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DD-$`\alpha`$AMG stands for **D**omain **D**ecomposition $`\pmb{\alpha}`$daptive **A**lgebraic **M**ulti**G**rid. Let's explore each term's meaning in the context of multigrid solvers.
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DD-$`\alpha`$AMG stands for **D**omain **D**ecomposition $`\pmb{\alpha}`$daptive **A**lgebraic **M**ulti**G**rid. We start by further elaborating on each term's meaning in the context of multigrid solvers.
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- **DD:** The smoother is a **D**omain **D**ecomposition method, specifically, the Schwarz Alternating Procedure (SAP).
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- **DD:** The smoother is a **D**omain **D**ecomposition 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 **M**ulti**G**rid method is of the **A**lgebraic type. More specifically, coarse grid variables are determined in an ***aggregation based*** manner.
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- **AMG:** The construction of the **M**ulti**G**rid method is of the **A**lgebraic 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 setup phase which, starting from scratch, determines a sequence of increasingly better prolongators and restrictors using the multigrid method built so far. |
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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. |
