mld2p4: final fixes for 1.1 release.

2026-10-06 14:44:55 +00:00 · 2009-03-16 08:47:03 +00:00
parent 5e0cfebc6d
commit 73dac6d963
56 changed files with 1275 additions and 1325 deletions
@@ -74,13 +74,13 @@ solution of the original problem from the local solutions
 [<A
 HREF="node25.html#Cai_Widlund_92">6</A>,<A
 HREF="node25.html#dd1_94">7</A>,<A
- HREF="node25.html#dd2_96">20</A>]. 
+ HREF="node25.html#dd2_96">21</A>]. 

 <P>
 <I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
 submatrices, i.e. with some common rows, to couple the local information
 related to the submatrices (see, e.g., [<A
- HREF="node25.html#dd2_96">20</A>]).
+ HREF="node25.html#dd2_96">21</A>]).
 The main motivation for choosing Additive Schwarz preconditioners is their
 intrinsic parallelism. A drawback of these
 preconditioners is that the number of iterations of the preconditioned solvers
@@ -99,7 +99,7 @@ correction. In this context, the one-level preconditioner is often
 called `smoother'. Different two-level preconditioners are obtained by varying the
 choice of the smoother and of the coarse-level correction, and the
 way they are combined [<A
- HREF="node25.html#dd2_96">20</A>]. The same reasoning can be applied starting
+ HREF="node25.html#dd2_96">21</A>]. The same reasoning can be applied starting
 from the coarse-level system, i.e. a coarse-space correction can be built
 from this system, thus obtaining <I>multi-level</I> preconditioners.

@@ -123,24 +123,25 @@ are considered. The algebraic approach builds coarse-space corrections using onl
 information. It performs a fully automatic coarsening and enforces the interplay between
 the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
 interpolation [<A
- HREF="node25.html#StubenGMD69_99">22</A>].
+ HREF="node25.html#StubenGMD69_99">23</A>].

 <P>
 MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
 starting from the original matrix. The algebraic approach is based on the <I>smoothed 
 aggregation</I> algorithm [<A
 HREF="node25.html#BREZINA_VANEK">1</A>,<A
- HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>]. A decoupled version
+ HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>]. A decoupled version
 of this algorithm is implemented, where the smoothed aggregation is applied locally
 to each submatrix [<A
- HREF="node25.html#TUMINARO_TONG">23</A>]. In the next two subsections we provide
+ HREF="node25.html#TUMINARO_TONG">24</A>]. In the next two subsections we provide
 a brief description of the multi-level Schwarz preconditioners and of the smoothed
 aggregation technique as implemented in MLD2P4. For further details the reader
 is referred to [<A
 HREF="node25.html#para_04">2</A>,<A
 HREF="node25.html#aaecc_07">3</A>,<A
- HREF="node25.html#apnum_07">4</A>,,<A
- HREF="node25.html#dd2_96">20</A>].
+ HREF="node25.html#apnum_07">4</A>,<A
+ HREF="node25.html#MLD2P4_TOMS">8</A>,<A
+ HREF="node25.html#dd2_96">21</A>].

 <P>
 <BR><HR>
@@ -299,7 +299,7 @@ ILU(<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img35.png"
 ALT="$p,t$">) [<A
- HREF="node25.html#Saad_book">19</A>, Chapter 10].
+ HREF="node25.html#Saad_book">20</A>, Chapter 10].

 <P>
 A variant of the classical AS preconditioner that outperforms it
@@ -307,7 +307,7 @@ in terms of convergence rate and of computation and communication
 time on parallel distributed-memory computers is the so-called <I>Restricted AS
 (RAS)</I> preconditioner&nbsp;[<A
 HREF="node25.html#CAI_SARKIS">5</A>,<A
- HREF="node25.html#EFSTATHIOU">13</A>]. It
+ HREF="node25.html#EFSTATHIOU">14</A>]. It
 is obtained by zeroing the components of <IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img32.png"
@@ -391,7 +391,7 @@ of <IMG
 SRC="img10.png"
 ALT="$W$"> increases [<A
 HREF="node25.html#dd1_94">7</A>,<A
- HREF="node25.html#dd2_96">20</A>]. To reduce the dependency
+ HREF="node25.html#dd2_96">21</A>]. To reduce the dependency
 of the number of iterations on the degree of parallelism we may
 introduce a global coupling among the overlapping partitions by defining 
 a coarse-space approximation <IMG
@@ -646,12 +646,12 @@ in which the coarse-level correction is re-applied starting from the current
 coarse-level system. The corresponding preconditioners, called <I>multi-level</I>
 preconditioners, can significantly reduce the computational cost of preconditioning
 with respect to the two-level case (see [<A
- HREF="node25.html#dd2_96">20</A>, Chapter 3]). 
+ HREF="node25.html#dd2_96">21</A>, Chapter 3]). 
 Additive and hybrid multilevel preconditioners
 are obtained as direct extensions of the two-level counterparts.
 For a detailed descrition of them, the reader is
 referred to [<A
- HREF="node25.html#dd2_96">20</A>, Chapter 3].
+ HREF="node25.html#dd2_96">21</A>, Chapter 3].
 The algorithm for the application of a multi-level hybrid 
 post-smoothed preconditioner <IMG
 WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
@@ -685,7 +685,7 @@ and the corresponding basic preconditioner at each level <IMG
 SRC="img65.png"
 ALT="$A_1=A$">, while the related restriction operator is
 denoted by <IMG
- WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img66.png"
 ALT="$R_l$">.

@@ -724,14 +724,14 @@ $w = y_1$;
 }$
 -->
 <IMG
- WIDTH="429" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="430" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
 SRC="img67.png"
 ALT="\framebox{
 \begin{minipage}{.85\textwidth} {\small
 \begin{tabbing}
 \quad \=\quad...
 ...= y_l+r_l$\\
-\textbf{endfor}  [1mm]
+\textbf{endfor} \ [1mm]
 $w = y_1$;
 \end{tabbing}}
 \end{minipage}}">
@@ -70,7 +70,7 @@ the coarse-level matrix <IMG
 ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I>
 algorithm described in [<A
 HREF="node25.html#BREZINA_VANEK">1</A>,<A
- HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>].
+ HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>].
 The basic idea of this algorithm is to build a coarse set of vertices
 <IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -120,7 +120,7 @@ Three main steps can be identified in the smoothed aggregation procedure:
 To perform the coarsening step, we have implemented the aggregation algorithm sketched
 in [<A
 HREF="node25.html#apnum_07">4</A>]. According to [<A
- HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>], a modification of
+ HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>], a modification of
 this algorithm has been actually considered,
 in which each aggregate <IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -159,7 +159,7 @@ for a given <!-- MATH
 ALT="$\theta \in [0,1]$">.
 Since this algorithm has a sequential nature, a <I>decoupled</I> version of
 it has been chosen, where each processor <IMG
- WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="10" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img74.png"
 ALT="$i$"> independently applies the algorithm to
 the set of vertices <IMG
@@ -178,7 +178,7 @@ since it has been shown to produce good results in practice
 [<A
 HREF="node25.html#aaecc_07">3</A>,<A
 HREF="node25.html#apnum_07">4</A>,<A
- HREF="node25.html#TUMINARO_TONG">23</A>].
+ HREF="node25.html#TUMINARO_TONG">24</A>].

 <P>
 The prolongator <IMG
@@ -189,7 +189,7 @@ The prolongator <IMG
 $P \in \Re^{n \times n_C}$
 -->
 <IMG
- WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img77.png"
 ALT="$P \in \Re^{n \times n_C}$">, defined as
 <BR>
@@ -257,7 +257,7 @@ in order to remove oscillatory components from the range of the prolongator
 and hence to improve the convergence properties of the multi-level
 Schwarz method [<A
 HREF="node25.html#BREZINA_VANEK">1</A>,<A
- HREF="node25.html#StubenGMD69_99">22</A>].
+ HREF="node25.html#StubenGMD69_99">23</A>].
 A simple choice for <IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img83.png"
@@ -286,7 +286,7 @@ where the value of <IMG
 SRC="img85.png"
 ALT="$\omega$"> can be chosen
 using some estimate of the spectral radius of <IMG
- WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="img86.png"
 ALT="$D^{-1}A$"> [<A
 HREF="node25.html#BREZINA_VANEK">1</A>].
@@ -63,7 +63,7 @@ Getting Started
 <P>
 We describe the basics for building and applying MLD2P4 one-level and multi-level
 Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A
- HREF="node25.html#PSBLASGUIDE">14</A>].
+ HREF="node25.html#PSBLASGUIDE">15</A>].
 The following steps are required:

 <OL>
@@ -79,7 +79,7 @@ in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
 Section&nbsp;<A HREF="node10.html#sec:ex_and_test">3.5</A>).
 For details on the use of the PSBLAS routines, see the PSBLAS User's
 Guide [<A
- HREF="node25.html#PSBLASGUIDE">14</A>].
+ HREF="node25.html#PSBLASGUIDE">15</A>].

 <P>
 The setup and application of the default multi-level
@@ -165,7 +165,7 @@ Figure&nbsp;<A HREF="#fig:ex_3lh">3</A> shows how to set a three-level hybrid Sc
 preconditioner, which uses block Jacobi with ILU(0) on the
 local blocks as post-smoother, has a coarsest matrix replicated on the processors,
 and solves the coarsest-level system with the LU factorization from UMFPACK&nbsp;[<A
- HREF="node25.html#UMFPACK">8</A>].
+ HREF="node25.html#UMFPACK">9</A>].
 The number of levels is specified by using <code>mld_precinit</code>; the other
 preconditioner parameters are set by calling <code>mld_precset</code>. Note that
 the type of multilevel framework (i.e. multiplicative among the levels
@@ -90,7 +90,7 @@ i.e.
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img21.png"
 ALT="$v$"> and <IMG
- WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img88.png"
 ALT="$w$"> involved in
  the preconditioner application <IMG
@@ -198,7 +198,7 @@ Parameters defining the one-level preconditioner used as smoother.
 <TR><TD ALIGN="LEFT"><code>mld_sub_ovr_</code></TD>
 <TD ALIGN="LEFT"><code>integer</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any&nbsp;int.&nbsp;num.&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img89.png"
 ALT="$\ge 0$"></TD>
 <TD ALIGN="LEFT">1</TD>
@@ -240,7 +240,7 @@ Parameters defining the one-level preconditioner used as smoother.
 <TR><TD ALIGN="LEFT"><code>mld_sub_fillin_</code></TD>
 <TD ALIGN="LEFT"><code>integer</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img89.png"
 ALT="$\ge 0$"></TD>
 <TD ALIGN="LEFT">0</TD>
@@ -252,7 +252,7 @@ Parameters defining the one-level preconditioner used as smoother.
 <TR><TD ALIGN="LEFT"><code>mld_sub_iluthrs_</code></TD>
 <TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;real&nbsp;num.&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img89.png"
 ALT="$\ge 0$"></TD>
 <TD ALIGN="LEFT">0</TD>
@@ -332,7 +332,7 @@ Parameters defining the aggregation algorithm.
                         smoothed aggregation should be computed:
                         either via an estimate of the spectral radius of
                         <IMG
- WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="img86.png"
 ALT="$D^{-1}A$">, or explicily
                         specified by the user.</TD>
@@ -342,7 +342,7 @@ Parameters defining the aggregation algorithm.
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'A_NORMI'</TT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'A_NORMI'</TT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>How to estimate the spectral radius of <IMG
- WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="img86.png"
 ALT="$D^{-1}A$">.
                           Currently only the infinity norm estimate
@@ -371,7 +371,7 @@ Parameters defining the aggregation algorithm.
 SRC="img94.png"
 ALT="$\rho(D^{-1}A)$"> of
                           <IMG
- WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="img86.png"
 ALT="$D^{-1}A$">.</TD>
 </TR>
@@ -441,7 +441,7 @@ level.</CAPTION>
 <TR><TD ALIGN="LEFT"><code>mld_coarse_sweeps_</code></TD>
 <TD ALIGN="LEFT"><code>integer</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img95.png"
 ALT="$&gt; 0$"></TD>
 <TD ALIGN="LEFT">4</TD>
@@ -451,7 +451,7 @@ level.</CAPTION>
 <TR><TD ALIGN="LEFT"><code>mld_coarse_fillin_</code></TD>
 <TD ALIGN="LEFT"><code>integer</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img89.png"
 ALT="$\ge 0$"></TD>
 <TD ALIGN="LEFT">0</TD>
@@ -463,7 +463,7 @@ level.</CAPTION>
 <TR><TD ALIGN="LEFT"><code>mld_coarse_iluthrs_</code></TD>
 <TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;real.&nbsp;num.&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img89.png"
 ALT="$\ge 0$"></TD>
 <TD ALIGN="LEFT">0</TD>
@@ -84,7 +84,7 @@ the user through the routines <code>mld_precinit</code> and <code>mld_precset</c
                to the real/complex, 
 single/double precision version of MLD2P4 under use.
                See the PSBLAS User's Guide for details [<A
- HREF="node25.html#PSBLASGUIDE">14</A>].</TD>
+ HREF="node25.html#PSBLASGUIDE">15</A>].</TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
@@ -92,7 +92,7 @@ single/double precision version of MLD2P4 under use.
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
                details [<A
- HREF="node25.html#PSBLASGUIDE">14</A>].</TD>
+ HREF="node25.html#PSBLASGUIDE">15</A>].</TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
@@ -72,14 +72,14 @@ This routine computes <!-- MATH
 $y = op(M^{-1})\, x$
 -->
 <IMG
- WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img96.png"
 ALT="$y = op(M^{-1})  x$">, where <IMG
 WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img59.png"
 ALT="$M$"> is a previously built
 preconditioner, stored into <code>p</code>, and <IMG
- WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img97.png"
 ALT="$op$">
 denotes the preconditioner itself or its transpose, according to
@@ -109,7 +109,7 @@ and hence it is completely transparent to the user.
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
- WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img98.png"
 ALT="$x$">. Note that <I>type</I> and   
                <I>kind_parameter</I> must be chosen according
@@ -120,7 +120,7 @@ and hence it is completely transparent to the user.
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img99.png"
 ALT="$y$">. Note that <I>type</I> and
                <I>kind_parameter</I> must be chosen according
@@ -72,7 +72,7 @@ will then take action, and whether
 an error message should be printed. These options may be set by using
 the PSBLAS error handling routines; for further details see the PSBLAS
 User's Guide [<A
- HREF="node25.html#PSBLASGUIDE">14</A>]. 
+ HREF="node25.html#PSBLASGUIDE">15</A>]. 

 <P>

@@ -73,7 +73,8 @@ Proceedings of PARA&nbsp;04 Workshop on State of the Art
 in Scientific Computing, Lecture Notes in Computer Science,
 Springer, 2005, 593-602.
 <P></P><DT><A NAME="aaecc_07">3</A>
-<DD> A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
+<DD> 
+A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
 <EM>2LEV-D2P4: a package of high-performance preconditioners
 for scientific and engineering applications</EM>,
 Applicable Algebra in Engineering, Communications and Computing, 
@@ -101,95 +102,101 @@ T.&nbsp;Chan and T.&nbsp;Mathew,
 <EM>Domain Decomposition Algorithms</EM>,
 in A.&nbsp;Iserles, editor, Acta Numerica 1994, 61-143.
 Cambridge University Press.
-<P></P><DT><A NAME="UMFPACK">8</A>
+<P></P><DT><A NAME="MLD2P4_TOMS">8</A>
+<DD> 
+P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
+<I>MLD2P4: a Package of Parallel Multilevel
+Algebraic Domain Decomposition Preconditioners
+in Fortran 95</I>, ICAR-CNR Technical Report RT-ICAR-NA-09-01, 2009.
+<P></P><DT><A NAME="UMFPACK">9</A>
 <DD>
 T.A.&nbsp;Davis, 
 <EM>Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
 Method with a Column Pre-ordering Strategy</EM>,
 ACM Transactions on Mathematical Software, 30, 2004, 196-199.
 (See also <TT>http://www.cise.ufl.edu/&nbsp;davis/</TT>)
-<P></P><DT><A NAME="SUPERLU">9</A>
+<P></P><DT><A NAME="SUPERLU">10</A>
 <DD>
 J.W.&nbsp;Demmel, S.C.&nbsp;Eisenstat, J.R.&nbsp;Gilbert, X.S.&nbsp;Li and J.W.H.&nbsp;Liu,
 A supernodal approach to sparse partial pivoting,
 SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.
-<P></P><DT><A NAME="blas3">10</A>
+<P></P><DT><A NAME="blas3">11</A>
 <DD>
 J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, I.&nbsp;S.&nbsp;Duff, S.&nbsp;Hammarling,
 <I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
 ACM Transactions on Mathematical Software, 16, 1990, 1-17.
-<P></P><DT><A NAME="blas2">11</A>
+<P></P><DT><A NAME="blas2">12</A>
 <DD>
 J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, S.&nbsp;Hammarling, R.&nbsp;J.&nbsp;Hanson,
 <I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
 ACM Transactions on Mathematical Software, 14, 1988, 1-17.
-<P></P><DT><A NAME="BLACS">12</A>
+<P></P><DT><A NAME="BLACS">13</A>
 <DD>
 J.&nbsp;J.&nbsp;Dongarra and R.&nbsp;C.&nbsp;Whaley,
 <EM>A User's Guide to the BLACS v.&nbsp;1.1</EM>,
 Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
 Tennessee, March 1995 (updated May 1997).
-<P></P><DT><A NAME="EFSTATHIOU">13</A>
+<P></P><DT><A NAME="EFSTATHIOU">14</A>
 <DD> 
 E.&nbsp;Efstathiou, J.&nbsp;G.&nbsp;Gander,
 <EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
 BIT Numerical Mathematics, 43, 2003, 945-959.
-<P></P><DT><A NAME="PSBLASGUIDE">14</A>
+<P></P><DT><A NAME="PSBLASGUIDE">15</A>
 <DD>
 S.&nbsp;Filippone, A.&nbsp;Buttari, 
 <EM>PSBLAS-2.3 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2008,
 available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
-<P></P><DT><A NAME="psblas_00">15</A>
+<P></P><DT><A NAME="psblas_00">16</A>
 <DD>
 S.&nbsp;Filippone, M.&nbsp;Colajanni, 
 <EM>PSBLAS: A Library for Parallel Linear Algebra
 Computation on Sparse Matrices</EM>,
 ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.
-<P></P><DT><A NAME="MPI2">16</A>
+<P></P><DT><A NAME="MPI2">17</A>
 <DD>
 W.&nbsp;Gropp, S.&nbsp;Huss-Lederman, A.&nbsp;Lumsdaine, E.&nbsp;Lusk, B.&nbsp;Nitzberg, W.&nbsp;Saphir, M.&nbsp;Snir, 
 <EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
 MIT Press, 1998.
-<P></P><DT><A NAME="blas1">17</A>
+<P></P><DT><A NAME="blas1">18</A>
 <DD>
 C.&nbsp;L.&nbsp;Lawson, R.&nbsp;J.&nbsp;Hanson, D.&nbsp;Kincaid, F.&nbsp;T.&nbsp;Krogh,
 <I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
 ACM Transactions on Mathematical Software, 5, 1979, 308-323.
-<P></P><DT><A NAME="SUPERLUDIST">18</A>
+<P></P><DT><A NAME="SUPERLUDIST">19</A>
 <DD>
 X.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;Demmel, <EM>SuperLU_DIST: A Scalable Distributed-memory
 Sparse Direct Solver for Unsymmetric Linear Systems</EM>,
 ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.
-<P></P><DT><A NAME="Saad_book">19</A>
+<P></P><DT><A NAME="Saad_book">20</A>
 <DD>
 Y.&nbsp;Saad,
 <I>Iterative methods for sparse linear systems</I>, 2nd edition,
 SIAM, 2003

 <P>
-<P></P><DT><A NAME="dd2_96">20</A>
+<P></P><DT><A NAME="dd2_96">21</A>
 <DD>
 B.&nbsp;Smith, P.&nbsp;Bjorstad, W.&nbsp;Gropp,
 <EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
 Partial Differential Equations</EM>,
 Cambridge University Press, 1996.
-<P></P><DT><A NAME="MPI1">21</A>
+<P></P><DT><A NAME="MPI1">22</A>
 <DD>
 M.&nbsp;Snir, S.&nbsp;Otto, S.&nbsp;Huss-Lederman, D.&nbsp;Walker, J.&nbsp;Dongarra,
 <EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
 MIT Press, 1998.
-<P></P><DT><A NAME="StubenGMD69_99">22</A>
+<P></P><DT><A NAME="StubenGMD69_99">23</A>
 <DD>
 K.&nbsp;St&#252;ben,
 <EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
 in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, editors, Multigrid,
 Academic Press, 2000.
-<P></P><DT><A NAME="TUMINARO_TONG">23</A>
+<P></P><DT><A NAME="TUMINARO_TONG">24</A>
 <DD>
 R.&nbsp;S.&nbsp;Tuminaro, C.&nbsp;Tong,
 <EM>Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines</EM>,
 in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.
-<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">24</A>
+<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">25</A>
 <DD>
 P.&nbsp;Vanek, J.&nbsp;Mandel and M.&nbsp;Brezina,
 <EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
@@ -67,7 +67,7 @@ Mathematics Department, Macquarie University, Sydney.
 The command line arguments were: <BR>
 <STRONG>latex2html</STRONG> <TT>-noaddress -dir ../../html userhtml.tex</TT>
 <P>
-The translation was initiated by Salvatore Filippone on 2009-03-13
+The translation was initiated by Salvatore Filippone on 2009-03-16
 <BR><HR>

 </BODY>
@@ -63,7 +63,7 @@ General Overview
 <P>
 The M<SMALL>ULTI-</SMALL>L<SMALL>EVEL </SMALL>D<SMALL>OMAIN </SMALL>D<SMALL>ECOMPOSITION </SMALL>P<SMALL>ARALLEL </SMALL>P<SMALL>RECONDITIONERS </SMALL>P<SMALL>ACKAGE BASED ON
 </SMALL>PSBLAS (MLD2P4) provides <I>multi-level Schwarz preconditioners</I>&nbsp;[<A
- HREF="node25.html#dd2_96">20</A>],
+ HREF="node25.html#dd2_96">21</A>],
 to be used in the iterative solutions of sparse linear systems:
 <BR>
 <DIV ALIGN="RIGHT">
@@ -102,7 +102,7 @@ explicitly using any information on the geometry of the original problem (e.g. t
 discretization of a PDE). The <I>smoothed aggregation</I> technique is applied
 as algebraic coarsening strategy&nbsp;[<A
 HREF="node25.html#BREZINA_VANEK">1</A>,<A
- HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>].
+ HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>].
 </LI>
 </UL>

@@ -120,7 +120,7 @@ real and the complex case, that can be used through a single interface.
 MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
 in the context of the <I>PSBLAS (Parallel Sparse BLAS)
 computational framework</I>&nbsp;[<A
- HREF="node25.html#psblas_00">15</A>]. 
+ HREF="node25.html#psblas_00">16</A>]. 
 PSBLAS is a library originally developed to address the parallel implementation of
 iterative solvers for sparse linear system, by providing basic linear algebra
 operators and data management facilities for distributed sparse matrices; it
@@ -133,10 +133,10 @@ portability, modularity ed extensibility in the development of the preconditione
 package. On the other hand, the implementation of MLD2P4 has led to some
 revisions and extentions of the PSBLAS kernels, leading to the
 recent PSBLAS 2.0 version&nbsp;[<A
- HREF="node25.html#PSBLASGUIDE">14</A>]. The inter-process comunication required
+ HREF="node25.html#PSBLASGUIDE">15</A>]. The inter-process comunication required
 by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
 MPI&nbsp;[<A
- HREF="node25.html#MPI1">21</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
+ HREF="node25.html#MPI1">22</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
 machine where PSBLAS and MPI implementations are available.

 <P>
@@ -64,9 +64,9 @@ The following base libraries are needed:
 <DL>
 <DT><STRONG>BLAS</STRONG></DT>
 <DD>[<A
- HREF="node25.html#blas3">10</A>,<A
- HREF="node25.html#blas2">11</A>,<A
- HREF="node25.html#blas1">17</A>] Many vendors provide optimized versions
+ HREF="node25.html#blas3">11</A>,<A
+ HREF="node25.html#blas2">12</A>,<A
+ HREF="node25.html#blas1">18</A>] Many vendors provide optimized versions
  of the Basic Linear Algebra Subprograms; if no vendor version is
  available for a given platform, the ATLAS software
  (<code>http://math-atlas.sourceforge.net/</code>)
@@ -81,13 +81,13 @@ The following base libraries are needed:
 </DD>
 <DT><STRONG>MPI</STRONG></DT>
 <DD>[<A
- HREF="node25.html#MPI2">16</A>,<A
- HREF="node25.html#MPI1">21</A>] A version of MPI is available on most
+ HREF="node25.html#MPI2">17</A>,<A
+ HREF="node25.html#MPI1">22</A>] A version of MPI is available on most
  high-performance computing systems; only version 1.1 is required.
 </DD>
 <DT><STRONG>BLACS</STRONG></DT>
 <DD>[<A
- HREF="node25.html#BLACS">12</A>] The Basic Linear Algebra Communication Subprograms
+ HREF="node25.html#BLACS">13</A>] The Basic Linear Algebra Communication Subprograms
  are available in source form from <code>http://www.netlib.org/blacs</code>;
  some vendors  include them in their parallel computing
  support libraries.
@@ -95,8 +95,8 @@ The following base libraries are needed:
 </DD>
 <DT><STRONG>PSBLAS</STRONG></DT>
 <DD>[<A
- HREF="node25.html#PSBLASGUIDE">14</A>,<A
- HREF="node25.html#psblas_00">15</A>] Parallel Sparse BLAS is
+ HREF="node25.html#PSBLASGUIDE">15</A>,<A
+ HREF="node25.html#psblas_00">16</A>] Parallel Sparse BLAS is
  available from 
 <BR><code>http://www.ce.uniroma2.it/psblas</code>; version 2.3.1
  (or later) is required. Indeed, all the prerequisites
@@ -68,7 +68,7 @@ for multilevel preconditioners may change to reflect their presence.
 <DL>
 <DT><STRONG>UMFPACK</STRONG></DT>
 <DD>[<A
- HREF="node25.html#UMFPACK">8</A>]
+ HREF="node25.html#UMFPACK">9</A>]
  A sparse direct factorization package available from 
 <BR>  <code>http://www.cise.ufl.edu/research/sparse/umfpack/</code>; 
  provides serial factorization and triangular system solution for double
@@ -77,7 +77,7 @@ for multilevel preconditioners may change to reflect their presence.
 </DD>
 <DT><STRONG>SuperLU</STRONG></DT>
 <DD>[<A
- HREF="node25.html#SUPERLU">9</A>]
+ HREF="node25.html#SUPERLU">10</A>]
  A sparse direct factorization package available from 
 <BR>  <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial
  factorization and triangular system solution for single and double precision,
@@ -85,7 +85,7 @@ for multilevel preconditioners may change to reflect their presence.
 </DD>
 <DT><STRONG>SuperLU_Dist</STRONG></DT>
 <DD>[<A
- HREF="node25.html#SUPERLUDIST">18</A>]
+ HREF="node25.html#SUPERLUDIST">19</A>]
  A sparse direct factorization package available
  from the same site as SuperLU; provides parallel factorization and
  triangular system solution for double precision real and complex data.
@@ -85,7 +85,7 @@

 TOPFILE   = userguide.tex
 HTMLFILE  = userhtml.tex
-SECFILE   = title.tex abstract.tex overview.tex distribution.tex \
+SECFILE   = abstract.tex overview.tex distribution.tex \
 		building.tex background.tex gettingstarted.tex userinterface.tex \
            errors.tex bibliography.tex license.tex 
 FIGDIR    = figures
@@ -28,7 +28,8 @@ Proceedings of PARA~04 Workshop on State of the Art
 in Scientific Computing, Lecture Notes in Computer Science,
 Springer, 2005, 593--602.
 %
-\bibitem{aaecc_07} A.~Buttari, P.~D'Ambra, D.~di~Serafino, S.~Filippone,
+\bibitem{aaecc_07} 
+A.~Buttari, P.~D'Ambra, D.~di~Serafino, S.~Filippone,
 {\em 2LEV-D2P4: a package of high-performance preconditioners
 for scientific and engineering applications},
 Applicable Algebra in Engineering, Communications and Computing, 
@@ -70,12 +71,11 @@ T.~Chan and T.~Mathew,
 in A.~Iserles, editor, Acta Numerica 1994, 61--143.
 Cambridge University Press.
 %
-%% \bibitem{MLD2P4_TOMS} 
-%% P.~D'Ambra, D.~di~Serafino, S.~Filippone,
-%% \emph{MLD2P4: a Package of Parallel Multilevel
-%% Algebraic Domain Decomposition Preconditioners
-%% in Fortran 95},
-%% COMPLETARE.
+\bibitem{MLD2P4_TOMS} 
+P.~D'Ambra, D.~di~Serafino, S.~Filippone,
+\emph{MLD2P4: a Package of Parallel Multilevel
+Algebraic Domain Decomposition Preconditioners
+in Fortran 95}, ICAR-CNR Technical Report RT-ICAR-NA-09-01, 2009.
 %
 \bibitem{UMFPACK}
 T.A.~Davis, 
@@ -1,72 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Contents: The title page
-% $Id: title.tex 1999 2007-10-29 15:25:27Z sfilippo $
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\ifcase\pdfoutput % We're not running pdftex
-{\Large\bfseries MLD2P4\\[.8ex] User's and Reference Guide}\\
-\emph{\large A guide for the Multi-Level Domain Decomposition \\[.6ex]
-Parallel Preconditioners Package
-based on PSBLAS}
-{\bfseries Pasqua D'Ambra}\\
- ICAR-CNR, Naples, Italy\\[3ex]
-{\bfseries Daniela di Serafino}\\
- Second University of Naples, Italy\\[3ex]
-{\bfseries Salvatore Filippone} \\
- University of Rome ``Tor Vergata'', Italy 
-%\\[10ex]
-%\today
-Software version: 1.0\\
-%\today
-July 24, 2008
-\or
-\pdfbookmark{MLD2P4 User's and Reference Guide}{title}
-\newlength{\centeroffset}
-%\setlength{\centeroffset}{-0.5\oddsidemargin}
-%\addtolength{\centeroffset}{0.5\evensidemargin}
-%\addtolength{\textwidth}{-\centeroffset}
-\thispagestyle{empty}
-\vspace*{\stretch{1}}
-\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
-\flushright
-{\Huge\bfseries MLD2P4\\[.8ex] User's and Reference Guide
-}
-\noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex]
-\hfill\emph{\Large A guide for the Multi-Level Domain Decomposition \\[.6ex]
-Parallel Preconditioners Package
-based on PSBLAS}
-\end{minipage}}
-
-\vspace{\stretch{1}}
-\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
-\flushright
-{\large\bfseries Pasqua D'Ambra}\\
-\large ICAR-CNR, Naples, Italy\\[3ex]
-{\large\bfseries Daniela di Serafino}\\
-\large Second University of Naples, Italy\\[3ex]
-{\large\bfseries Salvatore Filippone} \\
-\large University of Rome ``Tor Vergata'', Italy 
-%\\[10ex]
-%\today
-\end{minipage}}
-
-\vspace{\stretch{1}}
-\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
-\flushright
-\large Software version: 1.0\\
-%\today
-\large July 24, 2008
-\end{minipage}}
-%\addtolength{\textwidth}{\centeroffset}
-\vspace{\stretch{2}}
-\fi
-
-\endinput
-
-%
-
-% Local Variables:
-% TeX-master: "userguide"
-% mode: latex
-% mode: flyspell
-% End: