The Numerical Solution of Heat Equation by the Fourth-Order Iterative Alternating Decomposition Explicit Method with MPI
Simon Uzezi Ewedafe1, Rior Hirowati2, Shariffudin3
1Simon Uzezi Ewedafe, BSc. and MSc. Degrees, Industrial-Mathematics and Mathematics Delta Stae University.
2Rior Hirowati, Professor, Institute of Mathematical Sciences, Universiti Malaya, Malaysia.
3Shariffudin, Institute of Mathematical Sciences, Universiti Malaya, Malaysia.
Manuscript received on 27 September 2019 | Revised Manuscript received on 09 November 2019 | Manuscript Published on 22 November 2019 | PP: 4-9 | Volume-8 Issue-6S3 September 2019 | Retrieval Number: F10020986S319/19©BEIESP | DOI: 10.35940/ijeat.F1002.0986S319
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The numerical solution of the heat equation in one space dimension is obtained using the Fourth-Order Iterative Alternating Decomposition Explicit Method (4-IADE) on a parallel platform with Message Passing Interface (MPI). Here, a higher fourth-order Crank-Nicolson type scheme is used in the approximation which gives rise to a Penta diagonal matrix in the solution of the system at each time level. The method employs a splitting strategy which is applied alternately at each half time step. The method is shown to be computationally stable and appropriate parameters chosen to accelerate convergence. The accuracy of the method is comparable to that of existing well known methods. Results obtained by this method for several different problems were compared with the exact solution and agreed closely with those obtained by other finite-difference methods with correlation between speedup and efficiency.
Keywords: Efficiency, Heat Equation, MPI, Speedup, 4-IADE.
Scope of the Article: Heat Transfer