A New Parallel Iterative Algorithm for Solving 2D Poisson Equation

作者：Xu, Qiuyan; Wang, Wenqia^*

来源：Numerical Methods for Partial Differential Equations, 2011, 27(4): 829-853.

DOI：10.1002/num.20556

• convergence
• domain decomposition
• iterative algorithm
• parallel computation
• Poisson equation
• the convergence rate
• the optimal relaxation factor

In this article, a finite difference parallel iterative (FDPI) algorithm for solving 2D Poisson equation was presented. Based on the domain decomposition, the domain was divided into four sub-domains and the four iterative schemes were constructed from the classical five-point difference scheme to implement the algorithm differently with the number of iterations of odd or even. Although the iterative schemes are semi-implicit, they can be computed explicitly and in parallel in combining with the boundary conditions. The convergence of the presented algorithm was proved. Particularly, a relaxation factor. was added into the iterative schemes to improve the convergence rate and decrease the number of iterations. Finally, several numerical experiments were presented to examine the efficiency and accuracy of the iterative algorithm. Also, the comparison between the numerical results that were derived from Jacobi, Gauss-Seidel iterative algorithms, Mathematics Stencil (Fen et al., China Sci 35 (2005), 901-909) method, and the presented algorithm with the optimal relaxation factor.opt demonstrated that the presented algorithm has smaller number of iterations, shorter computational time, and faster convergence rate. Furthermore, the presented algorithm is also applicable to 2D variable coefficient elliptic problems.

• 出版日期2011-7
• 单位山东大学