New interface for MUMPS_IPAR_ENTRY and MUMPS_RPAR_ENTRY. Document same.
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@@ -67,7 +67,7 @@ Ax=b,
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<A NAME="eq:system"></A>
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<TABLE WIDTH="100%" ALIGN="CENTER">
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<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:system"></A><IMG
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WIDTH="57" HEIGHT="30" BORDER="0"
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WIDTH="58" HEIGHT="30" BORDER="0"
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SRC="img2.png"
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ALT="\begin{displaymath}
|
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Ax=b,
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@@ -116,8 +116,7 @@ a hierarchy of index spaces and a corresponding hierarchy of matrices,
|
||||
<IMG
|
||||
WIDTH="398" HEIGHT="30" BORDER="0"
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SRC="img7.png"
|
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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}">
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</DIV>
|
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<BR CLEAR="ALL">
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<P></P><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
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@@ -133,7 +132,7 @@ A vector space <!-- MATH
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$\mathbb{R}^{n_{k}}$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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WIDTH="33" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
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SRC="img8.png"
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ALT="$\mathbb{R}^{n_{k}}$"></SPAN> is associated with <SPAN CLASS="MATH"><IMG
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WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
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@@ -147,11 +146,11 @@ where <SPAN CLASS="MATH"><IMG
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SRC="img9.png"
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ALT="$\Omega^k$"></SPAN>.
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For all <SPAN CLASS="MATH"><IMG
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WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
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WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img11.png"
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ALT="$k < nlev$"></SPAN>, a restriction operator and a prolongation one are built,
|
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which connect two levels <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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WIDTH="14" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
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SRC="img12.png"
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ALT="$k$"></SPAN> and <SPAN CLASS="MATH"><IMG
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WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
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@@ -168,7 +167,7 @@ P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad
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-->
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<IMG
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WIDTH="253" HEIGHT="30" BORDER="0"
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WIDTH="254" HEIGHT="30" BORDER="0"
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SRC="img14.png"
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ALT="\begin{displaymath}
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P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad
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@@ -192,7 +191,7 @@ A^{k+1}=R^kA^kP^k.
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-->
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<IMG
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WIDTH="129" HEIGHT="27" BORDER="0"
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WIDTH="131" HEIGHT="28" BORDER="0"
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SRC="img16.png"
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ALT="\begin{displaymath}
|
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A^{k+1}=R^kA^kP^k.
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@@ -208,19 +207,19 @@ A smoother with iteration matrix <SPAN CLASS="MATH"><IMG
|
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WIDTH="32" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
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SRC="img18.png"
|
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ALT="$M^k$"></SPAN> is set up at each level <SPAN CLASS="MATH"><IMG
|
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WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
|
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WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img11.png"
|
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ALT="$k < nlev$"></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
|
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WIDTH="30" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
|
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SRC="img19.png"
|
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ALT="$LU$"></SPAN> factorization means computing
|
||||
and storing the <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
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SRC="img20.png"
|
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ALT="$L$"></SPAN> and <SPAN CLASS="MATH"><IMG
|
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WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img21.png"
|
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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.
|
||||
@@ -257,15 +256,8 @@ end
|
||||
<IMG
|
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WIDTH="333" HEIGHT="336" ALIGN="BOTTOM" BORDER="0"
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SRC="img22.png"
|
||||
ALT="\framebox{
|
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\begin{minipage}{.85\textwidth}
|
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\begin{tabbing}
|
||||
\quad \=\quad \=\quad...
|
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...[1mm]
|
||||
\>endif [1mm]
|
||||
\>return $u^k$ [1mm]
|
||||
end
|
||||
\end{tabbing}\end{minipage}}">
|
||||
ALT="\framebox{␍\begin{minipage}{.85\textwidth}␍\begin{tabbing}␍\quad \=\quad \=\quad...
|
||||
...mm]␍\>endif [1mm]␍\>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="48" BORDER="0"
|
||||
WIDTH="387" HEIGHT="49" 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="286" HEIGHT="51" BORDER="0"
|
||||
WIDTH="287" HEIGHT="52" BORDER="0"
|
||||
SRC="img34.png"
|
||||
ALT="\begin{displaymath}
|
||||
\bar{P}^k =(\bar{p}_{ij}^k), \quad \bar{p}_{ij}^k =
|
||||
@@ -265,9 +265,7 @@ 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">
|
||||
@@ -277,7 +275,7 @@ method [<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="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img38.png"
|
||||
ALT="$S^k$"></SPAN> is the damped Jacobi smoother:
|
||||
</BIG></BIG></BIG>
|
||||
@@ -292,9 +290,7 @@ 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">
|
||||
@@ -344,7 +340,7 @@ a_{ij}^k & \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="18" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="24" HEIGHT="20" 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="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="22" HEIGHT="20" 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="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="22" HEIGHT="20" 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="218" HEIGHT="59" BORDER="0"
|
||||
WIDTH="219" 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="18" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="25" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img67.png"
|
||||
ALT="$w^k$"></SPAN> to the subspaces <!-- MATH
|
||||
$\mathbb{R}^{n_{k,i}}$
|
||||
|
||||
@@ -343,7 +343,7 @@ Parameters defining the aggregation algorithm.
|
||||
$\lfloor 40 \sqrt[3]{n} \rfloor$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="64" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
|
||||
WIDTH="63" HEIGHT="37" 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="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img78.png"
|
||||
ALT="$> 1$"></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="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img78.png"
|
||||
ALT="$> 1$"></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="40" ALIGN="MIDDLE" BORDER="0"
|
||||
WIDTH="62" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img79.png"
|
||||
ALT="$A+A^T$"></SPAN>.</TD>
|
||||
</TR>
|
||||
@@ -471,7 +471,7 @@ number <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="15" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="13" HEIGHT="20" 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 <A HREF="node14.html#sec:aggregation">4.2</A>.
|
||||
@@ -897,7 +897,17 @@ Parameters defining the smoother or the details of the one-level preconditioner
|
||||
</SMALL></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><SMALL CLASS="SMALL"> 0
|
||||
</SMALL></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><SMALL CLASS="SMALL"> Set an entry in the MUMPS control array, as
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><SMALL CLASS="SMALL"> Set an entry in the MUMPS integer control array, as
|
||||
chosen via the <code>idx</code> optional argument. </SMALL></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><SMALL CLASS="SMALL"> <code>'MUMPS_RPAR_ENTRY'</code> </SMALL></TD>
|
||||
<TD ALIGN="LEFT"><SMALL CLASS="SMALL"> <code>real</code>
|
||||
</SMALL></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><SMALL CLASS="SMALL"> Any real number
|
||||
</SMALL></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><SMALL CLASS="SMALL"> 0
|
||||
</SMALL></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><SMALL CLASS="SMALL"> Set an entry in the MUMPS real control array, as
|
||||
chosen via the <code>idx</code> optional argument. </SMALL></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><SMALL CLASS="SMALL"> </SMALL></TD>
|
||||
|
||||
@@ -62,9 +62,9 @@ This method computes <!-- MATH
|
||||
$y = op(B^{-1})\, x$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
WIDTH="112" HEIGHT="37" 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="57" HEIGHT="30" BORDER="0"
|
||||
WIDTH="58" 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 2018-10-05<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
|
||||
The translation was initiated on 2018-10-21<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
|
||||
@@ -80,7 +80,7 @@ constant
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="173" HEIGHT="31" BORDER="0"
|
||||
WIDTH="172" HEIGHT="31" BORDER="0"
|
||||
SRC="img4.png"
|
||||
ALT="\begin{displaymath}\verb\vert mld_version_string_\vert\end{displaymath}">
|
||||
</DIV>
|
||||
|
||||
@@ -2,7 +2,7 @@
|
||||
%ÐÔÅØ
|
||||
145 0 obj
|
||||
<<
|
||||
/Length 1211
|
||||
/Length 1210
|
||||
>>
|
||||
stream
|
||||
0 g 0 G
|
||||
@@ -11,20 +11,20 @@ stream
|
||||
0 g 0 G
|
||||
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