The Automatic Multigrid Method
In this chapter, we describe the Automatic Multigrid (AutoMUG) iterative method for the solution of linear systems that use a 5-point stencil as in (3.8) on a uniform grid as in (3.6). The special advantage of this method is that it uses inexpensive 5-point stencils also on the coarse grids, which allows the use of the red-black point-GS relaxation in the entire V-cycle. AutoMUG has good convergence rates for problems with variable and even discontinuous coefficients, even when the discontinuity lines do not align with the coarse grid.
KeywordsCoarse Grid Uniform Grid Multigrid Method Spatial Direction Discontinuity Line
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