Alternating Asymmetric Iterative Algorithm Based on Domain Decomposition for 3D Poisson Problem

Qiuyan Xu and Zhiyong Liu
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Qiuyan Xu: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
Zhiyong Liu: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China

Mathematics, 2020, vol. 8, issue 2, 1-19

Abstract: Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several sub-domains, and eight asymmetric iterative schemes with the relaxation factor for 3D Poisson equation are constructed. When the numbers of iteration are odd or even, the computational process of the presented iterative algorithm are proposed respectively. In the calculation of the inner interfaces, the group explicit method is used, which makes the algorithm to be performed fast and in parallel, and avoids the difficulty of solving large-scale linear equations. Furthermore, the convergence of the algorithm is analyzed theoretically. Finally, by comparing with the numerical experimental results of Jacobi and Gauss Seidel iterative algorithms, it is shown that the alternating asymmetric iterative algorithm based on domain decomposition has shorter computation time, fewer iteration numbers and good parallelism.

Keywords: poisson equation; domain decomposition; asymmetric iterative schemes; group explicit; parallel computation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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