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Mathematical stencil and its application in finite difference approximation to the poisson equation

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Abstract

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

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Authors and Affiliations

  1. Department of Mathematics, Wuhan University, 430072, Wuhan, China

    Feng Hui, Zhang Baolin & Liu Yang

  2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, 100088, Beijing, China

    Zhang Baolin

Authors
  1. Feng Hui
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  2. Zhang Baolin
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  3. Liu Yang
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Correspondence to Feng Hui.

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Feng, H., Zhang, B. & Liu, Y. Mathematical stencil and its application in finite difference approximation to the poisson equation. Sci. China Ser. A-Math. 48, 1421–1429 (2005). https://doi.org/10.1360/04ys0103

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  • DOI: https://doi.org/10.1360/04ys0103

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