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Added remark on polynomial smoothers

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fdurastante
2024-11-18 14:41:59 +01:00
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@@ -147,7 +147,7 @@ default values, is given in Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\
\textbf{Remark 2.} A smoother is usually obtained by combining two objects:
a smoother (\fortinline|'SMOOTHER_TYPE'|) and a local solver (\fortinline|'SUB_SOLVE'|),
as specified in Tables~\ref{tab:p_smoother}-\ref{tab:p_smoother_1}.
as specified in Tables~\ref{tab:p_smoother}-\ref{tab:p_smoother_2}.
For example, the block-Jacobi smoother using
ILU(0) on the blocks is obtained by combining the block-Jacobi smoother
object with the ILU(0) solver object. Similarly,
@@ -176,7 +176,16 @@ Similar considerations apply to the point-Jacobi, Gauss-Seidel and block-Jacobi
coarsest-level solvers, and shortcuts are available
in this case too (see Table~\ref{tab:p_coarse_1}). \\
\textbf{Remark 3.} Many of the coarsest-level solvers apply to a
\textbf{Remark 3.} The polynomial-accelerated smoother described in Tables~\ref{tab:p_smoother}
and~\ref{tab:p_smoother_2} redefines a sweep or iteration as corresponding to the degree of
the polynomial used. Consequently, the \fortinline|'SMOOTHER_SWEEPS'| option is overridden by
the \fortinline|'POLY_DEGREE'| option. This smoother is paired with a base smoother
object, whose iterations are accelerated using the specified polynomial smoothing technique.
By default, the $\ell_1$-Jacobi smoother serves as the base smoother, offering theoretical
guarantees on the resulting convergence factor~\cite{DDFMT2024,LOTTES}. Alternative combinations
are experimental and lack established guarantees.\\
\textbf{Remark 4.} Many of the coarsest-level solvers apply to a
specific coarsest-matrix layout;
therefore, setting the solver after the layout may change the layout
to either distributed or replicated.
@@ -425,7 +434,7 @@ the parameter \texttt{ilev}.} \\
distributed, \texttt{MUMPS} can be used with either
a replicated or a distributed matrix. When any of the previous
solvers is specified, the matrix layout is set to a default
value which allows the use of the solver (see Remark 3, p.~24).
value which allows the use of the solver (see Remark 4, p.~21).
Note also that UMFPACK and SuperLU\_Dist
are available only in double precision. \\\hline%
\ifpdf
@@ -578,7 +587,7 @@ level (continued).\label{tab:p_coarse_1}}
& Type of smoother used in the multilevel preconditioner:
point-Jacobi, hybrid (forward) Gauss-Seidel,
hybrid backward Gauss-Seidel, block-Jacobi, $\ell_1$-Jacobi, $\ell_1$--hybrid (forward) Gauss-Seidel, $\ell_1$-point-Jacobi and
Additive Schwarz, polynomial accelerators; see~\cite{DDFMT2024} \par
Additive Schwarz, polynomial accelerators; see~\cite{DDFMT2024} and Remark~3 (p.~21).\par
It is ignored by one-level preconditioners. \\ \hline
\fortinline|'SUB_SOLVE'| & \fortinline|character(len=*)|
& \fortinline|'JACOBI'|