10.1007/s40096-023-00522-3

Sixth-order compact difference scheme and multigrid method for solving the Poisson equation

  • Xiaogang Li1,
  • Yongbin Ge*2,
  1. School of Civil and Hydraulic Engineering, Ningxia University, Yinchuan, 750021, CN
  2. School of Science, Dalian Minzu University, Dalian, 116600, CN

Published 2024-01-29

How to Cite

Li, X., & Ge, Y. (2024). Sixth-order compact difference scheme and multigrid method for solving the Poisson equation. Mathematical Sciences, 18(4 (December 2024). https://doi.org/10.1007/s40096-023-00522-3
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Abstract

Abstract This paper proposes a sixth-order compact difference scheme of Poisson equation based on the sixth-order compact difference operator of the second derivative. The biggest difference between the proposed scheme and other sixth-order scheme is that the right hand contains second partial derivation of source term; this term makes the proposed scheme more accurate than other sixth-order schemes. The proposed scheme is combined with the multigrid method to solve two- and three-dimensional Poisson equations with Dirichlet boundary conditions. The result is compared with other sixth-order schemes in several numerical experiments. The numerical results show that the proposed scheme achieves the desired accuracy and has smaller errors than other schemes of the same order. Further, the multigrid method is higher efficient than traditional iterative method in accelerating the convergence.

Keywords

  • Poisson equation,
  • Compact difference scheme,
  • Multigrid,
  • High accuracy

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