = {https://doi.org/10.14569/IJACSA.2019.0100979}
}