DD-
\alpha
AMG stands for Domain Decomposition \pmb{\alpha}
daptive Algebraic MultiGrid. We start by elaborating on the meaning of this acronym in the context of multigrid solvers.
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DD: The smoother is a Domain Decomposition method, specifically, the Schwarz Alternating Procedure (SAP). While nowadays we also include GMRES smoothing, using SAP was one of the main contributions of this software to the multigrid landscape in lattice QCD.
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AMG: The construction of the MultiGrid method is of the Algebraic type. More specifically, coarse grid variables are determined in an aggregation based manner, meaing that coarser lattice points are constructed by merging a block of lattice point into one single lattice point.
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\pmb{\alpha}: Stands for adaptive, i.e., there is a Bootstrap setup phase which, starting from scratch, determines a sequence of increasingly better prolongation and restriction operators using the multigrid method built so far.