Ml 3.1 smoothed aggregation user’s guide

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n £ n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial di®erential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package or to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative packages [19]. However, other solvers can be used by supplying a few functions. This document describes one speci¯c algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible °uid dy-namics problems). Other methods exist within ML but are not described in this document. Example