fdurastante/amg4psblas
1
0
Fork 0
mirror of https://github.com/sfilippone/amg4psblas.git synced 2026-10-07 07:04:59 +00:00
Code Issues Packages Projects Releases Wiki Activity

Update docs for version 2.2

Browse Source
This commit is contained in:
Salvatore Filippone
2018-11-29 13:45:36 +00:00
parent e7c6028aec
commit e7718084c7
37 changed files with 99 additions and 77 deletions
Download Patch File Download Diff File Expand all files Collapse all files
docs/html/node13.html
+20 -12
View File
@@ -67,7 +67,7 @@ Ax=b,
<A NAME="eq:system"></A>
<TABLE WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:system"></A><IMG
WIDTH="58" HEIGHT="30" BORDER="0"
WIDTH="57" HEIGHT="30" BORDER="0"
SRC="img2.png"
ALT="\begin{displaymath}
Ax=b,
@@ -116,7 +116,8 @@ a hierarchy of index spaces and a corresponding hierarchy of matrices,
<IMG
WIDTH="398" HEIGHT="30" BORDER="0"
SRC="img7.png"
ALT="\begin{displaymath}\Omega^1 \equiv \Omega \supset \Omega^2 \supset \ldots \supset \Omega^{nlev},␍\quad A^1 \equiv A, A^2, \ldots, A^{nlev}, \end{displaymath}">
ALT="\begin{displaymath}\Omega^1 \equiv \Omega \supset \Omega^2 \supset \ldots \supset \Omega^{nlev},
\quad A^1 \equiv A, A^2, \ldots, A^{nlev}, \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
@@ -132,7 +133,7 @@ A vector space <!-- MATH
$\mathbb{R}^{n_{k}}$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="33" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img8.png"
ALT="$\mathbb{R}^{n_{k}}$"></SPAN> is associated with <SPAN CLASS="MATH"><IMG
WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
@@ -146,11 +147,11 @@ where <SPAN CLASS="MATH"><IMG
SRC="img9.png"
ALT="$\Omega^k$"></SPAN>.
For all <SPAN CLASS="MATH"><IMG
WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="img11.png"
ALT="$k &lt; nlev$"></SPAN>, a restriction operator and a prolongation one are built,
which connect two levels <SPAN CLASS="MATH"><IMG
WIDTH="14" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img12.png"
ALT="$k$"></SPAN> and <SPAN CLASS="MATH"><IMG
WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
@@ -167,7 +168,7 @@ P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad
-->
<IMG
WIDTH="254" HEIGHT="30" BORDER="0"
WIDTH="253" HEIGHT="30" BORDER="0"
SRC="img14.png"
ALT="\begin{displaymath}
P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad
@@ -191,7 +192,7 @@ A^{k+1}=R^kA^kP^k.
-->
<IMG
WIDTH="131" HEIGHT="28" BORDER="0"
WIDTH="129" HEIGHT="27" BORDER="0"
SRC="img16.png"
ALT="\begin{displaymath}
A^{k+1}=R^kA^kP^k.
@@ -207,19 +208,19 @@ A smoother with iteration matrix <SPAN CLASS="MATH"><IMG
WIDTH="32" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img18.png"
ALT="$M^k$"></SPAN> is set up at each level <SPAN CLASS="MATH"><IMG
WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="img11.png"
ALT="$k &lt; nlev$"></SPAN>, and a solver
is set up at the coarsest level, so that they are ready for application
(for example, setting up a solver based on the <SPAN CLASS="MATH"><IMG
WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
WIDTH="30" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img19.png"
ALT="$LU$"></SPAN> factorization means computing
and storing the <SPAN CLASS="MATH"><IMG
WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$L$"></SPAN> and <SPAN CLASS="MATH"><IMG
WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img21.png"
ALT="$U$"></SPAN> factors). The construction of the hierarchy of AMG components
described so far corresponds to the so-called build phase of the preconditioner.
@@ -256,8 +257,15 @@ end
<IMG
WIDTH="333" HEIGHT="336" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="\framebox{␍\begin{minipage}{.85\textwidth}␍\begin{tabbing}␍\quad \=\quad \=\quad...
...mm]␍\&gt;endif [1mm]␍\&gt;return $u^k$ [1mm]␍end␍\end{tabbing}␍\end{minipage}␍}">
ALT="\framebox{
\begin{minipage}{.85\textwidth}
\begin{tabbing}
\quad \=\quad \=\quad...
...[1mm]
\&gt;endif \\ [1mm]
\&gt;return $u^k$\ \\ [1mm]
end
\end{tabbing}\end{minipage}}">
</DIV></TD></TR>
</TABLE>