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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:** The smoother is a **D**omain **D**ecomposition method, specifically, the Schwarz Alternating Procedure (SAP).
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**DD** The smoother is a \textbf{D}omain \textbf{D}ecomposition method, specifically, the Schwarz Alternating Procedure (SAP).
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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** This construction is of the \textbf{A}lgebraic type, in a \textbf{M}ulti\textbf{G}rid context. More specifically, coarse grid variables are determined in an \textit{aggregation based maner}.
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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 setup phase which, starting from scratch, determines a sequence of increasingly better prolongators and restrictors using the multigrid method built so far. |
