The iterative method for the Poisson equation based on domain decomposition

Authors

  • Jie Sun
  • Rui Zhang

DOI:

https://doi.org/10.54097/vd9zpw84

Keywords:

Poisson equation; iteration method; domain decomposition.

Abstract

This paper is concerned with 2D Poisson equation. A region-segmentation-based iteration algorithm for the numerical solution of the Poisson equation is presented. The problem can be solved in parallel, where numerical results test our method is effective.

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References

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Jie Wang, Weijun Zhong and Jun Zhang, “A general meshsize fourth-order compact difference diecretization scheme for 3D Poisson equation,” Applied Mathematics and Computation, vol. 183, pp. 804-812, 2006.

Yin Wang, Jun Zhang, “Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation,” Journal of Computational Physics, vol. 228, pp. 137-146, 2009.

Jumat Sulaiman, Mohammad Khatim Hasan, “Mohamed Othman,Samsul Ariffin Abdul Karim, MEGSOR iterative method for the triangle element solution of 2D Poisson equations,” Procedia Computer Science, vol. 1, pp. 377-385, 2010.

Yongbin Ge, “Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D poisson equation,” Journal of Computational Physics, vol. 229, pp. 6381-6391, 2010.

S Liu, J Li, “Solving 2D Poisson-type equations using meshless SPH method,” Results in Physics, vol. 13, 2019.

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Published

15-12-2023

How to Cite

Sun, J., & Zhang, R. (2023). The iterative method for the Poisson equation based on domain decomposition. Highlights in Science, Engineering and Technology, 72, 1231-1237. https://doi.org/10.54097/vd9zpw84