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Black Box Multigrid with coarsening by a factor of three
Author(s) -
Moulton J. D.
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.705
Subject(s) - multigrid method , interpolation (computer graphics) , mathematics , grid , discretization , solver , robustness (evolution) , algorithm , mathematical analysis , geometry , mathematical optimization , partial differential equation , computer science , animation , biochemistry , chemistry , computer graphics (images) , gene
Black Box Multigrid (BoxMG) is a robust variational multigrid solver for diffusion equations on logically structured grids. BoxMG standardly uses coarsening by a factor of two. It handles cell‐centered discretizations on logically rectangular grids by treating the cell‐centers as the unknowns to be coarsened. Such a strategy does not preserve the cell structure. That is, coarse‐grid cells are not the union of fine‐grid cells. In some applications, such as local grid refinement, it is desirable that the cell structure be preserved. In this paper, we develop a method that employs coarsening by a factor of three. It is a natural generalization of standard BoxMG, using operator‐induced interpolation (which approximately preserves the continuity of the normal flux), restriction as the transpose of interpolation, and Galerkin coarsening. In addition, we introduce a new colored block Gauss–Seidel scheme that is motivated by the form of the interpolation operator, dubbed ‘pattern’ relaxation. We present numerical results that demonstrate robustness of this method with respect to discontinuous diffusion coefficients, boundary conditions, and grid dimension. Published in 2010 by John Wiley & Sons, Ltd.