Domain Decomposition Method for a Nonlocal Coupled System in the Stationary Case

Mohamed Ali Ipopa; Brice Landry Doumbe Bangola; Armel Andami Ovono

doi:https://doi.org/10.14445/22315373/IJMTT-V68I11P503

International Journal of Mathematics Trends and Technology

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Volume 68 | Issue 11 | Year 2022 | Article Id. IJMTT-V68I11P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I11P503

Domain Decomposition Method for a Nonlocal Coupled System in the Stationary Case

Mohamed Ali Ipopa, Brice Landry Doumbe Bangola, Armel Andami Ovono

Received	Revised	Accepted	Published
01 Oct 2022	05 Nov 2022	17 Nov 2022	30 Nov 2022

Abstract

In this paper, we propose and study a domain decomposition method for a system of coupled equations with a nonlocal term in the stationary case. This algorithm combines an alternating direction scheme and a domain decomposition. The underlying idea is that with a good domain decomposition, we can better describe for each point the interaction neighbourhood. Moreover, the second step of this method is a good preconditioner of the first step. Indeed, the matrices of the first step are poorly dimensioned because of the nonlocal term. Finally, although combining the alternating direction scheme and the domain decomposition, our algorithm has a good degree of parallelism.

Keywords

Domain decomposition method, a coupled system equation with a nonlocal term, alternating direction scheme, preconditionner, a good degree of parallelism.

References

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Citation :

Mohamed Ali Ipopa, Brice Landry Doumbe Bangola, Armel Andami Ovono, "Domain Decomposition Method for a Nonlocal Coupled System in the Stationary Case," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 11, pp. 16-31, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I11P503