Topics on Algebraic Multigrid (AMG)

The algebraic multigrid (or AMG) concept was introduced in [BMcRr, BMcR] (see also [B86]), and gained popularity after the paper [RS87] appeared. Since then, much progress has been made and the present chapter reflects a number of major developments in this area.

There is no single AMG method. Loosely speaking, if the coarse hierarchy defined by respective interpolation matrices { Pk } is constructed by the user, the resulting MG method defines a class of AMG. AMG is typically defined as a two-level method, and the construction is used recursively, thus ending up with a multilevel AMG. That is why, for the most part of the presentation, we omit the level subscript k in the present chapter.


Element Matrice Sparsity Pattern Principal Submatrix Coarse Space Interpolation Matrix 
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© Springer Science+Business Media, LLC 2008

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