Update docs for version 2.2

2026-10-06 22:55:12 +00:00 · 2018-11-29 13:45:36 +00:00
parent e7c6028aec
commit e7718084c7
37 changed files with 99 additions and 77 deletions
@@ -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>
@@ -149,7 +149,7 @@ strongly-coupled neighborood of <SPAN CLASS="MATH"><IMG
 <A NAME="eq:strongly_coup"></A>
 <TABLE WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:strongly_coup"></A><IMG
- WIDTH="387" HEIGHT="49" BORDER="0"
+ WIDTH="387" HEIGHT="48" BORDER="0"
 SRC="img31.png"
 ALT="\begin{displaymath}
 \Omega^k_j \subset \mathcal{N}_i^k(\theta) =
@@ -212,7 +212,7 @@ MLD2P4, since it has been shown to produce good results in practice
 <A NAME="eq:tent_prol"></A>
 <TABLE WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:tent_prol"></A><IMG
- WIDTH="287" HEIGHT="52" BORDER="0"
+ WIDTH="286" HEIGHT="51" BORDER="0"
 SRC="img34.png"
 ALT="\begin{displaymath}
 \bar{P}^k =(\bar{p}_{ij}^k), \quad \bar{p}_{ij}^k =
@@ -265,7 +265,9 @@ P^k = S^k \bar{P}^k,
 <IMG
 WIDTH="90" HEIGHT="30" BORDER="0"
 SRC="img37.png"
- ALT="\begin{displaymath}␍P^k = S^k \bar{P}^k,␍\end{displaymath}">
+ ALT="\begin{displaymath}
+P^k = S^k \bar{P}^k,
+\end{displaymath}">
 </DIV>
 <BR CLEAR="ALL">
 <P></P><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
@@ -275,7 +277,7 @@ method&nbsp;[<A
 HREF="node36.html#BREZINA_VANEK">2</A>,<A
 HREF="node36.html#Stuben_01">24</A>].
 A simple choice for <SPAN CLASS="MATH"><IMG
- WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img38.png"
 ALT="$S^k$"></SPAN> is the damped Jacobi smoother:
 </BIG></BIG></BIG>
@@ -290,7 +292,9 @@ S^k = I - \omega^k (D^k)^{-1} A^k_F ,
 <IMG
 WIDTH="175" HEIGHT="31" BORDER="0"
 SRC="img39.png"
- ALT="\begin{displaymath}␍S^k = I - \omega^k (D^k)^{-1} A^k_F , ␍\end{displaymath}">
+ ALT="\begin{displaymath}
+S^k = I - \omega^k (D^k)^{-1} A^k_F ,
+\end{displaymath}">
 </DIV>
 <BR CLEAR="ALL">
 <P></P><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
@@ -340,7 +344,7 @@ a_{ij}^k &amp; \m...
 </TABLE>
 <BR CLEAR="ALL"></DIV><P></P><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
 and <SPAN CLASS="MATH"><IMG
- WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img44.png"
 ALT="$\omega^k$"></SPAN> is an approximation of <SPAN CLASS="MATH"><IMG
 WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
@@ -93,13 +93,13 @@ operator <!-- MATH
 SRC="img53.png"
 ALT="$R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$"></SPAN>
 that maps a vector <SPAN CLASS="MATH"><IMG
- WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img54.png"
 ALT="$x^k$"></SPAN> to the vector <SPAN CLASS="MATH"><IMG
 WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img55.png"
 ALT="$x_i^k$"></SPAN> made of the components of <SPAN CLASS="MATH"><IMG
- WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img54.png"
 ALT="$x^k$"></SPAN>
 with indices in <SPAN CLASS="MATH"><IMG
@@ -141,7 +141,7 @@ The classical AS preconditioner <SPAN CLASS="MATH"><IMG
 -->

 <IMG
- WIDTH="219" HEIGHT="59" BORDER="0"
+ WIDTH="218" HEIGHT="59" BORDER="0"
 SRC="img59.png"
 ALT="\begin{displaymath}
 ( M^k_{AS} )^{-1} = \sum_{i=1}^{m_k} P_i^k (A_i^k)^{-1} R_i^{k},
@@ -205,7 +205,7 @@ multilevel application phase, requires
 </BIG></BIG></BIG>
 <UL>
 <LI>the restriction of <SPAN CLASS="MATH"><IMG
- WIDTH="25" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img67.png"
 ALT="$w^k$"></SPAN> to the subspaces <!-- MATH
 $\mathbb{R}^{n_{k,i}}$
@@ -54,7 +54,7 @@ Method init
 </H2><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
 <P>
 <BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
-<DIV ALIGN="CENTER"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><code>call p%init(ptype,info)</code>
+<DIV ALIGN="CENTER"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><code>call p%init(icontx,ptype,info)</code>
 </BIG></BIG></BIG></DIV><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
 <P>
 <BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
@@ -68,6 +68,14 @@ This method allocates and initializes the preconditioner
 <P>
 <BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG><TABLE CELLPADDING=3>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
+<code>icontxt</code> </BIG></BIG></BIG></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <code>integer, intent(in)</code>.</BIG></BIG></BIG></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> 
+          </BIG></BIG></BIG></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">  The communication context.</BIG></BIG></BIG></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> 
 <code>ptype</code>  </BIG></BIG></BIG></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <code>character(len=*), intent(in)</code>.</BIG></BIG></BIG></TD>
 </TR>
@@ -343,7 +343,7 @@ Parameters defining the aggregation algorithm.
 $\lfloor 40 \sqrt[3]{n} \rfloor$
 -->
 <SPAN CLASS="MATH"><IMG
- WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="64" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img76.png"
 ALT="$\lfloor 40 \sqrt[3]{n} \rfloor$"></SPAN>, where <SPAN CLASS="MATH"><IMG
 WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
@@ -361,7 +361,7 @@ Parameters defining the aggregation algorithm.
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number 
 <P>
 <SPAN CLASS="MATH"><IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img78.png"
 ALT="$&gt; 1$"></SPAN></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82>1.5</TD>
@@ -375,7 +375,7 @@ Parameters defining the aggregation algorithm.
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any integer 
 <P>
 number <SPAN CLASS="MATH"><IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img78.png"
 ALT="$&gt; 1$"></SPAN></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82>20</TD>
@@ -393,7 +393,7 @@ Currently, only the
                           <code>SYMDEC</code> option  applies decoupled
                           aggregation to  the sparsity pattern
                           of <SPAN CLASS="MATH"><IMG
- WIDTH="62" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="62" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img79.png"
 ALT="$A+A^T$"></SPAN>.</TD>
 </TR>
@@ -471,7 +471,7 @@ number&nbsp;<SPAN CLASS="MATH"><IMG
 ALT="$\in [0, 1]$"></SPAN></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>0.01</TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>The threshold <SPAN CLASS="MATH"><IMG
- WIDTH="13" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img81.png"
 ALT="$\theta$"></SPAN> in the aggregation algorithm,
                            see (<A HREF="node14.html#eq:strongly_coup">3</A>) in Section&nbsp;<A HREF="node14.html#sec:aggregation">4.2</A>.
@@ -62,9 +62,9 @@ This method computes <!-- MATH
 $y = op(B^{-1})\, x$
 -->
 <SPAN CLASS="MATH"><IMG
- WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img86.png"
- ALT="$y = op(B^{-1})  x$"></SPAN>, where <SPAN CLASS="MATH"><IMG
+ ALT="$y = op(B^{-1})\, x$"></SPAN>, where <SPAN CLASS="MATH"><IMG
 WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img24.png"
 ALT="$B$"></SPAN> is a previously built
@@ -72,7 +72,7 @@ Ax=b,
 <A NAME="system1"></A>
 <TABLE WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="system1"></A><IMG
- WIDTH="58" HEIGHT="30" BORDER="0"
+ WIDTH="57" HEIGHT="30" BORDER="0"
 SRC="img2.png"
 ALT="\begin{displaymath}
 Ax=b,
@@ -60,7 +60,7 @@ Mathematics Department, Macquarie University, Sydney.
 The command line arguments were: <BR>
 <STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
 <P>
-The translation was initiated on 2018-10-25<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
+The translation was initiated on 2018-11-29<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
 <BR><HR>

 </BODY>
@@ -80,7 +80,7 @@ constant
 -->

 <IMG
- WIDTH="172" HEIGHT="31" BORDER="0"
+ WIDTH="173" HEIGHT="31" BORDER="0"
 SRC="img4.png"
 ALT="\begin{displaymath}\verb\vert mld_version_string_\vert\end{displaymath}">
 </DIV>