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.
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© 2008 Springer Science+Business Media, LLC
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(2008). The Automatic Multigrid Method. In: Shapira, Y. (eds) Matrix-Based Multigrid. Numerical Methods and Algorithms, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-49765-5_7
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DOI: https://doi.org/10.1007/978-0-387-49765-5_7
Publisher Name: Springer, Boston, MA
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