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A Smoothing Process of Multicolor Relaxation for Solving Partial Differential Equation by Multigrid Method

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  • Xingwen Zhu
  • Lixiang Zhang

Abstract

This paper is concerned with a novel methodology of smoothing analysis process of multicolor point relaxation by multigrid method for solving elliptically partial differential equations (PDEs). The objective was firstly focused on the two-color relaxation technique on the local Fourier analysis (LFA) and then generalized to the multicolor problem. As a key starting point of the problems under consideration, the mathematical constitutions among Fourier modes with various frequencies were constructed as a base to expand two-color to multicolor smoothing analyses. Two different invariant subspaces based on the 2 h -harmonics for the two-color relaxation with two and four Fourier modes were constructed and successfully used in smoothing analysis process of Poisson’s equation for the two-color point Jacobi relaxation. Finally, the two-color smoothing analysis was generalized to the multicolor smoothing analysis problems by multigrid method based on the invariant subspaces constructed.

Suggested Citation

  • Xingwen Zhu & Lixiang Zhang, 2014. "A Smoothing Process of Multicolor Relaxation for Solving Partial Differential Equation by Multigrid Method," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, September.
    • Handle: RePEc:hin:jnlmpe:490156
    DOI: 10.1155/2014/490156
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