From 8ecc4d7200da18df2bff89aac4aca04cf44c9cab Mon Sep 17 00:00:00 2001
From: Salvatore Filippone <salvatore.filippone@cranfield.ac.uk>
Date: Wed, 9 Aug 2017 14:31:44 +0100
Subject: [PATCH] Fixed doc copyright vs contribution

---
 docs/html/index.html      |   73 +-
 docs/html/node1.html      |   32 +-
 docs/html/node10.html     |   61 +-
 docs/html/node11.html     |  152 +--
 docs/html/node12.html     |  355 ++----
 docs/html/node13.html     |  451 +++-----
 docs/html/node14.html     |  486 +++++---
 docs/html/node15.html     |  366 +++---
 docs/html/node16.html     |  403 +++----
 docs/html/node17.html     |  332 ++++--
 docs/html/node18.html     |  175 +--
 docs/html/node19.html     |  822 +-------------
 docs/html/node2.html      |   84 +-
 docs/html/node20.html     |  834 +++++++++++++-
 docs/html/node21.html     |   57 +-
 docs/html/node22.html     |   47 +-
 docs/html/node23.html     |  147 +--
 docs/html/node24.html     |  155 ++-
 docs/html/node25.html     |   80 +-
 docs/html/node26.html     |  166 +--
 docs/html/node27.html     |  149 ++-
 docs/html/node28.html     |   68 +-
 docs/html/node29.html     |  175 +--
 docs/html/node3.html      |   68 +-
 docs/html/node30.html     |  163 ++-
 docs/html/node31.html     |   52 +-
 docs/html/node4.html      |   35 +-
 docs/html/node5.html      |  112 +-
 docs/html/node6.html      |  157 ++-
 docs/html/node7.html      |  113 +-
 docs/html/node8.html      |  279 ++---
 docs/html/node9.html      |  253 ++++-
 docs/html/userhtml.html   |   73 +-
 docs/mld2p4-2.1-guide.pdf | 2271 +++++++++++++++++++------------------
 docs/src/license.tex      |    2 -
 35 files changed, 4653 insertions(+), 4595 deletions(-)

diff --git a/docs/html/index.html b/docs/html/index.html
index 82c86e2e..dfbb0955 100644
--- a/docs/html/index.html
+++ b/docs/html/index.html
@@ -98,70 +98,75 @@ July 31, 2017
   HREF="node3.html">General Overview</A>
 <LI><A NAME="tex2html29"
   HREF="node4.html">Code Distribution</A>
-<LI><A NAME="tex2html30"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
 <UL>
+<LI><A NAME="tex2html30"
+  HREF="node5.html">Contributors</A>
+</UL>
+<BR>
 <LI><A NAME="tex2html31"
-  HREF="node6.html">Prerequisites</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
+<UL>
 <LI><A NAME="tex2html32"
-  HREF="node7.html">Optional third party libraries</A>
+  HREF="node7.html">Prerequisites</A>
 <LI><A NAME="tex2html33"
-  HREF="node8.html">Configuration options</A>
+  HREF="node8.html">Optional third party libraries</A>
 <LI><A NAME="tex2html34"
-  HREF="node9.html">Bug reporting</A>
+  HREF="node9.html">Configuration options</A>
 <LI><A NAME="tex2html35"
-  HREF="node10.html">Example and test programs</A>
+  HREF="node10.html">Bug reporting</A>
+<LI><A NAME="tex2html36"
+  HREF="node11.html">Example and test programs</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html36"
-  HREF="node11.html">Multigrid Background</A>
-<UL>
 <LI><A NAME="tex2html37"
-  HREF="node12.html">AMG preconditioners</A>
+  HREF="node12.html">Multigrid Background</A>
+<UL>
 <LI><A NAME="tex2html38"
-  HREF="node13.html">Smoothed Aggregation</A>
+  HREF="node13.html">AMG preconditioners</A>
 <LI><A NAME="tex2html39"
-  HREF="node14.html">Smoothers and coarsest-level solvers</A>
+  HREF="node14.html">Smoothed Aggregation</A>
+<LI><A NAME="tex2html40"
+  HREF="node15.html">Smoothers and coarsest-level solvers</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html40"
-  HREF="node15.html">Getting Started</A>
-<UL>
 <LI><A NAME="tex2html41"
-  HREF="node16.html">Examples</A>
+  HREF="node16.html">Getting Started</A>
+<UL>
+<LI><A NAME="tex2html42"
+  HREF="node17.html">Examples</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html42"
-  HREF="node17.html">User Interface</A>
-<UL>
 <LI><A NAME="tex2html43"
-  HREF="node18.html">Subroutine init</A>
+  HREF="node18.html">User Interface</A>
+<UL>
 <LI><A NAME="tex2html44"
-  HREF="node19.html">Subroutine set</A>
+  HREF="node19.html">Subroutine init</A>
 <LI><A NAME="tex2html45"
-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
 <LI><A NAME="tex2html46"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
 <LI><A NAME="tex2html47"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
 <LI><A NAME="tex2html48"
-  HREF="node23.html">Subroutine apply</A>
+  HREF="node23.html">Subroutine smoothers_build</A>
 <LI><A NAME="tex2html49"
-  HREF="node24.html">Subroutine free</A>
+  HREF="node24.html">Subroutine apply</A>
 <LI><A NAME="tex2html50"
-  HREF="node25.html">Subroutine descr</A>
+  HREF="node25.html">Subroutine free</A>
+<LI><A NAME="tex2html51"
+  HREF="node26.html">Subroutine descr</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html51"
-  HREF="node26.html">Adding new  smoother and solver objects to MLD2P4</A>
 <LI><A NAME="tex2html52"
-  HREF="node27.html">Error Handling</A>
+  HREF="node27.html">Adding new  smoother and solver objects to MLD2P4</A>
 <LI><A NAME="tex2html53"
-  HREF="node28.html">License</A>
+  HREF="node28.html">Error Handling</A>
 <LI><A NAME="tex2html54"
-  HREF="node29.html">Bibliography</A>
+  HREF="node29.html">License</A>
 <LI><A NAME="tex2html55"
-  HREF="node30.html">About this document ...</A>
+  HREF="node30.html">Bibliography</A>
+<LI><A NAME="tex2html56"
+  HREF="node31.html">About this document ...</A>
 </UL>
 <!--End of Table of Child-Links-->
 <BR><HR>
diff --git a/docs/html/node1.html b/docs/html/node1.html
index ce6ac925..537f9b98 100644
--- a/docs/html/node1.html
+++ b/docs/html/node1.html
@@ -26,26 +26,26 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <BODY >
 <!--Navigation Panel-->
-<A NAME="tex2html66"
+<A NAME="tex2html67"
   HREF="node2.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html62"
+<A NAME="tex2html63"
   HREF="userhtml.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html56"
+<A NAME="tex2html57"
   HREF="userhtml.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html64"
+<A NAME="tex2html65"
   HREF="node2.html">
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 <BR>
-<B> Next:</B> <A NAME="tex2html67"
+<B> Next:</B> <A NAME="tex2html68"
   HREF="node2.html">Contents</A>
-<B> Up:</B> <A NAME="tex2html63"
+<B> Up:</B> <A NAME="tex2html64"
   HREF="userhtml.html">userhtml</A>
-<B> Previous:</B> <A NAME="tex2html57"
+<B> Previous:</B> <A NAME="tex2html58"
   HREF="userhtml.html">userhtml</A>
- &nbsp; <B>  <A NAME="tex2html65"
+ &nbsp; <B>  <A NAME="tex2html66"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
@@ -92,26 +92,26 @@ the user interface of MLD2P4.
   
   </FONT></FONT></FONT><HR>
 <!--Navigation Panel-->
-<A NAME="tex2html66"
+<A NAME="tex2html67"
   HREF="node2.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html62"
+<A NAME="tex2html63"
   HREF="userhtml.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html56"
+<A NAME="tex2html57"
   HREF="userhtml.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html64"
+<A NAME="tex2html65"
   HREF="node2.html">
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
-<B> Next:</B> <A NAME="tex2html67"
+<B> Next:</B> <A NAME="tex2html68"
   HREF="node2.html">Contents</A>
-<B> Up:</B> <A NAME="tex2html63"
+<B> Up:</B> <A NAME="tex2html64"
   HREF="userhtml.html">userhtml</A>
-<B> Previous:</B> <A NAME="tex2html57"
+<B> Previous:</B> <A NAME="tex2html58"
   HREF="userhtml.html">userhtml</A>
- &nbsp; <B>  <A NAME="tex2html65"
+ &nbsp; <B>  <A NAME="tex2html66"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
 
diff --git a/docs/html/node10.html b/docs/html/node10.html
index 1eb7127a..0993cfcf 100644
--- a/docs/html/node10.html
+++ b/docs/html/node10.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Example and test programs</TITLE>
-<META NAME="description" CONTENT="Example and test programs">
+<TITLE>Bug reporting</TITLE>
+<META NAME="description" CONTENT="Bug reporting">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -18,65 +18,50 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
 
+<LINK REL="next" HREF="node11.html">
 <LINK REL="previous" HREF="node9.html">
-<LINK REL="up" HREF="node5.html">
+<LINK REL="up" HREF="node6.html">
 <LINK REL="next" HREF="node11.html">
 </HEAD>
 
 <BODY >
 <!--Navigation Panel-->
-<A NAME="tex2html202"
+<A NAME="tex2html204"
   HREF="node11.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html198"
-  HREF="node5.html">
+<A NAME="tex2html200"
+  HREF="node6.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html194"
   HREF="node9.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html200"
+<A NAME="tex2html202"
   HREF="node2.html">
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
-<B> Next:</B> <A NAME="tex2html203"
-  HREF="node11.html">Multigrid Background</A>
-<B> Up:</B> <A NAME="tex2html199"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
+<B> Next:</B> <A NAME="tex2html205"
+  HREF="node11.html">Example and test programs</A>
+<B> Up:</B> <A NAME="tex2html201"
+  HREF="node6.html">Configuring and Building MLD2P4</A>
 <B> Previous:</B> <A NAME="tex2html195"
-  HREF="node9.html">Bug reporting</A>
- &nbsp; <B>  <A NAME="tex2html201"
+  HREF="node9.html">Configuration options</A>
+ &nbsp; <B>  <A NAME="tex2html203"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00055000000000000000"></A><A NAME="sec:ex_and_test"></A>
-<BR>
-Example and test programs
+<H2><A NAME="SECTION00054000000000000000">
+Bug reporting</A>
 </H2><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-The package contains the <code>examples</code> and <code>tests</code> directories;
-both of them are further divided into <code>fileread</code> and
-<code>pdegen</code> subdirectories. Their purpose is as follows:
-</FONT></FONT></FONT><DL>
-<DT><STRONG><TT>examples</TT></STRONG></DT>
-<DD>contains a set of simple example programs with a
-  predefined choice of preconditioners, selectable via integer
-  values. These are intended to get an acquaintance with the
-  multi-level preconditioners available in MLD2P4.
-</DD>
-<DT><STRONG><TT>tests</TT></STRONG></DT>
-<DD>contains a set of more sophisticated examples that
-  will allow the user, via the input files in the <code>runs</code>
-  subdirectories, to experiment with the full range of preconditioners
-  implemented in the package.
-</DD>
-</DL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-The <code>fileread</code> directories contain sample programs that read
-sparse matrices from files, according to the Matrix Market or the
-Harwell-Boeing storage format; the <code>pdegen</code> programs generate
-matrices in full parallel mode from the discretization of a sample partial
-differential equation. 
+If you find any bugs in our codes, please send an email to <BR><TT>pasqua.dambra@cnr.it</TT> 
+<BR><TT>daniela.diserafino@unicampania.it</TT> 
+<BR><TT>salvatore.filippone@cranfield.ac.uk</TT> <BR>
+You should be aware that the amount of information needed to reproduce a problem
+in a parallel program may vary quite a lot.
 </FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <BR><HR>
 
 </BODY>
diff --git a/docs/html/node11.html b/docs/html/node11.html
index 28beb567..6c27253f 100644
--- a/docs/html/node11.html
+++ b/docs/html/node11.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Multigrid Background</TITLE>
-<META NAME="description" CONTENT="Multigrid Background">
+<TITLE>Example and test programs</TITLE>
+<META NAME="description" CONTENT="Example and test programs">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -18,9 +18,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
 
-<LINK REL="next" HREF="node15.html">
-<LINK REL="previous" HREF="node5.html">
-<LINK REL="up" HREF="userhtml.html">
+<LINK REL="previous" HREF="node10.html">
+<LINK REL="up" HREF="node6.html">
 <LINK REL="next" HREF="node12.html">
 </HEAD>
 
@@ -30,9 +29,9 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node12.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html210"
-  HREF="userhtml.html">
+  HREF="node6.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html204"
+<A NAME="tex2html206"
   HREF="node10.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
 <A NAME="tex2html212"
@@ -40,126 +39,45 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html215"
-  HREF="node12.html">AMG preconditioners</A>
+  HREF="node12.html">Multigrid Background</A>
 <B> Up:</B> <A NAME="tex2html211"
-  HREF="userhtml.html">userhtml</A>
-<B> Previous:</B> <A NAME="tex2html205"
-  HREF="node10.html">Example and test programs</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
+<B> Previous:</B> <A NAME="tex2html207"
+  HREF="node10.html">Bug reporting</A>
  &nbsp; <B>  <A NAME="tex2html213"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
+<H2><A NAME="SECTION00055000000000000000"></A><A NAME="sec:ex_and_test"></A>
 <BR>
-Multigrid Background
-</H1><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Multigrid preconditioners, coupled with Krylov iterative
-solvers, are widely used in the parallel solution of large and sparse linear systems,
-because of their optimality in the solution of linear systems arising from the
-discretization of scalar elliptic Partial Differential Equations (PDEs) on regular grids.
-Optimality, also known as algorithmic scalability, is the property 
-of having a computational cost per iteration that depends linearly on
-the problem size, and a convergence rate that is independent of the problem size.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Multigrid preconditioners are based on a recursive application of a two-grid process
-consisting of smoother iterations and a coarse-space (or coarse-level) correction.
-The smoothers may be either basic iterative methods, such as the Jacobi and Gauss-Seidel ones,
-or more complex subspace-correction methods, such as the Schwarz ones.
-The coarse-space correction consists of solving, in an appropriately chosen
-coarse space, the residual equation associated with the approximate solution computed
-by the smoother, and of using the solution of this equation to correct the
-previous approximation. The transfer of information between the original
-(fine) space and the coarse one is performed by using suitable restriction and
-prolongation operators. The construction of the coarse space and the corresponding
-transfer operators is carried out by applying a so-called coarsening algorithm to the system
-matrix. Two main approaches can be used to perform coarsening: the geometric approach,
-which exploits the knowledge of some physical grid associated with the matrix
-and requires the user to define transfer operators from the fine
-to the coarse level and vice versa, and the algebraic approach, which builds
-the coarse-space correction and the associate transfer operators using only matrix
-information. The first approach may be difficult when the system comes from
-discretizations on complex geometries;
-furthermore, ad hoc one-level smoothers may be required to get an efficient
-interplay between fine and coarse levels, e.g., when matrices with highly varying coefficients
-are considered. The second approach performs a fully automatic coarsening and enforces the
-interplay between fine and coarse level by suitably choosing the coarse space and
-the coarse-to-fine interpolation (see, e.g., [<A
- HREF="node29.html#Briggs2000">3</A>,<A
- HREF="node29.html#Stuben_01">23</A>,<A
- HREF="node29.html#dd2_96">21</A>] for details.)
+Example and test programs
+</H2><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+The package contains the <code>examples</code> and <code>tests</code> directories;
+both of them are further divided into <code>fileread</code> and
+<code>pdegen</code> subdirectories. Their purpose is as follows:
+</FONT></FONT></FONT><DL>
+<DT><STRONG><TT>examples</TT></STRONG></DT>
+<DD>contains a set of simple example programs with a
+  predefined choice of preconditioners, selectable via integer
+  values. These are intended to get an acquaintance with the
+  multi-level preconditioners available in MLD2P4.
+</DD>
+<DT><STRONG><TT>tests</TT></STRONG></DT>
+<DD>contains a set of more sophisticated examples that
+  will allow the user, via the input files in the <code>runs</code>
+  subdirectories, to experiment with the full range of preconditioners
+  implemented in the package.
+</DD>
+</DL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+The <code>fileread</code> directories contain sample programs that read
+sparse matrices from files, according to the Matrix Market or the
+Harwell-Boeing storage format; the <code>pdegen</code> programs generate
+matrices in full parallel mode from the discretization of a sample partial
+differential equation. 
 </FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">MLD2P4 uses a pure algebraic approach, based on the smoothed 
-aggregation algorithm [<A
- HREF="node29.html#BREZINA_VANEK">2</A>,<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>],
-for building the sequence of coarse matrices and transfer operators,
-starting from the original one.
-A decoupled version of this algorithm is implemented, where the smoothed
-aggregation is applied locally to each submatrix [<A
- HREF="node29.html#TUMINARO_TONG">24</A>].
-A brief description of the AMG preconditioners implemented in MLD2P4 is given in 
-Sections&nbsp;<A HREF="node12.html#sec:multilevel">4.1</A>-<A HREF="node14.html#sec:smoothers">4.3</A>. For further details the reader
-is referred to [<A
- HREF="node29.html#para_04">4</A>,<A
- HREF="node29.html#aaecc_07">5</A>,<A
- HREF="node29.html#apnum_07">7</A>,<A
- HREF="node29.html#MLD2P4_TOMS">8</A>].
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We note that optimal multigrid preconditioners do not necessarily correspond
-to minimum execution times in a parallel setting. Indeed, to obtain effective parallel
-multigrid preconditioners, a tradeoff between the optimality and the cost of building and
-applying the smoothers and the coarse-space corrections must be achieved. Effective
-parallel preconditioners require algorithmic scalability to be coupled with implementation
-scalability, i.e., a computational cost per iteration which remains (almost) constant as
-the number of parallel processors increases.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <BR><HR>
-<!--Table of Child-Links-->
-<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
-
-<UL>
-<LI><A NAME="tex2html216"
-  HREF="node12.html">AMG preconditioners</A>
-<LI><A NAME="tex2html217"
-  HREF="node13.html">Smoothed Aggregation</A>
-<LI><A NAME="tex2html218"
-  HREF="node14.html">Smoothers and coarsest-level solvers</A>
-</UL>
-<!--End of Table of Child-Links-->
-<HR>
-<!--Navigation Panel-->
-<A NAME="tex2html214"
-  HREF="node12.html">
-<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
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@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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-<H2><A NAME="SECTION00061000000000000000"></A><A NAME="sec:multilevel"></A>
-<BR>
-AMG preconditioners
-</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to describe the AMG preconditioners available in MLD2P4, we consider a
-linear system
-</FONT></FONT></FONT>
+<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
 <BR>
-<DIV ALIGN="RIGHT">
+Multigrid Background
+</H1><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
 
-<!-- MATH
- \begin{equation}
-Ax=b,
-\end{equation}
- -->
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:system"></A><IMG
- WIDTH="58" HEIGHT="30" BORDER="0"
- SRC="img2.png"
- ALT="\begin{displaymath}
-Ax=b,
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(2)</TD></TR>
-</TABLE>
-<BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-where <!-- MATH
- $A=(a_{ij}) \in \mathbb{R}^{n \times n}$
- -->
-<IMG
- WIDTH="137" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img5.png"
- ALT="$A=(a_{ij}) \in \mathbb{R}^{n \times n}$"> is a nonsingular sparse matrix;
-for ease of presentation we assume <IMG
- WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img3.png"
- ALT="$A$"> is real, but the
-results are valid for the complex case as well. 
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Let us assume as finest index space the set of row (column) indices of <IMG
- WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img3.png"
- ALT="$A$">, i.e.,
-<!-- MATH
- $\Omega = \{1, 2, \ldots, n\}$
- -->
-<IMG
- WIDTH="132" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
- SRC="img6.png"
- ALT="$\Omega = \{1, 2, \ldots, n\}$">. 
-Any algebraic multilevel preconditioners implemented in MLD2P4 generates
-a hierarchy of index spaces and a corresponding hierarchy of matrices,
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Multigrid preconditioners, coupled with Krylov iterative
+solvers, are widely used in the parallel solution of large and sparse linear systems,
+because of their optimality in the solution of linear systems arising from the
+discretization of scalar elliptic Partial Differential Equations (PDEs) on regular grids.
+Optimality, also known as algorithmic scalability, is the property 
+of having a computational cost per iteration that depends linearly on
+the problem size, and a convergence rate that is independent of the problem size.
 </FONT></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH
- \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}
- -->
-
-<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}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-by using the information contained in <IMG
- WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img3.png"
- ALT="$A$">, without assuming any
-knowledge of the geometry of the problem from which <IMG
- WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img3.png"
- ALT="$A$"> originates.
-A vector space <!-- MATH
- $\mathbb{R}^{n_{k}}$
- -->
-<IMG
- WIDTH="33" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.png"
- ALT="$\mathbb{R}^{n_{k}}$"> is associated with <IMG
- WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img9.png"
- ALT="$\Omega^k$">,
-where <IMG
- WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img10.png"
- ALT="$n_k$"> is the size of <IMG
- WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img9.png"
- ALT="$\Omega^k$">.
-For all <IMG
- WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
- SRC="img11.png"
- ALT="$k &lt; nlev$">, a restriction operator and a prolongation one are built,
-which connect two levels <IMG
- WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img12.png"
- ALT="$k$"> and <IMG
- WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
- SRC="img13.png"
- ALT="$k+1$">:
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Multigrid preconditioners are based on a recursive application of a two-grid process
+consisting of smoother iterations and a coarse-space (or coarse-level) correction.
+The smoothers may be either basic iterative methods, such as the Jacobi and Gauss-Seidel ones,
+or more complex subspace-correction methods, such as the Schwarz ones.
+The coarse-space correction consists of solving, in an appropriately chosen
+coarse space, the residual equation associated with the approximate solution computed
+by the smoother, and of using the solution of this equation to correct the
+previous approximation. The transfer of information between the original
+(fine) space and the coarse one is performed by using suitable restriction and
+prolongation operators. The construction of the coarse space and the corresponding
+transfer operators is carried out by applying a so-called coarsening algorithm to the system
+matrix. Two main approaches can be used to perform coarsening: the geometric approach,
+which exploits the knowledge of some physical grid associated with the matrix
+and requires the user to define transfer operators from the fine
+to the coarse level and vice versa, and the algebraic approach, which builds
+the coarse-space correction and the associate transfer operators using only matrix
+information. The first approach may be difficult when the system comes from
+discretizations on complex geometries;
+furthermore, ad hoc one-level smoothers may be required to get an efficient
+interplay between fine and coarse levels, e.g., when matrices with highly varying coefficients
+are considered. The second approach performs a fully automatic coarsening and enforces the
+interplay between fine and coarse level by suitably choosing the coarse space and
+the coarse-to-fine interpolation (see, e.g., [<A
+ HREF="node30.html#Briggs2000">3</A>,<A
+ HREF="node30.html#Stuben_01">23</A>,<A
+ HREF="node30.html#dd2_96">21</A>] for details.)
 </FONT></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH
- \begin{displaymath}
-P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad 
-    R^k \in \mathbb{R}^{n_{k+1}\times n_k};
-\end{displaymath}
- -->
-
-<IMG
- WIDTH="254" HEIGHT="30" BORDER="0"
- SRC="img14.png"
- ALT="\begin{displaymath}
 P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad 
 R^k \in \mathbb{R}^{n_{k+1}\times n_k};
\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-the matrix <IMG
- WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img15.png"
- ALT="$A^{k+1}$"> is computed by using the previous operators according
-to the Galerkin approach, i.e.,
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">MLD2P4 uses a pure algebraic approach, based on the smoothed 
+aggregation algorithm [<A
+ HREF="node30.html#BREZINA_VANEK">2</A>,<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>],
+for building the sequence of coarse matrices and transfer operators,
+starting from the original one.
+A decoupled version of this algorithm is implemented, where the smoothed
+aggregation is applied locally to each submatrix [<A
+ HREF="node30.html#TUMINARO_TONG">24</A>].
+A brief description of the AMG preconditioners implemented in MLD2P4 is given in 
+Sections&nbsp;<A HREF="node13.html#sec:multilevel">4.1</A>-<A HREF="node15.html#sec:smoothers">4.3</A>. For further details the reader
+is referred to [<A
+ HREF="node30.html#para_04">4</A>,<A
+ HREF="node30.html#aaecc_07">5</A>,<A
+ HREF="node30.html#apnum_07">7</A>,<A
+ HREF="node30.html#MLD2P4_TOMS">8</A>].
 </FONT></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH
- \begin{displaymath}
-A^{k+1}=R^kA^kP^k.
-\end{displaymath}
- -->
-
-<IMG
- WIDTH="131" HEIGHT="27" BORDER="0"
- SRC="img16.png"
- ALT="\begin{displaymath}
 A^{k+1}=R^kA^kP^k.
\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-In the current implementation of MLD2P4 we have <IMG
- WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img17.png"
- ALT="$R^k=(P^k)^T$">
-A smoother with iteration matrix <IMG
- WIDTH="32" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img18.png"
- ALT="$M^k$"> is set up at each level <IMG
- WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
- SRC="img11.png"
- ALT="$k &lt; nlev$">, 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 <IMG
- WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img19.png"
- ALT="$LU$"> factorization means computing
-and storing the <IMG
- WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img20.png"
- ALT="$L$"> and <IMG
- WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img21.png"
- ALT="$U$"> factors). The construction of the hierarchy of AMG components
-described so far corresponds to the so-called build phase of the preconditioner.
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We note that optimal multigrid preconditioners do not necessarily correspond
+to minimum execution times in a parallel setting. Indeed, to obtain effective parallel
+multigrid preconditioners, a tradeoff between the optimality and the cost of building and
+applying the smoothers and the coarse-space corrections must be achieved. Effective
+parallel preconditioners require algorithmic scalability to be coupled with implementation
+scalability, i.e., a computational cost per iteration which remains (almost) constant as
+the number of parallel processors increases.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><A NAME="fig:application_alg"></A><A NAME="517"></A>
-<TABLE>
-<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
-Application phase of a V-cycle preconditioner.</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<!-- MATH
- $\framebox{
-\begin{minipage}{.85\textwidth}
-\begin{tabbing}
-\quad \=\quad \=\quad \=\quad \\[-3mm]
-procedure V-cycle$\left(k,A^k,b^k,u^k\right)$\  \\[2mm]
-\>if $\left(k \ne nlev \right)$\  then \\[1mm]
-\>\> $u^k = u^k + M^k \left(b^k - A^k u^k\right)$\  \\[1mm]
-\>\> $b^{k+1} = R^{k+1}\left(b^k - A^k u^k\right)$\  \\[1mm]
-\>\> $u^{k+1} =$\  V-cycle$\left(k+1,A^{k+1},b^{k+1},0\right)$\  \\[1mm]
-\>\> $u^k = u^k + P^{k+1} u^{k+1}$\  \\[1mm]
-\>\> $u^k = u^k + M^k \left(b^k - A^k u^k\right)$\  \\[1mm]
-\>else \\[1mm]
-\>\> $u^k = \left(A^k\right)^{-1} b^k$\\[1mm]
-\>endif \\[1mm]
-\>return $u^k$\  \\[1mm]
-end
-\end{tabbing}
-\end{minipage}
-}$
- -->
-<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}
}">
+<BR><HR>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
 
-</DIV></TD></TR>
-</TABLE>
-</DIV>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The components produced in the build phase may be combined in several ways
-to obtain different multilevel preconditioners;
-this is  done in the application phase, i.e., in the computation of a vector
-of type <IMG
- WIDTH="82" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img23.png"
- ALT="$w=B^{-1}v$">, where <IMG
- WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img24.png"
- ALT="$B$"> denotes the preconditioner, usually within an iteration
-of a Krylov solver [<A
- HREF="node29.html#Saad_book">20</A>]. An example of such a combination, known as
-V-cycle, is given in Figure&nbsp;<A HREF="#fig:application_alg">1</A>. In this case, a single iteration
-of the same smoother is used before and after the the recursive call to the V-cycle (i.e.,
-in the pre-smoothing and post-smoothing phases); however, different choices can be
-performed. Other cycles can be defined; in MLD2P4, we implemented the standard V-cycle
-and W-cycle&nbsp;[<A
- HREF="node29.html#Briggs2000">3</A>], and a version of the K-cycle described
-in&nbsp;[<A
- HREF="node29.html#Notay2008">19</A>].  
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
+<UL>
+<LI><A NAME="tex2html228"
+  HREF="node13.html">AMG preconditioners</A>
+<LI><A NAME="tex2html229"
+  HREF="node14.html">Smoothed Aggregation</A>
+<LI><A NAME="tex2html230"
+  HREF="node15.html">Smoothers and coarsest-level solvers</A>
+</UL>
+<!--End of Table of Child-Links-->
+<HR>
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diff --git a/docs/html/node13.html b/docs/html/node13.html
index 2e779069..ff0c3b63 100644
--- a/docs/html/node13.html
+++ b/docs/html/node13.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Smoothed Aggregation</TITLE>
-<META NAME="description" CONTENT="Smoothed Aggregation">
+<TITLE>AMG preconditioners</TITLE>
+<META NAME="description" CONTENT="AMG preconditioners">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node14.html">
 <LINK REL="previous" HREF="node12.html">
-<LINK REL="up" HREF="node11.html">
+<LINK REL="up" HREF="node12.html">
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 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node14.html">
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-  HREF="node11.html">
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@@ -40,336 +40,247 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
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+  HREF="node14.html">Smoothed Aggregation</A>
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-  HREF="node11.html">Multigrid Background</A>
+  HREF="node12.html">Multigrid Background</A>
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-<H2><A NAME="SECTION00062000000000000000"></A><A NAME="sec:aggregation"></A>
+<H2><A NAME="SECTION00061000000000000000"></A><A NAME="sec:multilevel"></A>
 <BR>
-Smoothed Aggregation
+AMG preconditioners
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to define the prolongator <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.png"
- ALT="$P^k$">, used to compute
-the coarse-level matrix <IMG
- WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img15.png"
- ALT="$A^{k+1}$">, MLD2P4 uses the smoothed aggregation
-algorithm described in [<A
- HREF="node29.html#BREZINA_VANEK">2</A>,<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>].
-The basic idea of this algorithm is to build a coarse set of indices
-<IMG
- WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img26.png"
- ALT="$\Omega^{k+1}$"> by suitably grouping the indices of <IMG
- WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img9.png"
- ALT="$\Omega^k$"> into disjoint
-subsets (aggregates), and to define the coarse-to-fine space transfer operator
-<IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.png"
- ALT="$P^k$"> by applying a suitable smoother to a simple piecewise constant
-prolongation operator, with the aim of improving the quality of the coarse-space correction.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Three main steps can be identified in the smoothed aggregation procedure:
-</FONT></FONT></FONT>
-<OL>
-<LI>aggregation of the indices of <IMG
- WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img9.png"
- ALT="$\Omega^k$"> to obtain <IMG
- WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img26.png"
- ALT="$\Omega^{k+1}$">;
-</LI>
-<LI>construction of the prolongator <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.png"
- ALT="$P^k$">;
-</LI>
-<LI>application of <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.png"
- ALT="$P^k$"> and <IMG
- WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img17.png"
- ALT="$R^k=(P^k)^T$"> to build <IMG
- WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img15.png"
- ALT="$A^{k+1}$">.
-</LI>
-</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to perform the coarsening step, the smoothed aggregation algorithm
-described in&nbsp;[<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>] is used. In this algorithm,
-each index <!-- MATH
- $j \in \Omega^{k+1}$
- -->
-<IMG
- WIDTH="72" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img27.png"
- ALT="$j \in \Omega^{k+1}$"> corresponds to an aggregate <IMG
- WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img28.png"
- ALT="$\Omega^k_j$"> of <IMG
- WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img9.png"
- ALT="$\Omega^k$">,
-consisting of a suitably chosen index <!-- MATH
- $i \in \Omega^k$
- -->
-<IMG
- WIDTH="52" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img29.png"
- ALT="$i \in \Omega^k$"> and indices that are (usually) contained in a
-strongly-coupled neighborood of <IMG
- WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img30.png"
- ALT="$i$">, i.e.,
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to describe the AMG preconditioners available in MLD2P4, we consider a
+linear system
 </FONT></FONT></FONT>
 <BR>
 <DIV ALIGN="RIGHT">
 
 <!-- MATH
  \begin{equation}
-\Omega^k_j \subset \mathcal{N}_i^k(\theta) = 
-   \left\{ r \in \Omega^k: |a_{ir}^k| > \theta \sqrt{|a_{ii}^ka_{rr}^k|} \right \} \cup \left\{ i \right\},
+Ax=b,
 \end{equation}
  -->
 <TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:strongly_coup"></A><IMG
- WIDTH="387" HEIGHT="72" BORDER="0"
- SRC="img31.png"
+<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:system"></A><IMG
+ WIDTH="58" HEIGHT="30" BORDER="0"
+ SRC="img2.png"
  ALT="\begin{displaymath}
-\Omega^k_j \subset \mathcal{N}_i^k(\theta) = 
 \left\{ r ...
-...vert a_{ii}^ka_{rr}^k\vert} \right \} \cup \left\{ i \right\},
\end{displaymath}"></TD>
+Ax=b,
+\end{displaymath}"></TD>
 <TD WIDTH=10 ALIGN="RIGHT">
-(3)</TD></TR>
+(2)</TD></TR>
 </TABLE>
 <BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-for a given threshold <!-- MATH
- $\theta \in [0,1]$
+where <!-- MATH
+ $A=(a_{ij}) \in \mathbb{R}^{n \times n}$
  -->
 <IMG
- WIDTH="69" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
- SRC="img32.png"
- ALT="$\theta \in [0,1]$"> (see&nbsp;[<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>] for the details).
-Since this algorithm has a sequential nature, a decoupled
-version of it is applied, where each processor independently executes
-the algorithm on the set of indices assigned to it in the initial data
-distribution. This version is embarrassingly parallel, since it does not require any data 
-communication. On the other hand, it may produce some nonuniform aggregates
-and is strongly dependent on the number of processors and on the initial partitioning
-of the matrix <IMG
+ WIDTH="137" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ SRC="img5.png"
+ ALT="$A=(a_{ij}) \in \mathbb{R}^{n \times n}$"> is a nonsingular sparse matrix;
+for ease of presentation we assume <IMG
  WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
  SRC="img3.png"
- ALT="$A$">. Nevertheless, this parallel algorithm has been chosen for
-MLD2P4, since it has been shown to produce good results in practice
-[<A
- HREF="node29.html#aaecc_07">5</A>,<A
- HREF="node29.html#apnum_07">7</A>,<A
- HREF="node29.html#TUMINARO_TONG">24</A>].
+ ALT="$A$"> is real, but the
+results are valid for the complex case as well. 
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The prolongator <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.png"
- ALT="$P^k$"> is built starting from a tentative prolongator
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Let us assume as finest index space the set of row (column) indices of <IMG
+ WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img3.png"
+ ALT="$A$">, i.e.,
 <!-- MATH
- $\bar{P}^k \in \mathbb{R}^{n_k \times n_{k+1}}$
+ $\Omega = \{1, 2, \ldots, n\}$
  -->
 <IMG
- WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img33.png"
- ALT="$\bar{P}^k \in \mathbb{R}^{n_k \times n_{k+1}}$">, defined as
+ WIDTH="132" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ SRC="img6.png"
+ ALT="$\Omega = \{1, 2, \ldots, n\}$">. 
+Any algebraic multilevel preconditioners implemented in MLD2P4 generates
+a hierarchy of index spaces and a corresponding hierarchy of matrices,
 </FONT></FONT></FONT>
-<BR>
-<DIV ALIGN="RIGHT">
-
+<BR><P></P>
+<DIV ALIGN="CENTER">
 <!-- MATH
- \begin{equation}
-\bar{P}^k =(\bar{p}_{ij}^k), \quad  \bar{p}_{ij}^k = 
-\left\{ \begin{array}{ll}
-1 & \quad \mbox{if} \; i \in \Omega^k_j, \\
-0 & \quad \mbox{otherwise},
-\end{array} \right.
-\end{equation}
- -->
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:tent_prol"></A><IMG
- WIDTH="287" HEIGHT="51" BORDER="0"
- SRC="img34.png"
- ALT="\begin{displaymath}
\bar{P}^k =(\bar{p}_{ij}^k), \quad \bar{p}_{ij}^k = 
\left\{...
-...ega^k_j, \ 
0 &amp; \quad \mbox{otherwise},
\end{array} \right.
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(4)</TD></TR>
-</TABLE>
-<BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-where <IMG
- WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img28.png"
- ALT="$\Omega^k_j$"> is the aggregate of <IMG
- WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img9.png"
- ALT="$\Omega^k$">
-corresponding to the index <!-- MATH
- $j \in \Omega^{k+1}$
+ \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}
  -->
+
 <IMG
- WIDTH="72" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img27.png"
- ALT="$j \in \Omega^{k+1}$">.
-<IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.png"
- ALT="$P^k$"> is obtained by applying to <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img35.png"
- ALT="$\bar{P}^k$"> a smoother
-<!-- MATH
- $S^k \in \mathbb{R}^{n_k \times n_k}$
+ 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}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+by using the information contained in <IMG
+ WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img3.png"
+ ALT="$A$">, without assuming any
+knowledge of the geometry of the problem from which <IMG
+ WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img3.png"
+ ALT="$A$"> originates.
+A vector space <!-- MATH
+ $\mathbb{R}^{n_{k}}$
  -->
 <IMG
- WIDTH="101" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img36.png"
- ALT="$S^k \in \mathbb{R}^{n_k \times n_k}$">:
+ WIDTH="33" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img8.png"
+ ALT="$\mathbb{R}^{n_{k}}$"> is associated with <IMG
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img9.png"
+ ALT="$\Omega^k$">,
+where <IMG
+ WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img10.png"
+ ALT="$n_k$"> is the size of <IMG
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img9.png"
+ ALT="$\Omega^k$">.
+For all <IMG
+ WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
+ SRC="img11.png"
+ ALT="$k &lt; nlev$">, a restriction operator and a prolongation one are built,
+which connect two levels <IMG
+ WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img12.png"
+ ALT="$k$"> and <IMG
+ WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
+ SRC="img13.png"
+ ALT="$k+1$">:
 </FONT></FONT></FONT>
 <BR><P></P>
 <DIV ALIGN="CENTER">
 <!-- MATH
  \begin{displaymath}
-P^k = S^k \bar{P}^k,
+P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad 
+    R^k \in \mathbb{R}^{n_{k+1}\times n_k};
 \end{displaymath}
  -->
 
 <IMG
- WIDTH="90" HEIGHT="30" BORDER="0"
- SRC="img37.png"
- ALT="\begin{displaymath}
P^k = S^k \bar{P}^k,
\end{displaymath}">
+ WIDTH="254" HEIGHT="30" BORDER="0"
+ SRC="img14.png"
+ ALT="\begin{displaymath}
 P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad 
 R^k \in \mathbb{R}^{n_{k+1}\times n_k};
\end{displaymath}">
 </DIV>
 <BR CLEAR="ALL">
 <P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-in order to remove nonsmooth components from the range of the prolongator,
-and hence to improve the convergence properties of the multi-level
-method&nbsp;[<A
- HREF="node29.html#BREZINA_VANEK">2</A>,<A
- HREF="node29.html#Stuben_01">23</A>].
-A simple choice for <IMG
- WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
- SRC="img38.png"
- ALT="$S^k$"> is the damped Jacobi smoother:
+the matrix <IMG
+ WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img15.png"
+ ALT="$A^{k+1}$"> is computed by using the previous operators according
+to the Galerkin approach, i.e.,
 </FONT></FONT></FONT>
 <BR><P></P>
 <DIV ALIGN="CENTER">
 <!-- MATH
  \begin{displaymath}
-S^k = I - \omega^k (D^k)^{-1} A^k_F ,
+A^{k+1}=R^kA^kP^k.
 \end{displaymath}
  -->
 
 <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}">
+ WIDTH="131" HEIGHT="27" BORDER="0"
+ SRC="img16.png"
+ ALT="\begin{displaymath}
 A^{k+1}=R^kA^kP^k.
\end{displaymath}">
 </DIV>
 <BR CLEAR="ALL">
 <P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-where <IMG
- WIDTH="28" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img40.png"
- ALT="$D^k$"> is the diagonal matrix with the same diagonal entries as <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img41.png"
- ALT="$A^k$">,
+In the current implementation of MLD2P4 we have <IMG
+ WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img17.png"
+ ALT="$R^k=(P^k)^T$">
+A smoother with iteration matrix <IMG
+ WIDTH="32" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img18.png"
+ ALT="$M^k$"> is set up at each level <IMG
+ WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
+ SRC="img11.png"
+ ALT="$k &lt; nlev$">, 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 <IMG
+ WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.png"
+ ALT="$LU$"> factorization means computing
+and storing the <IMG
+ WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img20.png"
+ ALT="$L$"> and <IMG
+ WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img21.png"
+ ALT="$U$"> factors). The construction of the hierarchy of AMG components
+described so far corresponds to the so-called build phase of the preconditioner.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><A NAME="fig:application_alg"></A><A NAME="524"></A>
+<TABLE>
+<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
+Application phase of a V-cycle preconditioner.</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
 <!-- MATH
- $A^k_F = (\bar{a}_{ij}^k)$
+ $\framebox{
+\begin{minipage}{.85\textwidth}
+\begin{tabbing}
+\quad \=\quad \=\quad \=\quad \\[-3mm]
+procedure V-cycle$\left(k,A^k,b^k,u^k\right)$\  \\[2mm]
+\>if $\left(k \ne nlev \right)$\  then \\[1mm]
+\>\> $u^k = u^k + M^k \left(b^k - A^k u^k\right)$\  \\[1mm]
+\>\> $b^{k+1} = R^{k+1}\left(b^k - A^k u^k\right)$\  \\[1mm]
+\>\> $u^{k+1} =$\  V-cycle$\left(k+1,A^{k+1},b^{k+1},0\right)$\  \\[1mm]
+\>\> $u^k = u^k + P^{k+1} u^{k+1}$\  \\[1mm]
+\>\> $u^k = u^k + M^k \left(b^k - A^k u^k\right)$\  \\[1mm]
+\>else \\[1mm]
+\>\> $u^k = \left(A^k\right)^{-1} b^k$\\[1mm]
+\>endif \\[1mm]
+\>return $u^k$\  \\[1mm]
+end
+\end{tabbing}
+\end{minipage}
+}$
  -->
 <IMG
- WIDTH="87" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img42.png"
- ALT="$A^k_F = (\bar{a}_{ij}^k)$"> is the filtered matrix defined as
-</FONT></FONT></FONT>
-<BR>
-<DIV ALIGN="RIGHT">
+ 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}
}">
 
-<!-- MATH
- \begin{equation}
-\bar{a}_{ij}^k =
-   \left \{ \begin{array}{ll}
-   a_{ij}^k & \mbox{if } j \in \mathcal{N}_i^k(\theta), \\
-   0            & \mbox{otherwise},
-   \end{array} \right.
-   \; (j \ne i),
-   \qquad
-   \bar{a}_{ii}^k = a_{ii}^k - \sum_{j \ne i} (a_{ij}^k - \bar{a}_{ij}^k),
-\end{equation}
- -->
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:filtered"></A><IMG
- WIDTH="514" HEIGHT="74" BORDER="0"
- SRC="img43.png"
- ALT="\begin{displaymath}
-\bar{a}_{ij}^k =
 \left \{ \begin{array}{ll}
 a_{ij}^k &amp; ...
-...ii}^k = a_{ii}^k - \sum_{j \ne i} (a_{ij}^k - \bar{a}_{ij}^k),
\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(5)</TD></TR>
+</DIV></TD></TR>
 </TABLE>
-<BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-and <IMG
- WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
- SRC="img44.png"
- ALT="$\omega^k$"> is an approximation of <IMG
- WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img45.png"
- ALT="$4/(3\rho^k)$">, where
-<IMG
- WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img46.png"
- ALT="$\rho^k$"> is the spectral radius of <!-- MATH
- $(D^k)^{-1}A^k_F$
- -->
-<IMG
- WIDTH="83" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img47.png"
- ALT="$(D^k)^{-1}A^k_F$"> [<A
- HREF="node29.html#BREZINA_VANEK">2</A>].
-In MLD2P4 this approximation is obtained by using <!-- MATH
- $\| A^k_F \|_\infty$
- -->
-<IMG
- WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img48.png"
- ALT="$\Vert A^k_F \Vert _\infty$"> as an estimate
-of <IMG
- WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img46.png"
- ALT="$\rho^k$">. Note that for systems coming from uniformly elliptic
-problems, filtering the matrix <IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img41.png"
- ALT="$A^k$"> has little or no effect, and
-<IMG
- WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img41.png"
- ALT="$A^k$"> can be used instead of <IMG
- WIDTH="29" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img49.png"
- ALT="$A^k_F$">. The latter choice is the default in MLD2P4.
+</DIV>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The components produced in the build phase may be combined in several ways
+to obtain different multilevel preconditioners;
+this is  done in the application phase, i.e., in the computation of a vector
+of type <IMG
+ WIDTH="82" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
+ SRC="img23.png"
+ ALT="$w=B^{-1}v$">, where <IMG
+ WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img24.png"
+ ALT="$B$"> denotes the preconditioner, usually within an iteration
+of a Krylov solver [<A
+ HREF="node30.html#Saad_book">20</A>]. An example of such a combination, known as
+V-cycle, is given in Figure&nbsp;<A HREF="#fig:application_alg">1</A>. In this case, a single iteration
+of the same smoother is used before and after the the recursive call to the V-cycle (i.e.,
+in the pre-smoothing and post-smoothing phases); however, different choices can be
+performed. Other cycles can be defined; in MLD2P4, we implemented the standard V-cycle
+and W-cycle&nbsp;[<A
+ HREF="node30.html#Briggs2000">3</A>], and a version of the K-cycle described
+in&nbsp;[<A
+ HREF="node30.html#Notay2008">19</A>].  
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
@@ -378,7 +289,7 @@ problems, filtering the matrix <IMG
   HREF="node14.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html237"
-  HREF="node11.html">
+  HREF="node12.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html231"
   HREF="node12.html">
@@ -388,11 +299,11 @@ problems, filtering the matrix <IMG
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html242"
-  HREF="node14.html">Smoothers and coarsest-level solvers</A>
+  HREF="node14.html">Smoothed Aggregation</A>
 <B> Up:</B> <A NAME="tex2html238"
-  HREF="node11.html">Multigrid Background</A>
+  HREF="node12.html">Multigrid Background</A>
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-  HREF="node12.html">AMG preconditioners</A>
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@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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-<H2><A NAME="SECTION00063000000000000000"></A><A NAME="sec:smoothers"></A>
+<H2><A NAME="SECTION00062000000000000000"></A><A NAME="sec:aggregation"></A>
 <BR>
-Smoothers and coarsest-level solvers
+Smoothed Aggregation
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The smoothers implemented in MLD2P4 include the Jacobi and block-Jacobi methods,
-a hybrid version of the forward and backward Gauss-Seidel methods, and the
-additive Schwarz (AS) ones (see, e.g., [<A
- HREF="node29.html#Saad_book">20</A>,<A
- HREF="node29.html#dd2_96">21</A>]). 
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to define the prolongator <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img25.png"
+ ALT="$P^k$">, used to compute
+the coarse-level matrix <IMG
+ WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img15.png"
+ ALT="$A^{k+1}$">, MLD2P4 uses the smoothed aggregation
+algorithm described in [<A
+ HREF="node30.html#BREZINA_VANEK">2</A>,<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>].
+The basic idea of this algorithm is to build a coarse set of indices
+<IMG
+ WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img26.png"
+ ALT="$\Omega^{k+1}$"> by suitably grouping the indices of <IMG
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img9.png"
+ ALT="$\Omega^k$"> into disjoint
+subsets (aggregates), and to define the coarse-to-fine space transfer operator
+<IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img25.png"
+ ALT="$P^k$"> by applying a suitable smoother to a simple piecewise constant
+prolongation operator, with the aim of improving the quality of the coarse-space correction.
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The hybrid Gauss-Seidel
-version is considered because the original Gauss-Seidel method is inherently sequential.
-At each iteration of the hybrid version, each parallel process uses the most recent values
-of its own local variables and the values of the non-local variables computed at the
-previous iteration, obtained by exchanging data with other processes before
-the beginning of the current iteration.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Three main steps can be identified in the smoothed aggregation procedure:
 </FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In the AS methods, the index space <IMG
+<OL>
+<LI>aggregation of the indices of <IMG
  WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
  SRC="img9.png"
- ALT="$\Omega^k$"> is divided into <IMG
- WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img50.png"
- ALT="$m_k$">
-subsets <IMG
+ ALT="$\Omega^k$"> to obtain <IMG
+ WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img26.png"
+ ALT="$\Omega^{k+1}$">;
+</LI>
+<LI>construction of the prolongator <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img25.png"
+ ALT="$P^k$">;
+</LI>
+<LI>application of <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img25.png"
+ ALT="$P^k$"> and <IMG
+ WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img17.png"
+ ALT="$R^k=(P^k)^T$"> to build <IMG
+ WIDTH="43" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img15.png"
+ ALT="$A^{k+1}$">.
+</LI>
+</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to perform the coarsening step, the smoothed aggregation algorithm
+described in&nbsp;[<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>] is used. In this algorithm,
+each index <!-- MATH
+ $j \in \Omega^{k+1}$
+ -->
+<IMG
+ WIDTH="72" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img27.png"
+ ALT="$j \in \Omega^{k+1}$"> corresponds to an aggregate <IMG
  WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img51.png"
- ALT="$\Omega^k_i$"> of size <IMG
- WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img52.png"
- ALT="$n_{k,i}$">,  possibly
-overlapping. For each <IMG
+ SRC="img28.png"
+ ALT="$\Omega^k_j$"> of <IMG
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img9.png"
+ ALT="$\Omega^k$">,
+consisting of a suitably chosen index <!-- MATH
+ $i \in \Omega^k$
+ -->
+<IMG
+ WIDTH="52" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img29.png"
+ ALT="$i \in \Omega^k$"> and indices that are (usually) contained in a
+strongly-coupled neighborood of <IMG
  WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
  SRC="img30.png"
- ALT="$i$"> we consider the restriction
-operator <!-- MATH
- $R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$
+ ALT="$i$">, i.e.,
+</FONT></FONT></FONT>
+<BR>
+<DIV ALIGN="RIGHT">
+
+<!-- MATH
+ \begin{equation}
+\Omega^k_j \subset \mathcal{N}_i^k(\theta) = 
+   \left\{ r \in \Omega^k: |a_{ir}^k| > \theta \sqrt{|a_{ii}^ka_{rr}^k|} \right \} \cup \left\{ i \right\},
+\end{equation}
+ -->
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:strongly_coup"></A><IMG
+ WIDTH="387" HEIGHT="72" BORDER="0"
+ SRC="img31.png"
+ ALT="\begin{displaymath}
+\Omega^k_j \subset \mathcal{N}_i^k(\theta) = 
 \left\{ r ...
+...vert a_{ii}^ka_{rr}^k\vert} \right \} \cup \left\{ i \right\},
\end{displaymath}"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(3)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+for a given threshold <!-- MATH
+ $\theta \in [0,1]$
  -->
 <IMG
- WIDTH="110" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img53.png"
- ALT="$R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$">
-that maps a vector <IMG
- WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
- SRC="img54.png"
- ALT="$x^k$"> to the vector <IMG
- WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img55.png"
- ALT="$x_i^k$"> made of the components of <IMG
- WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
- SRC="img54.png"
- ALT="$x^k$">
-with indices in <IMG
- WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img51.png"
- ALT="$\Omega^k_i$">, and the prolongation operator
+ WIDTH="69" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ SRC="img32.png"
+ ALT="$\theta \in [0,1]$"> (see&nbsp;[<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>] for the details).
+Since this algorithm has a sequential nature, a decoupled
+version of it is applied, where each processor independently executes
+the algorithm on the set of indices assigned to it in the initial data
+distribution. This version is embarrassingly parallel, since it does not require any data 
+communication. On the other hand, it may produce some nonuniform aggregates
+and is strongly dependent on the number of processors and on the initial partitioning
+of the matrix <IMG
+ WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img3.png"
+ ALT="$A$">. Nevertheless, this parallel algorithm has been chosen for
+MLD2P4, since it has been shown to produce good results in practice
+[<A
+ HREF="node30.html#aaecc_07">5</A>,<A
+ HREF="node30.html#apnum_07">7</A>,<A
+ HREF="node30.html#TUMINARO_TONG">24</A>].
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The prolongator <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img25.png"
+ ALT="$P^k$"> is built starting from a tentative prolongator
 <!-- MATH
- $P^k_i = (R_i^k)^T$
+ $\bar{P}^k \in \mathbb{R}^{n_k \times n_{k+1}}$
  -->
 <IMG
- WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img56.png"
- ALT="$P^k_i = (R_i^k)^T$">. These operators are then  used to build
+ WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img33.png"
+ ALT="$\bar{P}^k \in \mathbb{R}^{n_k \times n_{k+1}}$">, defined as
+</FONT></FONT></FONT>
+<BR>
+<DIV ALIGN="RIGHT">
+
 <!-- MATH
- $A_i^k=R_i^kA^kP_i^k$
+ \begin{equation}
+\bar{P}^k =(\bar{p}_{ij}^k), \quad  \bar{p}_{ij}^k = 
+\left\{ \begin{array}{ll}
+1 & \quad \mbox{if} \; i \in \Omega^k_j, \\
+0 & \quad \mbox{otherwise},
+\end{array} \right.
+\end{equation}
  -->
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:tent_prol"></A><IMG
+ WIDTH="287" HEIGHT="51" BORDER="0"
+ SRC="img34.png"
+ ALT="\begin{displaymath}
\bar{P}^k =(\bar{p}_{ij}^k), \quad \bar{p}_{ij}^k = 
\left\{...
+...ega^k_j,  
0 &amp; \quad \mbox{otherwise},
\end{array} \right.
+\end{displaymath}"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(4)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+where <IMG
+ WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img28.png"
+ ALT="$\Omega^k_j$"> is the aggregate of <IMG
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img9.png"
+ ALT="$\Omega^k$">
+corresponding to the index <!-- MATH
+ $j \in \Omega^{k+1}$
+ -->
+<IMG
+ WIDTH="72" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img27.png"
+ ALT="$j \in \Omega^{k+1}$">.
 <IMG
- WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img57.png"
- ALT="$A_i^k=R_i^kA^kP_i^k$">, which is the restriction of <IMG
  WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img41.png"
- ALT="$A^k$"> to the index
-space <IMG
- WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img51.png"
- ALT="$\Omega^k_i$">.
-The classical AS preconditioner <IMG
- WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img58.png"
- ALT="$M^k_{AS}$"> is defined as
+ SRC="img25.png"
+ ALT="$P^k$"> is obtained by applying to <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img35.png"
+ ALT="$\bar{P}^k$"> a smoother
+<!-- MATH
+ $S^k \in \mathbb{R}^{n_k \times n_k}$
+ -->
+<IMG
+ WIDTH="101" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img36.png"
+ ALT="$S^k \in \mathbb{R}^{n_k \times n_k}$">:
 </FONT></FONT></FONT>
 <BR><P></P>
 <DIV ALIGN="CENTER">
 <!-- MATH
  \begin{displaymath}
-( M^k_{AS} )^{-1} = \sum_{i=1}^{m_k} P_i^k (A_i^k)^{-1} R_i^{k},
+P^k = S^k \bar{P}^k,
 \end{displaymath}
  -->
 
 <IMG
- 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},
\end{displaymath}">
+ WIDTH="90" HEIGHT="30" BORDER="0"
+ SRC="img37.png"
+ ALT="\begin{displaymath}
P^k = S^k \bar{P}^k,
\end{displaymath}">
 </DIV>
 <BR CLEAR="ALL">
 <P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-where <IMG
- WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img60.png"
- ALT="$A_i^k$"> is supposed to be nonsingular. We observe that an approximate
-inverse of <IMG
- WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img60.png"
- ALT="$A_i^k$"> is usually considered instead of <IMG
- WIDTH="57" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img61.png"
- ALT="$(A_i^k)^{-1}$">.
-The setup of <IMG
- WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img58.png"
- ALT="$M^k_{AS}$"> during the multilevel build phase
-involves
+in order to remove nonsmooth components from the range of the prolongator,
+and hence to improve the convergence properties of the multi-level
+method&nbsp;[<A
+ HREF="node30.html#BREZINA_VANEK">2</A>,<A
+ HREF="node30.html#Stuben_01">23</A>].
+A simple choice for <IMG
+ WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
+ SRC="img38.png"
+ ALT="$S^k$"> is the damped Jacobi smoother:
 </FONT></FONT></FONT>
-<UL>
-<LI>the definition of the index subspaces <IMG
- WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img62.png"
- ALT="$\Omega_i^k$"> and of the corresponding 
-  operators <IMG
- WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img63.png"
- ALT="$R_i^k$"> (and <IMG
- WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img64.png"
- ALT="$P_i^k$">);
-</LI>
-<LI>the computation of the submatrices <IMG
- WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img60.png"
- ALT="$A_i^k$">;
-</LI>
-<LI>the computation of their inverses (usually approximated
-    through  some form  of incomplete factorization).
-</LI>
-</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-The computation of <!-- MATH
- $z^k=M^k_{AS}w^k$
+<BR><P></P>
+<DIV ALIGN="CENTER">
+<!-- MATH
+ \begin{displaymath}
+S^k = I - \omega^k (D^k)^{-1} A^k_F ,
+\end{displaymath}
  -->
+
 <IMG
- WIDTH="102" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img65.png"
- ALT="$z^k=M^k_{AS}w^k$">, with <!-- MATH
- $w^k \in \mathbb{R}^{n_k}$
+ 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}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+where <IMG
+ WIDTH="28" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img40.png"
+ ALT="$D^k$"> is the diagonal matrix with the same diagonal entries as <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img41.png"
+ ALT="$A^k$">,
+<!-- MATH
+ $A^k_F = (\bar{a}_{ij}^k)$
  -->
 <IMG
- WIDTH="76" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img66.png"
- ALT="$w^k \in \mathbb{R}^{n_k}$">, during the
-multilevel application phase, requires
+ WIDTH="87" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img42.png"
+ ALT="$A^k_F = (\bar{a}_{ij}^k)$"> is the filtered matrix defined as
 </FONT></FONT></FONT>
-<UL>
-<LI>the restriction of <IMG
- WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
- SRC="img67.png"
- ALT="$w^k$"> to the subspaces <!-- MATH
- $\mathbb{R}^{n_{k,i}}$
+<BR>
+<DIV ALIGN="RIGHT">
+
+<!-- MATH
+ \begin{equation}
+\bar{a}_{ij}^k =
+   \left \{ \begin{array}{ll}
+   a_{ij}^k & \mbox{if } j \in \mathcal{N}_i^k(\theta), \\
+   0            & \mbox{otherwise},
+   \end{array} \right.
+   \; (j \ne i),
+   \qquad
+   \bar{a}_{ii}^k = a_{ii}^k - \sum_{j \ne i} (a_{ij}^k - \bar{a}_{ij}^k),
+\end{equation}
  -->
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:filtered"></A><IMG
+ WIDTH="514" HEIGHT="74" BORDER="0"
+ SRC="img43.png"
+ ALT="\begin{displaymath}
+\bar{a}_{ij}^k =
 \left \{ \begin{array}{ll}
 a_{ij}^k &amp; ...
+...ii}^k = a_{ii}^k - \sum_{j \ne i} (a_{ij}^k - \bar{a}_{ij}^k),
\end{displaymath}"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(5)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+and <IMG
+ WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
+ SRC="img44.png"
+ ALT="$\omega^k$"> is an approximation of <IMG
+ WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img45.png"
+ ALT="$4/(3\rho^k)$">, where
 <IMG
- WIDTH="41" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img68.png"
- ALT="$\mathbb{R}^{n_{k,i}}$">,
-	  i.e. <!-- MATH
- $w_i^k = R_i^{k} w^k$
+ WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img46.png"
+ ALT="$\rho^k$"> is the spectral radius of <!-- MATH
+ $(D^k)^{-1}A^k_F$
  -->
 <IMG
- WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img69.png"
- ALT="$w_i^k = R_i^{k} w^k$">;
-</LI>
-<LI>the computation of the vectors <!-- MATH
- $z_i^k=(A_i^k)^{-1} w_i^k$
+ WIDTH="83" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img47.png"
+ ALT="$(D^k)^{-1}A^k_F$"> [<A
+ HREF="node30.html#BREZINA_VANEK">2</A>].
+In MLD2P4 this approximation is obtained by using <!-- MATH
+ $\| A^k_F \|_\infty$
  -->
 <IMG
- WIDTH="119" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img70.png"
- ALT="$z_i^k=(A_i^k)^{-1} w_i^k$">;
-</LI>
-<LI>the prolongation and the sum of the previous vectors,
-    i.e. <!-- MATH
- $z^k = \sum_{i=1}^{m_k} P_i^k z_i^k$
- -->
+ WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img48.png"
+ ALT="$\Vert A^k_F \Vert _\infty$"> as an estimate
+of <IMG
+ WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img46.png"
+ ALT="$\rho^k$">. Note that for systems coming from uniformly elliptic
+problems, filtering the matrix <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img41.png"
+ ALT="$A^k$"> has little or no effect, and
 <IMG
- WIDTH="127" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img71.png"
- ALT="$z^k = \sum_{i=1}^{m_k} P_i^k z_i^k$">.
-</LI>
-</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-Variants of the classical AS method, which use modifications of the
-restriction and prolongation operators, are also implemented in MLD2P4.
-Among them, the Restricted AS (RAS) preconditioner usually
-outperforms the classical AS preconditioner in terms of convergence
-rate and of computation and communication time on parallel distributed-memory
-computers, and is therefore the most widely used among the AS
-preconditioners&nbsp;[<A
- HREF="node29.html#CAI_SARKIS">6</A>]. 
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Direct solvers based on sparse LU factorizations, implemented in the
-third-party libraries reported in Section&nbsp;<A HREF="node7.html#sec:third-party">3.2</A>, can be applied
-as coarsest-level solvers by MLD2P4. Native inexact solvers based on
-incomplete LU factorizations, as well as Jacobi, hybrid (forward) Gauss-Seidel,
-and block Jacobi preconditioners are also available. Direct solvers usually
-lead to more effective preconditioners in terms of algorithmic scalability;
-however, this does not guarantee parallel efficiency.
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img41.png"
+ ALT="$A^k$"> can be used instead of <IMG
+ WIDTH="29" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img49.png"
+ ALT="$A^k_F$">. The latter choice is the default in MLD2P4.
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT><HR>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
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-<H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A>
+<H2><A NAME="SECTION00063000000000000000"></A><A NAME="sec:smoothers"></A>
 <BR>
-Getting Started
-</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+Smoothers and coarsest-level solvers
+</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We describe the basics for building and applying MLD2P4 one-level and multi-level
-(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].
-The following steps are required:
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The smoothers implemented in MLD2P4 include the Jacobi and block-Jacobi methods,
+a hybrid version of the forward and backward Gauss-Seidel methods, and the
+additive Schwarz (AS) ones (see, e.g., [<A
+ HREF="node30.html#Saad_book">20</A>,<A
+ HREF="node30.html#dd2_96">21</A>]). 
 </FONT></FONT></FONT>
- 
-<OL>
-<LI><I>Declare the preconditioner data structure</I>. It is a derived data type,
-  <code>mld_</code><I>x</I><code>prec_</code> <code>type</code>, where <I>x</I> may be <code>s</code>, <code>d</code>, <code>c</code>
-	or <code>z</code>, according to the basic data type of the sparse matrix
-	(<code>s</code> = real single precision; <code>d</code> = real double precision;
-	<code>c</code> = complex single precision; <code>z</code> = complex double precision).
-	This data structure is accessed by the user only through the MLD2P4 routines,
-	following an object-oriented approach.
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The hybrid Gauss-Seidel
+version is considered because the original Gauss-Seidel method is inherently sequential.
+At each iteration of the hybrid version, each parallel process uses the most recent values
+of its own local variables and the values of the non-local variables computed at the
+previous iteration, obtained by exchanging data with other processes before
+the beginning of the current iteration.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In the AS methods, the index space <IMG
+ WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img9.png"
+ ALT="$\Omega^k$"> is divided into <IMG
+ WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img50.png"
+ ALT="$m_k$">
+subsets <IMG
+ WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img51.png"
+ ALT="$\Omega^k_i$"> of size <IMG
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img52.png"
+ ALT="$n_{k,i}$">,  possibly
+overlapping. For each <IMG
+ WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img30.png"
+ ALT="$i$"> we consider the restriction
+operator <!-- MATH
+ $R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$
+ -->
+<IMG
+ WIDTH="110" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img53.png"
+ ALT="$R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$">
+that maps a vector <IMG
+ WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
+ SRC="img54.png"
+ ALT="$x^k$"> to the vector <IMG
+ WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img55.png"
+ ALT="$x_i^k$"> made of the components of <IMG
+ WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
+ SRC="img54.png"
+ ALT="$x^k$">
+with indices in <IMG
+ WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img51.png"
+ ALT="$\Omega^k_i$">, and the prolongation operator
+<!-- MATH
+ $P^k_i = (R_i^k)^T$
+ -->
+<IMG
+ WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img56.png"
+ ALT="$P^k_i = (R_i^k)^T$">. These operators are then  used to build
+<!-- MATH
+ $A_i^k=R_i^kA^kP_i^k$
+ -->
+<IMG
+ WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img57.png"
+ ALT="$A_i^k=R_i^kA^kP_i^k$">, which is the restriction of <IMG
+ WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img41.png"
+ ALT="$A^k$"> to the index
+space <IMG
+ WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img51.png"
+ ALT="$\Omega^k_i$">.
+The classical AS preconditioner <IMG
+ WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img58.png"
+ ALT="$M^k_{AS}$"> is defined as
+</FONT></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER">
+<!-- MATH
+ \begin{displaymath}
+( M^k_{AS} )^{-1} = \sum_{i=1}^{m_k} P_i^k (A_i^k)^{-1} R_i^{k},
+\end{displaymath}
+ -->
+
+<IMG
+ 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},
\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+where <IMG
+ WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img60.png"
+ ALT="$A_i^k$"> is supposed to be nonsingular. We observe that an approximate
+inverse of <IMG
+ WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img60.png"
+ ALT="$A_i^k$"> is usually considered instead of <IMG
+ WIDTH="57" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img61.png"
+ ALT="$(A_i^k)^{-1}$">.
+The setup of <IMG
+ WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img58.png"
+ ALT="$M^k_{AS}$"> during the multilevel build phase
+involves
+</FONT></FONT></FONT>
+<UL>
+<LI>the definition of the index subspaces <IMG
+ WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img62.png"
+ ALT="$\Omega_i^k$"> and of the corresponding 
+  operators <IMG
+ WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img63.png"
+ ALT="$R_i^k$"> (and <IMG
+ WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img64.png"
+ ALT="$P_i^k$">);
 </LI>
-<LI><I>Allocate and initialize the preconditioner data structure, according to
-	a preconditioner type chosen by the user</I>. This is performed by the routine
-	<code>init</code>, which also sets defaults for each preconditioner
-	type selected by the user. The preconditioner types and the defaults associated
-	with them are given in Table&nbsp;<A HREF="#tab:precinit">1</A>, where the strings used by
-	<code>init</code> to identify the preconditioner types are also given.
-	Note that these strings are valid also if uppercase letters are substituted by
-	corresponding lowercase ones.
+<LI>the computation of the submatrices <IMG
+ WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img60.png"
+ ALT="$A_i^k$">;
 </LI>
-<LI><I>Modify the selected preconditioner type, by properly setting
-  preconditioner parameters.</I> This is performed by the routine <code>set</code>.
-  This routine must be called only if the user wants to modify the default values
-  of the parameters associated with the selected preconditioner type, to obtain a variant
-  of that preconditioner. Examples of use of <code>set</code> are given in
-  Section&nbsp;<A HREF="node16.html#sec:examples">5.1</A>; a complete list of all the
-  preconditioner parameters and their allowed and default values is provided in 
-  Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
+<LI>the computation of their inverses (usually approximated
+    through  some form  of incomplete factorization).
 </LI>
-<LI><I>Build the preconditioner for a given matrix</I>. If the selected preconditioner
- is multi-level, then two steps must be performed, as specified next.
-<DL COMPACT>
-<DT>4.1</DT>
-<DD><I>Build the aggregation hierarchy for a given matrix.</I> This is
-performed by the routine <code>hierarchy_build</code>.
-</DD>
-<DT>4.2</DT>
-<DD><I>Build the preconditioner for a given matrix.</I> This is performed
-by the routine <code>smoothers_build</code>.
-</DD>
-</DL>
- If the selected preconditioner is one-level, it is built in a single step,
-performed by the routine <code>bld</code>.
+</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+The computation of <!-- MATH
+ $z^k=M^k_{AS}w^k$
+ -->
+<IMG
+ WIDTH="102" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img65.png"
+ ALT="$z^k=M^k_{AS}w^k$">, with <!-- MATH
+ $w^k \in \mathbb{R}^{n_k}$
+ -->
+<IMG
+ WIDTH="76" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img66.png"
+ ALT="$w^k \in \mathbb{R}^{n_k}$">, during the
+multilevel application phase, requires
+</FONT></FONT></FONT>
+<UL>
+<LI>the restriction of <IMG
+ WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
+ SRC="img67.png"
+ ALT="$w^k$"> to the subspaces <!-- MATH
+ $\mathbb{R}^{n_{k,i}}$
+ -->
+<IMG
+ WIDTH="41" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img68.png"
+ ALT="$\mathbb{R}^{n_{k,i}}$">,
+	  i.e. <!-- MATH
+ $w_i^k = R_i^{k} w^k$
+ -->
+<IMG
+ WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img69.png"
+ ALT="$w_i^k = R_i^{k} w^k$">;
 </LI>
-<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
-  This is performed by the routine <code>aply</code>. When using the PSBLAS Krylov solvers,
-  this step is completely transparent to the user, since <code>aply</code> is called
-  by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
+<LI>the computation of the vectors <!-- MATH
+ $z_i^k=(A_i^k)^{-1} w_i^k$
+ -->
+<IMG
+ WIDTH="119" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img70.png"
+ ALT="$z_i^k=(A_i^k)^{-1} w_i^k$">;
 </LI>
-<LI><I>Free the preconditioner data structure</I>. This is performed by
-  the routine <code>free</code>. This step is complementary to step 1 and should
-  be performed when the preconditioner is no more used.
+<LI>the prolongation and the sum of the previous vectors,
+    i.e. <!-- MATH
+ $z^k = \sum_{i=1}^{m_k} P_i^k z_i^k$
+ -->
+<IMG
+ WIDTH="127" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img71.png"
+ ALT="$z^k = \sum_{i=1}^{m_k} P_i^k z_i^k$">.
 </LI>
-</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the previous routines are available as methods of the preconditioner object.
-A detailed description of them is given in Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A>.
-Examples showing the basic use of MLD2P4 are reported in Section&nbsp;<A HREF="node16.html#sec:examples">5.1</A>.
+</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+Variants of the classical AS method, which use modifications of the
+restriction and prolongation operators, are also implemented in MLD2P4.
+Among them, the Restricted AS (RAS) preconditioner usually
+outperforms the classical AS preconditioner in terms of convergence
+rate and of computation and communication time on parallel distributed-memory
+computers, and is therefore the most widely used among the AS
+preconditioners&nbsp;[<A
+ HREF="node30.html#CAI_SARKIS">6</A>]. 
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="897"></A>
-<TABLE>
-<CAPTION><STRONG>Table 1:</STRONG>
-Preconditioner types, corresponding strings and default choices.
-</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT"><SMALL>TYPE</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><SMALL>STRING</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
-</TR>
-<TR><TD ALIGN="LEFT">No preconditioner</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NOPREC'</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered only to use the PSBLAS
-                                    Krylov solvers with no preconditioner.</TD>
-</TR>
-<TR><TD ALIGN="LEFT">Diagonal</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'DIAG'</code> or <code>'JACOBI'</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Diagonal preconditioner.
-                         For any zero diagonal entry of the matrix to be preconditioned,
-                         the corresponding entry of the preconditioner is set to&nbsp;1.</TD>
-</TR>
-<TR><TD ALIGN="LEFT">Block Jacobi</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'BJAC'</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Block-Jacobi with ILU(0) on the local blocks.</TD>
-</TR>
-<TR><TD ALIGN="LEFT">Additive Schwarz</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'AS'</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Restricted Additive Schwarz (RAS),
-                                    with overlap&nbsp;1 and ILU(0) on the local blocks.</TD>
-</TR>
-<TR><TD ALIGN="LEFT">Multilevel</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'ML'</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>V-cycle with one hybrid forward Gauss-Seidel
-                                    (GS) sweep as pre-smoother and one hybrid backward 
-                                    GS sweep as post-smoother, basic smoothed aggregation
-                                   as coarsening algorithm, and LU (plus triangular solve)
-                                   as coarsest-level solver. See the default values in
-                                   Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>
-                                   for further details of the preconditioner.</TD>
-</TR>
-</TABLE>
-</DIV></TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Note that the module <code>mld_prec_mod</code>, containing the definition of the 
-preconditioner data type and the interfaces to the routines of MLD2P4,
-must be used in any program calling such routines.
-The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
-data types, and <code>psb_krylov_mod</code>, for interfacing with the
-Krylov solvers, must be also used (see Section&nbsp;<A HREF="node16.html#sec:examples">5.1</A>). 
-<BR></FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 1.</B> Coarsest-level solvers based on the LU factorization,
-such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist,
-usually lead to smaller numbers of preconditioned Krylov
-iterations than inexact solvers, when the linear system comes from
-a standard discretization of basic scalar elliptic PDE problems. However,
-this does not necessarily correspond to the smallest execution time
-on parallel computers. </FONT></FONT></FONT>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Direct solvers based on sparse LU factorizations, implemented in the
+third-party libraries reported in Section&nbsp;<A HREF="node8.html#sec:third-party">3.2</A>, can be applied
+as coarsest-level solvers by MLD2P4. Native inexact solvers based on
+incomplete LU factorizations, as well as Jacobi, hybrid (forward) Gauss-Seidel,
+and block Jacobi preconditioners are also available. Direct solvers usually
+lead to more effective preconditioners in terms of algorithmic scalability;
+however, this does not guarantee parallel efficiency.
+</FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><HR>
-<!--Table of Child-Links-->
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-<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
+<H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A>
 <BR>
-Examples
-</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The code reported in Figure&nbsp;<A HREF="#fig:ex1">2</A> shows how to set and apply the default
-multi-level preconditioner available in the real double precision version
-of MLD2P4 (see Table&nbsp;<A HREF="#tab:precinit">1</A>). This preconditioner is chosen
-by simply specifying <code>'ML'</code> as the second argument of <code>P%init</code>
-(a call to <code>P%set</code> is not needed) and is applied with the CG
-solver provided by PSBLAS (the matrix of the system to be solved is
-assumed to be positive definite). As previously observed, the modules
-<code>psb_base_mod</code>, <code>mld_prec_mod</code> and <code>psb_krylov_mod</code>
-must be used by the example program.
-</FONT></FONT></FONT>
+Getting Started
+</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The part of the code concerning the
-reading and assembling of the sparse matrix and the right-hand side vector, performed
-through the PSBLAS routines for sparse matrix and vector management, is not reported
-here for brevity; the statements concerning the deallocation of the PSBLAS
-data structure are neglected too.
-The complete code can be found in the example program file <code>mld_dexample_ml.f90</code>,
-in the directory <code>examples/fileread</code> of the MLD2P4 implementation (see
-Section&nbsp;<A HREF="node10.html#sec:ex_and_test">3.5</A>). A sample test problem along with the relevant
-input data is available in <code>examples/fileread/runs</code>.
-For details on the use of the PSBLAS routines, see the PSBLAS User's
-Guide&nbsp;[<A
- HREF="node29.html#PSBLASGUIDE">13</A>].
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We describe the basics for building and applying MLD2P4 one-level and multi-level
+(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
+ HREF="node30.html#PSBLASGUIDE">13</A>].
+The following steps are required:
 </FONT></FONT></FONT>
+ 
+<OL>
+<LI><I>Declare the preconditioner data structure</I>. It is a derived data type,
+  <code>mld_</code><I>x</I><code>prec_</code> <code>type</code>, where <I>x</I> may be <code>s</code>, <code>d</code>, <code>c</code>
+	or <code>z</code>, according to the basic data type of the sparse matrix
+	(<code>s</code> = real single precision; <code>d</code> = real double precision;
+	<code>c</code> = complex single precision; <code>z</code> = complex double precision).
+	This data structure is accessed by the user only through the MLD2P4 routines,
+	following an object-oriented approach.
+</LI>
+<LI><I>Allocate and initialize the preconditioner data structure, according to
+	a preconditioner type chosen by the user</I>. This is performed by the routine
+	<code>init</code>, which also sets defaults for each preconditioner
+	type selected by the user. The preconditioner types and the defaults associated
+	with them are given in Table&nbsp;<A HREF="#tab:precinit">1</A>, where the strings used by
+	<code>init</code> to identify the preconditioner types are also given.
+	Note that these strings are valid also if uppercase letters are substituted by
+	corresponding lowercase ones.
+</LI>
+<LI><I>Modify the selected preconditioner type, by properly setting
+  preconditioner parameters.</I> This is performed by the routine <code>set</code>.
+  This routine must be called only if the user wants to modify the default values
+  of the parameters associated with the selected preconditioner type, to obtain a variant
+  of that preconditioner. Examples of use of <code>set</code> are given in
+  Section&nbsp;<A HREF="node17.html#sec:examples">5.1</A>; a complete list of all the
+  preconditioner parameters and their allowed and default values is provided in 
+  Section&nbsp;<A HREF="node18.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
+</LI>
+<LI><I>Build the preconditioner for a given matrix</I>. If the selected preconditioner
+ is multi-level, then two steps must be performed, as specified next.
+<DL COMPACT>
+<DT>4.1</DT>
+<DD><I>Build the aggregation hierarchy for a given matrix.</I> This is
+performed by the routine <code>hierarchy_build</code>.
+</DD>
+<DT>4.2</DT>
+<DD><I>Build the preconditioner for a given matrix.</I> This is performed
+by the routine <code>smoothers_build</code>.
+</DD>
+</DL>
+ If the selected preconditioner is one-level, it is built in a single step,
+performed by the routine <code>bld</code>.
+</LI>
+<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
+  This is performed by the routine <code>aply</code>. When using the PSBLAS Krylov solvers,
+  this step is completely transparent to the user, since <code>aply</code> is called
+  by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
+</LI>
+<LI><I>Free the preconditioner data structure</I>. This is performed by
+  the routine <code>free</code>. This step is complementary to step 1 and should
+  be performed when the preconditioner is no more used.
+</LI>
+</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The setup and application of the default multi-level preconditioner
-for the real single precision and the complex, single and double
-precision, versions are obtained with straightforward modifications of the previous
-example (see Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A> for details). If these versions are installed,
-the corresponding codes are available in <code>examples/fileread/</code>.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the previous routines are available as methods of the preconditioner object.
+A detailed description of them is given in Section&nbsp;<A HREF="node18.html#sec:userinterface">6</A>.
+Examples showing the basic use of MLD2P4 are reported in Section&nbsp;<A HREF="node17.html#sec:examples">5.1</A>.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><A NAME="fig:ex1"></A><A NAME="900"></A>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="904"></A>
 <TABLE>
-<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
-setup and application of the default multi-level preconditioner (example 1).
+<CAPTION><STRONG>Table 1:</STRONG>
+Preconditioner types, corresponding strings and default choices.
 </CAPTION>
 <TR><TD>
 <DIV ALIGN="CENTER">
-</DIV><TABLE  WIDTH="90%">
-<TR><TD> 
-<PRE>
-  use psb_base_mod
-  use mld_prec_mod
-  use psb_krylov_mod
-... ...
-!
-! sparse matrix
-  type(psb_dspmat_type) :: A
-! sparse matrix descriptor
-  type(psb_desc_type)   :: desc_A
-! preconditioner
-  type(mld_dprec_type)  :: P
-! right-hand side and solution vectors
-  type(psb_d_vect_type) :: b, x
-... ...
-!
-! initialize the parallel environment
-  call psb_init(ictxt)
-  call psb_info(ictxt,iam,np)
-... ...
-!
-! read and assemble the spd matrix A and the right-hand side b 
-! using PSBLAS routines for sparse matrix / vector management
-... ...
-!
-! initialize the default multi-level preconditioner, i.e. V-cycle
-! with basic smoothed aggregation, 1 hybrid forward/backward
-! GS sweep as pre/post-smoother and UMFPACK as coarsest-level
-! solver
-  call P%init('ML',info)
-!
-! build the preconditioner
-  call P%hierarchy_build(A,desc_A,info)
-  call P%smoothers_build(A,desc_A,info)
-
-!
-! set the solver parameters and the initial guess
-  ... ...
-!
-! solve Ax=b with preconditioned CG
-  call psb_krylov('CG',A,P,b,x,tol,desc_A,info)
-  ... ...
-!
-! deallocate the preconditioner
-  call P%free(info)
-!
-! deallocate other data structures
-  ... ...
-!
-! exit the parallel environment
-  call psb_exit(ictxt)
-  stop
-</PRE>
-</TD></TR>
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT"><SMALL>TYPE</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><SMALL>STRING</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
+</TR>
+<TR><TD ALIGN="LEFT">No preconditioner</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NOPREC'</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered only to use the PSBLAS
+                                    Krylov solvers with no preconditioner.</TD>
+</TR>
+<TR><TD ALIGN="LEFT">Diagonal</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'DIAG'</code> or <code>'JACOBI'</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Diagonal preconditioner.
+                         For any zero diagonal entry of the matrix to be preconditioned,
+                         the corresponding entry of the preconditioner is set to&nbsp;1.</TD>
+</TR>
+<TR><TD ALIGN="LEFT">Block Jacobi</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'BJAC'</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Block-Jacobi with ILU(0) on the local blocks.</TD>
+</TR>
+<TR><TD ALIGN="LEFT">Additive Schwarz</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'AS'</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Restricted Additive Schwarz (RAS),
+                                    with overlap&nbsp;1 and ILU(0) on the local blocks.</TD>
+</TR>
+<TR><TD ALIGN="LEFT">Multilevel</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'ML'</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>V-cycle with one hybrid forward Gauss-Seidel
+                                    (GS) sweep as pre-smoother and one hybrid backward 
+                                    GS sweep as post-smoother, basic smoothed aggregation
+                                   as coarsening algorithm, and LU (plus triangular solve)
+                                   as coarsest-level solver. See the default values in
+                                   Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>
+                                   for further details of the preconditioner.</TD>
+</TR>
 </TABLE>
-<DIV ALIGN="CENTER">
-
 </DIV></TD></TR>
 </TABLE>
-</DIV>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Different versions of the multi-level preconditioner can be obtained by changing
-the default values of the preconditioner parameters. The code reported in
-Figure&nbsp;<A HREF="#fig:ex2">3</A> shows how to set a V-cycle preconditioner
-which applies 1 block-Jacobi sweep as pre- and post-smoother,
-and solves the coarsest-level system with 8 block-Jacobi sweeps.
-Note that the ILU(0) factorization (plus triangular solve) is used as
-local solver for the block-Jacobi sweeps, since this is the default associated
-with block-Jacobi and set by&nbsp;<code>P%init</code>.
-Furthermore, specifying block-Jacobi as coarsest-level
-solver implies that the coarsest-level matrix is distributed
-among the processes.
-Figure&nbsp;<A HREF="#fig:ex3">4</A> shows how to set a W-cycle preconditioner which
-applies 2 hybrid Gauss-Seidel sweeps as pre- and post-smoother,
-and solves the coarsest-level system with the multifrontal LU factorization
-implemented in MUMPS. It is specified that the coarsest-level
-matrix is distributed, since MUMPS can be used on both
-replicated and distributed matrices, and by default
-it is used on replicated ones. The code fragments shown in Figures&nbsp;<A HREF="#fig:ex2">3</A> and <A HREF="#fig:ex3">4</A> are
-included in the example program file <code>mld_dexample_ml.f90</code> too.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Finally, Figure&nbsp;<A HREF="#fig:ex4">5</A> shows the setup of a one-level
-additive Schwarz preconditioner, i.e., RAS with overlap 2.
-Note also that a Krylov method different from CG must be used to solve
-the preconditioned system, since the preconditione in nonsymmetric.
-The corresponding example program is available in the file
-<code>mld_dexample_1lev.f90</code>. 
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For all the previous preconditioners, example programs where the sparse matrix and
-the right-hand side are generated by discretizing a PDE with Dirichlet
-boundary conditions are also available in the directory <code>examples/pdegen</code>.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><A NAME="fig:ex2"></A><A NAME="902"></A>
-<TABLE>
-<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
-setup of a multi-level preconditioner</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-</DIV><TABLE  WIDTH="90%">
-<TR><TD> 
-<PRE>
-... ...
-! build a V-cycle preconditioner with 1 block-Jacobi sweep (with 
-! ILU(0) on the blocks) as pre- and post-smoother, and 8  block-Jacobi
-! sweeps (with ILU(0) on the blocks) as coarsest-level solver
-  call P%init('ML',info)
-  call_P%set('SMOOTHER_TYPE','BJAC',info)
-  call P%set('COARSE_SOLVE','BJAC',info)
-  call P%set('COARSE_SWEEPS',8,info)
-  call P%hierarchy_build(A,desc_A,info)
-  call P%smoothers_build(A,desc_A,info)
-... ...
-</PRE>
-</TD></TR>
-</TABLE>
-<DIV ALIGN="CENTER">
-</DIV>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<DIV ALIGN="CENTER">
-</DIV></TD></TR>
-</TABLE>
-</DIV>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Note that the module <code>mld_prec_mod</code>, containing the definition of the 
+preconditioner data type and the interfaces to the routines of MLD2P4,
+must be used in any program calling such routines.
+The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
+data types, and <code>psb_krylov_mod</code>, for interfacing with the
+Krylov solvers, must be also used (see Section&nbsp;<A HREF="node17.html#sec:examples">5.1</A>). 
+<BR></FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><A NAME="fig:ex3"></A><A NAME="904"></A>
-<TABLE>
-<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
-setup of a multi-level preconditioner</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-</DIV><TABLE  WIDTH="90%">
-<TR><TD> 
-<PRE>
-... ...
-! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
-! as pre- and post-smoother, a distributed coarsest
-! matrix, and MUMPS as coarsest-level solver
-  call P%init('ML',info)
-  call P%set('ML_CYCLE','WCYCLE',info)
-  call P%set('SMOOTHER_TYPE','FBGS',info)
-  call P%set('SMOOTHER_SWEEPS',2,info)
-  call P%set('COARSE_SOLVE','MUMPS',info)
-  call P%set('COARSE_MAT','DIST',info)
-  call P%hierarchy_build(A,desc_A,info)
-  call P%smoothers_build(A,desc_A,info)
-... ...
-</PRE>
-</TD></TR>
-</TABLE>
-<DIV ALIGN="CENTER">
-
-</DIV></TD></TR>
-</TABLE>
-</DIV>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 1.</B> Coarsest-level solvers based on the LU factorization,
+such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist,
+usually lead to smaller numbers of preconditioned Krylov
+iterations than inexact solvers, when the linear system comes from
+a standard discretization of basic scalar elliptic PDE problems. However,
+this does not necessarily correspond to the smallest execution time
+on parallel computers. </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><A NAME="fig:ex4"></A><A NAME="906"></A>
-<TABLE>
-<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
-setup of a one-level Schwarz preconditioner.</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-</DIV><TABLE  WIDTH="90%">
-<TR><TD> 
-<PRE>
-... ...
-! set RAS with overlap 2 and ILU(0) on the local blocks
-  call P%init('AS',info)
-  call P%set('SUB_OVR',2,info)
-  call P%bld(A,desc_A,info)
-... ...
-! solve Ax=b with preconditioned BiCGSTAB
-  call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info)
-</PRE>
-</TD></TR>
-</TABLE>
-<DIV ALIGN="CENTER">
+<BR><HR>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
 
-</DIV></TD></TR>
-</TABLE>
-</DIV>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT><HR>
+<UL>
+<LI><A NAME="tex2html277"
+  HREF="node17.html">Examples</A>
+</UL>
+<!--End of Table of Child-Links-->
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diff --git a/docs/html/node17.html b/docs/html/node17.html
index c5dc1094..3d749561 100644
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@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
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@@ -30,9 +29,9 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
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-<H1><A NAME="SECTION00080000000000000000"></A><A NAME="sec:userinterface"></A>
+<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
 <BR>
-User Interface
-</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+Examples
+</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The code reported in Figure&nbsp;<A HREF="#fig:ex1">2</A> shows how to set and apply the default
+multi-level preconditioner available in the real double precision version
+of MLD2P4 (see Table&nbsp;<A HREF="#tab:precinit">1</A>). This preconditioner is chosen
+by simply specifying <code>'ML'</code> as the second argument of <code>P%init</code>
+(a call to <code>P%set</code> is not needed) and is applied with the CG
+solver provided by PSBLAS (the matrix of the system to be solved is
+assumed to be positive definite). As previously observed, the modules
+<code>psb_base_mod</code>, <code>mld_prec_mod</code> and <code>psb_krylov_mod</code>
+must be used by the example program.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The part of the code concerning the
+reading and assembling of the sparse matrix and the right-hand side vector, performed
+through the PSBLAS routines for sparse matrix and vector management, is not reported
+here for brevity; the statements concerning the deallocation of the PSBLAS
+data structure are neglected too.
+The complete code can be found in the example program file <code>mld_dexample_ml.f90</code>,
+in the directory <code>examples/fileread</code> of the MLD2P4 implementation (see
+Section&nbsp;<A HREF="node11.html#sec:ex_and_test">3.5</A>). A sample test problem along with the relevant
+input data is available in <code>examples/fileread/runs</code>.
+For details on the use of the PSBLAS routines, see the PSBLAS User's
+Guide&nbsp;[<A
+ HREF="node30.html#PSBLASGUIDE">13</A>].
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The setup and application of the default multi-level preconditioner
+for the real single precision and the complex, single and double
+precision, versions are obtained with straightforward modifications of the previous
+example (see Section&nbsp;<A HREF="node18.html#sec:userinterface">6</A> for details). If these versions are installed,
+the corresponding codes are available in <code>examples/fileread/</code>.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><A NAME="fig:ex1"></A><A NAME="907"></A>
+<TABLE>
+<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
+setup and application of the default multi-level preconditioner (example 1).
+</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+</DIV><TABLE  WIDTH="90%">
+<TR><TD> 
+<PRE>
+  use psb_base_mod
+  use mld_prec_mod
+  use psb_krylov_mod
+... ...
+!
+! sparse matrix
+  type(psb_dspmat_type) :: A
+! sparse matrix descriptor
+  type(psb_desc_type)   :: desc_A
+! preconditioner
+  type(mld_dprec_type)  :: P
+! right-hand side and solution vectors
+  type(psb_d_vect_type) :: b, x
+... ...
+!
+! initialize the parallel environment
+  call psb_init(ictxt)
+  call psb_info(ictxt,iam,np)
+... ...
+!
+! read and assemble the spd matrix A and the right-hand side b 
+! using PSBLAS routines for sparse matrix / vector management
+... ...
+!
+! initialize the default multi-level preconditioner, i.e. V-cycle
+! with basic smoothed aggregation, 1 hybrid forward/backward
+! GS sweep as pre/post-smoother and UMFPACK as coarsest-level
+! solver
+  call P%init('ML',info)
+!
+! build the preconditioner
+  call P%hierarchy_build(A,desc_A,info)
+  call P%smoothers_build(A,desc_A,info)
+
+!
+! set the solver parameters and the initial guess
+  ... ...
+!
+! solve Ax=b with preconditioned CG
+  call psb_krylov('CG',A,P,b,x,tol,desc_A,info)
+  ... ...
+!
+! deallocate the preconditioner
+  call P%free(info)
+!
+! deallocate other data structures
+  ... ...
+!
+! exit the parallel environment
+  call psb_exit(ictxt)
+  stop
+</PRE>
+</TD></TR>
+</TABLE>
+<DIV ALIGN="CENTER">
+
+</DIV></TD></TR>
+</TABLE>
+</DIV>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The basic user interface of MLD2P4 consists of eight routines. The six
-routines <code>init</code>, <code>set</code>,
-<code>hierarchy_build</code>, <code>smoothers_build</code>,
-<code>bld</code>, and <code>apply</code> encapsulate all the
-functionalities for the setup and the application of any multi-level and one-level
-preconditioner implemented in the package. 
-The routine <code>free</code> deallocates the preconditioner data structure, while
-<code>descr</code> prints a description of the preconditioner setup by the user.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Different versions of the multi-level preconditioner can be obtained by changing
+the default values of the preconditioner parameters. The code reported in
+Figure&nbsp;<A HREF="#fig:ex2">3</A> shows how to set a V-cycle preconditioner
+which applies 1 block-Jacobi sweep as pre- and post-smoother,
+and solves the coarsest-level system with 8 block-Jacobi sweeps.
+Note that the ILU(0) factorization (plus triangular solve) is used as
+local solver for the block-Jacobi sweeps, since this is the default associated
+with block-Jacobi and set by&nbsp;<code>P%init</code>.
+Furthermore, specifying block-Jacobi as coarsest-level
+solver implies that the coarsest-level matrix is distributed
+among the processes.
+Figure&nbsp;<A HREF="#fig:ex3">4</A> shows how to set a W-cycle preconditioner which
+applies 2 hybrid Gauss-Seidel sweeps as pre- and post-smoother,
+and solves the coarsest-level system with the multifrontal LU factorization
+implemented in MUMPS. It is specified that the coarsest-level
+matrix is distributed, since MUMPS can be used on both
+replicated and distributed matrices, and by default
+it is used on replicated ones. The code fragments shown in Figures&nbsp;<A HREF="#fig:ex2">3</A> and <A HREF="#fig:ex3">4</A> are
+included in the example program file <code>mld_dexample_ml.f90</code> too.
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the routines are available as methods of the preconditioner object.
-For each routine, the same user interface is overloaded with
-respect to the real/ complex case and the single/double precision;
-arguments with appropriate data types must be passed to the routine,
-i.e.,
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Finally, Figure&nbsp;<A HREF="#fig:ex4">5</A> shows the setup of a one-level
+additive Schwarz preconditioner, i.e., RAS with overlap 2.
+Note also that a Krylov method different from CG must be used to solve
+the preconditioned system, since the preconditione in nonsymmetric.
+The corresponding example program is available in the file
+<code>mld_dexample_1lev.f90</code>. 
 </FONT></FONT></FONT>
-<UL>
-<LI>the sparse matrix data structure, containing the matrix to be
-  preconditioned, must be of type <code>psb_</code><I>x</I><code>spmat_type</code>
-	with <I>x</I> = <code>s</code> for real single precision, <I>x</I> = <code>d</code>
-	for real double precision, <I>x</I> = <code>c</code> for complex single precision,
-	<I>x</I> = <code>z</code> for complex double precision;
-</LI>
-<LI>the preconditioner data structure must be of type
-  <code>mld_</code><I>x</I><code>prec_type</code>, with <I>x</I> =    
-  <code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, according to the sparse
-  matrix data structure;
-</LI>
-<LI>the arrays containing the vectors <IMG
- WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img72.png"
- ALT="$v$"> and <IMG
- WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img73.png"
- ALT="$w$"> involved in
-  the preconditioner application <IMG
- WIDTH="82" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img23.png"
- ALT="$w=B^{-1}v$"> must be of type   
-  <code>psb_</code><I>x</I><code>vect_type</code> with <I>x</I> =    
-  <code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, in a manner completely
-  analogous to the sparse matrix type;
-</LI>
-<LI>real parameters defining the preconditioner must be declared
-  according to the precision of the sparse matrix and preconditioner
-  data structures (see Section&nbsp;<A HREF="node19.html#sec:precset">6.2</A>).
-</LI>
-</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-A description of each routine is given in the remainder of this section.
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For all the previous preconditioners, example programs where the sparse matrix and
+the right-hand side are generated by discretizing a PDE with Dirichlet
+boundary conditions are also available in the directory <code>examples/pdegen</code>.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><A NAME="fig:ex2"></A><A NAME="909"></A>
+<TABLE>
+<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
+setup of a multi-level preconditioner</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+</DIV><TABLE  WIDTH="90%">
+<TR><TD> 
+<PRE>
+... ...
+! build a V-cycle preconditioner with 1 block-Jacobi sweep (with 
+! ILU(0) on the blocks) as pre- and post-smoother, and 8  block-Jacobi
+! sweeps (with ILU(0) on the blocks) as coarsest-level solver
+  call P%init('ML',info)
+  call_P%set('SMOOTHER_TYPE','BJAC',info)
+  call P%set('COARSE_SOLVE','BJAC',info)
+  call P%set('COARSE_SWEEPS',8,info)
+  call P%hierarchy_build(A,desc_A,info)
+  call P%smoothers_build(A,desc_A,info)
+... ...
+</PRE>
+</TD></TR>
+</TABLE>
+<DIV ALIGN="CENTER">
+</DIV>
+<P>
+<DIV ALIGN="CENTER">
+</DIV></TD></TR>
+</TABLE>
+</DIV>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><HR>
-<!--Table of Child-Links-->
-<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
+<DIV ALIGN="CENTER"><A NAME="fig:ex3"></A><A NAME="911"></A>
+<TABLE>
+<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
+setup of a multi-level preconditioner</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+</DIV><TABLE  WIDTH="90%">
+<TR><TD> 
+<PRE>
+... ...
+! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
+! as pre- and post-smoother, a distributed coarsest
+! matrix, and MUMPS as coarsest-level solver
+  call P%init('ML',info)
+  call P%set('ML_CYCLE','WCYCLE',info)
+  call P%set('SMOOTHER_TYPE','FBGS',info)
+  call P%set('SMOOTHER_SWEEPS',2,info)
+  call P%set('COARSE_SOLVE','MUMPS',info)
+  call P%set('COARSE_MAT','DIST',info)
+  call P%hierarchy_build(A,desc_A,info)
+  call P%smoothers_build(A,desc_A,info)
+... ...
+</PRE>
+</TD></TR>
+</TABLE>
+<DIV ALIGN="CENTER">
 
-<UL>
-<LI><A NAME="tex2html288"
-  HREF="node18.html">Subroutine init</A>
-<LI><A NAME="tex2html289"
-  HREF="node19.html">Subroutine set</A>
-<LI><A NAME="tex2html290"
-  HREF="node20.html">Subroutine build</A>
-<LI><A NAME="tex2html291"
-  HREF="node21.html">Subroutine hierarchy_build</A>
-<LI><A NAME="tex2html292"
-  HREF="node22.html">Subroutine smoothers_build</A>
-<LI><A NAME="tex2html293"
-  HREF="node23.html">Subroutine apply</A>
-<LI><A NAME="tex2html294"
-  HREF="node24.html">Subroutine free</A>
-<LI><A NAME="tex2html295"
-  HREF="node25.html">Subroutine descr</A>
-</UL>
-<!--End of Table of Child-Links-->
-<HR>
+</DIV></TD></TR>
+</TABLE>
+</DIV>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><A NAME="fig:ex4"></A><A NAME="913"></A>
+<TABLE>
+<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
+setup of a one-level Schwarz preconditioner.</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+</DIV><TABLE  WIDTH="90%">
+<TR><TD> 
+<PRE>
+... ...
+! set RAS with overlap 2 and ILU(0) on the local blocks
+  call P%init('AS',info)
+  call P%set('SUB_OVR',2,info)
+  call P%bld(A,desc_A,info)
+... ...
+! solve Ax=b with preconditioned BiCGSTAB
+  call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info)
+</PRE>
+</TD></TR>
+</TABLE>
+<DIV ALIGN="CENTER">
+
+</DIV></TD></TR>
+</TABLE>
+</DIV>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT><HR>
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diff --git a/docs/html/node18.html b/docs/html/node18.html
index 4479d15b..8a65faa0 100644
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+++ b/docs/html/node18.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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-<H2><A NAME="SECTION00081000000000000000"></A><A NAME="sec:precinit"></A>
+<H1><A NAME="SECTION00080000000000000000"></A><A NAME="sec:userinterface"></A>
 <BR>
-Subroutine init
-</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+User Interface
+</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%init(ptype,info)</code>
-</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine allocates and initializes the preconditioner
-<code>p</code>, according to the preconditioner type chosen by the user.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The basic user interface of MLD2P4 consists of eight routines. The six
+routines <code>init</code>, <code>set</code>,
+<code>hierarchy_build</code>, <code>smoothers_build</code>,
+<code>bld</code>, and <code>apply</code> encapsulate all the
+functionalities for the setup and the application of any multi-level and one-level
+preconditioner implemented in the package. 
+The routine <code>free</code> deallocates the preconditioner data structure, while
+<code>descr</code> prints a description of the preconditioner setup by the user.
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
-<P></P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>ptype</code>  </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=*), intent(in)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The type of preconditioner. Its values are specified
-              in Table&nbsp;<A HREF="#tab:precinit">1</A>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Note that the strings are case insensitive.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>info</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
-</TR>
-</TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For compatibility with the previous versions of MLD2P4, this routine can be also invoked
-as follows:
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the routines are available as methods of the preconditioner object.
+For each routine, the same user interface is overloaded with
+respect to the real/ complex case and the single/double precision;
+arguments with appropriate data types must be passed to the routine,
+i.e.,
+</FONT></FONT></FONT>
+<UL>
+<LI>the sparse matrix data structure, containing the matrix to be
+  preconditioned, must be of type <code>psb_</code><I>x</I><code>spmat_type</code>
+	with <I>x</I> = <code>s</code> for real single precision, <I>x</I> = <code>d</code>
+	for real double precision, <I>x</I> = <code>c</code> for complex single precision,
+	<I>x</I> = <code>z</code> for complex double precision;
+</LI>
+<LI>the preconditioner data structure must be of type
+  <code>mld_</code><I>x</I><code>prec_type</code>, with <I>x</I> =    
+  <code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, according to the sparse
+  matrix data structure;
+</LI>
+<LI>the arrays containing the vectors <IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img72.png"
+ ALT="$v$"> and <IMG
+ WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img73.png"
+ ALT="$w$"> involved in
+  the preconditioner application <IMG
+ WIDTH="82" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
+ SRC="img23.png"
+ ALT="$w=B^{-1}v$"> must be of type   
+  <code>psb_</code><I>x</I><code>vect_type</code> with <I>x</I> =    
+  <code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, in a manner completely
+  analogous to the sparse matrix type;
+</LI>
+<LI>real parameters defining the preconditioner must be declared
+  according to the precision of the sparse matrix and preconditioner
+  data structures (see Section&nbsp;<A HREF="node20.html#sec:precset">6.2</A>).
+</LI>
+</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+A description of each routine is given in the remainder of this section.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precinit(p,ptype,info)</code>
-</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
+<BR><HR>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
+
+<UL>
+<LI><A NAME="tex2html300"
+  HREF="node19.html">Subroutine init</A>
+<LI><A NAME="tex2html301"
+  HREF="node20.html">Subroutine set</A>
+<LI><A NAME="tex2html302"
+  HREF="node21.html">Subroutine build</A>
+<LI><A NAME="tex2html303"
+  HREF="node22.html">Subroutine hierarchy_build</A>
+<LI><A NAME="tex2html304"
+  HREF="node23.html">Subroutine smoothers_build</A>
+<LI><A NAME="tex2html305"
+  HREF="node24.html">Subroutine apply</A>
+<LI><A NAME="tex2html306"
+  HREF="node25.html">Subroutine free</A>
+<LI><A NAME="tex2html307"
+  HREF="node26.html">Subroutine descr</A>
+</UL>
+<!--End of Table of Child-Links-->
+<HR>
 <!--Navigation Panel-->
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+<A NAME="tex2html298"
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+<B> Next:</B> <A NAME="tex2html299"
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diff --git a/docs/html/node19.html b/docs/html/node19.html
index 9f0ff2a6..2211e4c2 100644
--- a/docs/html/node19.html
+++ b/docs/html/node19.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine set</TITLE>
-<META NAME="description" CONTENT="Subroutine set">
+<TITLE>Subroutine init</TITLE>
+<META NAME="description" CONTENT="Subroutine init">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
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-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
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@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
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-  HREF="node17.html">
+  HREF="node18.html">
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@@ -40,30 +40,29 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
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-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
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-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
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-  HREF="node18.html">Subroutine init</A>
+  HREF="node18.html">User Interface</A>
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-<H2><A NAME="SECTION00082000000000000000"></A><A NAME="sec:precset"></A>
+<H2><A NAME="SECTION00081000000000000000"></A><A NAME="sec:precinit"></A>
 <BR>
-Subroutine set
+Subroutine init
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%set(what,val,info [,ilev, ilmax, pos])</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%init(ptype,info)</code>
 </FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine sets the parameters defining the preconditioner <code>p</code>. More
-precisely, the parameter identified by <code>what</code> is assigned the value
-contained in <code>val</code>. 
+This routine allocates and initializes the preconditioner
+<code>p</code>, according to the preconditioner type chosen by the user.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -71,28 +70,17 @@ contained in <code>val</code>.
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>what</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=*)</code>. </FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>ptype</code>  </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=*), intent(in)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The parameter to be set. It can be specified through its name;
-                the string is case-insensitive. See
-                Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">  
-<code>val </code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer</code> <I>or</I> <code>character(len=*)</code> <I>or</I>
-                <code>real(psb_spk_)</code> <I>or</I> <code>real(psb_dpk_)</code>,
-                <code>intent(in)</code>.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The type of preconditioner. Its values are specified
+              in Table&nbsp;<A HREF="#tab:precinit">1</A>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The value of the parameter to be set. The list of allowed
-                values and the corresponding data types is given in
-                Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
-                When the value is of type <code>character(len=*)</code>,
-                it is also treated as case insensitive.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Note that the strings are case insensitive.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
 <code>info</code>   </FONT></FONT></FONT></TD>
@@ -100,49 +88,7 @@ contained in <code>val</code>.
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A>
-                for details.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>ilev</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, optional, intent(in)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> For the multi-level preconditioner, the level at which the
-                preconditioner parameter has to be set.
-                The levels are numbered in increasing
-                order starting from the finest one, i.e., level 1 is the finest level.
-                If <code>ilev</code> is not present, the parameter identified by <code>what</code>
-                is set at all the appropriate levels (see
-                Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>).</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>ilmax</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, optional, intent(in)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> For the multi-level preconditioner, when both
-                <code>ilev</code> and <code>ilmax</code> are present, the settings
-                are applied at all levels <code>ilev:ilmax</code>. When
-                <code>ilev</code> is present but <code>ilmax</code> is not, then
-                the default is <code>ilmax=ilev</code>.
-                The levels are numbered in increasing
-                order starting from the finest one, i.e., level 1 is the finest level. </FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>pos</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>charater(len=*), optional, intent(in)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Whether the other arguments apply only to the pre-smoother (<code>'PRE'</code>)
-                or to the post-smoother (<code>'POST'</code>). If <code>pos</code> is not present,
-                the other arguments are applied to both smoothers.
-                If the preconditioner is one-level or the parameter identified by <code>what</code>
-                does not concern the smoothers, <code>pos</code> is ignored.
-</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
@@ -151,731 +97,9 @@ as follows:
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precset(p,what,val,info)</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precinit(p,ptype,info)</code>
 </FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-However, in this case the optional arguments <code>ilev</code>, <code>ilmax</code>, and <code>pos</code>
-cannot be used. 
-<BR></FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">A variety of preconditioners can be obtained
-by a suitable setting of the preconditioner parameters. These parameters
-can be logically divided into four groups, i.e., parameters defining
-</FONT></FONT></FONT>
-<OL>
-<LI>the type of multi-level cycle and how many cycles must be applied;
-</LI>
-<LI>the aggregation algorithm;
-</LI>
-<LI>the coarse-space correction at the coarsest level (for multi-level
-                 preconditioners only);
-</LI>
-<LI>the smoother of the multi-level preconditioners, or the one-level
-                  preconditioner.
-
-<P>
-</LI>
-</OL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-A list of the parameters that can be set, along with their allowed and
-default values, is given in Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
-For a description of the meaning of the parameters, please
-refer also to Section&nbsp;<A HREF="node11.html#sec:background">4</A>. 
-<BR></FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 2.</B> A smoother is usually obtained by combining two objects:
-a smoother (<code>SMOOTHER_TYPE</code>) and a local solver (<code>SUB_SOLVE</code>),
-as specified in Tables&nbsp;<A HREF="#tab:p_smoother">7</A>-<A HREF="#tab:p_smoother_1">8</A>.
-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,
-the hybrid Gauss-Seidel smoother (see Note in Table&nbsp;<A HREF="#tab:p_smoother">7</A>)
-is obtained by combining the block-Jacobi smoother object with a single sweep
-of the Gauss-Seidel solver object, while the point-Jacobi smoother is the
-result of combining the block-Jacobi smoother object with a single sweep
-of the pointwise-Jacobi solver object. However, for simplicity, shortcuts are
-provided to set point-Jacobi, hybrid (forward) Gauss-Seidel, and
-hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined
-by setting only <code>SMOOTHER_TYPE</code> to appropriate values (see
-Tables&nbsp;<A HREF="#tab:p_smoother">7</A>), i.e., without setting
-<code>SUB_SOLVE</code> too.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The smoother and solver objects are arranged in a
-hierarchical manner. When specifying a smoother object, its parameters,
-including the local solver, are set to their default values, and when a solver
-object is specified, its defaults are also set, overriding in both
-cases any previous settings even if explicitly specified. Therefore if
-the user sets a smoother, and wishes to use a solver
-different from  the default one, the call to set the solver must come
-<I>after</I> the call to set the smoother. 
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">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&nbsp;<A HREF="#tab:p_coarse">5</A>). 
-<BR></FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 3.</B> In general, a coarsest-level solver cannot be used with
-both the replicated and distributed coarsest-matrix layout;
-therefore, setting the solver after the layout may change the layout.
-Similarly, setting the layout after the solver may change the solver.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">More precisely, UMFPACK and SuperLU require the coarsest-level
-matrix to be replicated, while SuperLU_Dist requires it to be distributed.
-In these cases, setting the coarsest-level solver implies that
-the layout is redefined according to the solver, ovverriding any
-previous settings. MUMPS,  point-Jacobi,
-hybrid Gauss-Seidel and block-Jacobi can be applied to
-replicated and distributed matrices, thus their choice
-does not modify any previously specified layout.
-It is worth noting that, when the matrix is replicated,
-the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers
-reduce to the corresponding local solver objects (see Remark&nbsp;2).
-For the point-Jacobi and Gauss-Seidel solvers, these objects
-correspond to a <I>single</I> point-Jacobi sweep and a <I>single</I> 
-Gauss-Seidel sweep, respectively, which are very poor solvers.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">On the other hand, the distributed layout can be used with any solver
-but UMFPACK and SuperLU; therefore, if any of these two solvers has already
-been selected, the coarsest-level solver is changed to block-Jacobi,
-with the previously chosen solver applied to the local blocks.
-Likewise, the replicated layout can be used with any solver but SuperLu_Dist;
-therefore, if SuperLu_Dist has been previously set, the coarsest-level
-solver is changed to the default sequential solver.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1330"></A>
-<TABLE>
-<CAPTION><STRONG>Table 2:</STRONG>
-Parameters defining the multi-level cycle and the number of cycles to
-be applied.
-</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>what</code></TD>
-<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><code>val</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><SMALL>DEFAULT</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204><SMALL>COMMENTS</SMALL></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>'ML_CYCLE'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'VCYCLE'</TT> 
-<P>
-<TT>'WCYCLE'</TT>   
-<P>
-<TT>'KCYCLE'</TT> 
-<P>
-<TT>'MULT'</TT> 
-<P>
-<TT>'ADD'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'VCYCLE'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204>Multi-level cycle: V-cycle, W-cycle, K-cycle, hybrid Multiplicative Schwarz,
-                           and Additive Schwarz. 
-<P>
-Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and
-                           is included for compatibility with previous versions of MLD2P4.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>'OUTER_SWEEPS'</code></TD>
-<TD ALIGN="LEFT"><TT>integer</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any integer 
-<P>
-number <IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img74.png"
- ALT="$\ge 1$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>1</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204>Number of multi-level cycles.</TD>
-</TR>
-</TABLE>
-</DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1335"></A>
-<TABLE>
-<CAPTION><STRONG>Table 3:</STRONG>
-Parameters defining the aggregation algorithm.
-</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>what</code></TD>
-<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><code>val</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><SMALL>DEFAULT</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196><SMALL>COMMENTS</SMALL></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'MIN_COARSE_SIZE'</code></TD>
-<TD ALIGN="LEFT"><code>integer</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number 
-<P>
-<IMG
- WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img75.png"
- ALT="$&gt; 0$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><!-- MATH
- $\lfloor 40 \sqrt[3]{n} \rfloor$
- -->
-<IMG
- WIDTH="63" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img76.png"
- ALT="$\lfloor 40 \sqrt[3]{n} \rfloor$">, where <IMG
- WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img77.png"
- ALT="$n$"> is the dimension
-                            of the matrix at the finest level</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Coarse size threshold. The aggregation stops
-                            if  the global number of variables of the
-                            computed coarsest matrix
-                            is lower than or equal to this threshold
-                           (see Note).</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'MIN_CR_RATIO'</code></TD>
-<TD ALIGN="LEFT"><code>real</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number 
-<P>
-<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img78.png"
- ALT="$&gt; 1$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82>1.5</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Minimum coarsening ratio. The aggregation stops
-                            if the ratio between the matrix dimensions
-                            at two consecutive levels is lower than or equal to this
-                            threshold (see Note).</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'MAX_LEVS'</code></TD>
-<TD ALIGN="LEFT"><code>integer</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any integer 
-<P>
-number <IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img78.png"
- ALT="$&gt; 1$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82>20</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Maximum number of levels. The aggregation stops
-                           if the number of levels reaches this value (see Note).</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'PAR_AGGR'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'DEC'</TT>, <TT>'SYMDEC'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><TT>'DEC'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Parallel aggregation algorithm. 
-<P>
-Currently, only the
-                         decoupled aggregation (<code>DEC</code>) is available; the
-                           <code>SYMDEC</code> option  applies decoupled
-                           aggregation to  the sparsity pattern
-                           of <IMG
- WIDTH="63" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
- SRC="img79.png"
- ALT="$A+A^T$">.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'AGGR_TYPE'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><B><TT>'VMB'</TT></B></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><B><TT>'VMB'</TT></B></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Type of aggregation algorithm: currently, the scalar aggregation
-                             algorithm by Vanek, Mandel and Brezina is implemented
-                             [<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>].</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'AGGR_PROL'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'SMOOTHED'</TT>, <TT>'UNSMOOTHED'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><TT>'SMOOTHED'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Prolongator used by the aggregation algorithm: smoothed or unsmoothed
-                         (i.e., tentative prolongator).</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> The aggregation algorithm stops when
-at least one of the following criteria is met: 
-the coarse size threshold, the</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5>maximum coarsening ratio, or the maximum number
-of levels is reached. Therefore, the actual number of levels may be</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5>smaller than the specified maximum number
-of levels.</TD>
-</TR>
-</TABLE>
-</DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1339"></A>
-<TABLE>
-<CAPTION><STRONG>Table 4:</STRONG>
-Parameters defining the aggregation algorithm (continued).
-</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>what</code></TD>
-<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><code>val</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><SMALL>DEFAULT</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187><SMALL>COMMENTS</SMALL></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>'AGGR_ORD'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'NATURAL'</TT> 
-<P>
-<TT>'DEGREE'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'NATURAL'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>Initial ordering of indices for the aggregation
-                            algorithm: either natural ordering or sorted by
-                            descending degrees of the nodes in the
-                            matrix graph.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>'AGGR_THRESH'</code></TD>
-<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71>Any&nbsp;real 
-<P>
-number&nbsp;<IMG
- WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
- SRC="img80.png"
- ALT="$\in [0, 1]$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>0.05</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>The threshold <IMG
- WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img81.png"
- ALT="$\theta$"> in the aggregation algorithm,
-                            see (<A HREF="node13.html#eq:strongly_coup">3</A>) in Section&nbsp;<A HREF="node13.html#sec:aggregation">4.2</A>.
-                            See also the note at the bottom of this table.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>'AGGR_FILTER'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'FILTER'</TT> 
-<P>
-<TT>'NOFILTER'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'NOFILTER'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>Matrix used in computing the smoothed
-                           prolongator: filtered or unfiltered (see&nbsp;(<A HREF="node13.html#eq:filtered">5</A>) in Section&nbsp;<A HREF="node13.html#sec:aggregation">4.2</A>).</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> Different thresholds at different levels, such as
-those used in [<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>, Section&nbsp;5.1], can be easily set  by 
-invoking the rou-</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5>tine <TT>set</TT> with
-the parameter <TT>ilev</TT>.</TD>
-</TR>
-</TABLE>
-</DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1344"></A>
-<TABLE>
-<CAPTION><STRONG>Table 5:</STRONG>
-Parameters defining the coarse-space correction at the coarsest
-level.</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>what</code></TD>
-<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><code>val</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><SMALL>DEFAULT</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244><SMALL>COMMENTS</SMALL></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_MAT'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'DIST'</TT> 
-<P>
-<TT>'REPL'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'REPL'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Coarsest matrix layout: distributed among the processes or
-                           replicated on each of them.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_SOLVE'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'MUMPS'</TT> 
-<P>
-<TT>'UMF'</TT> 
-<P>
-<TT>'SLU'</TT> 
-<P>
-<TT>'SLUDIST'</TT> 
-<P>
-<TT>'JACOBI'</TT> 
-<P>
-<TT>'GS'</TT> 
-<P>
-<TT>'BJAC'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48>See&nbsp;Note.</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Solver used at the coarsest level: sequential
-                           LU from MUMPS, UMFPACK, or SuperLU
-                           (plus triangular solve); 
-                           distributed LU from MUMPS or SuperLU_Dist
-                           (plus triangular solve);
-                           point-Jacobi, hybrid Gauss-Seidel or block-Jacobi. 
-<P>
-Note that <TT>UMF</TT> and <TT>SLU</TT> require the coarsest
-                           matrix to be replicated, <TT>SLUDIST</TT>,  <TT>JACOBI</TT>,
-                           <TT>GS</TT> and <TT>BJAC</TT> require it to be
-                           distributed, <TT>MUMPS</TT> 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 
-                          value UMFPACK and SuperLU_Dist
-                           are available only in double precision.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_SUBSOLVE'</code></TD>
-<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'ILU'</TT> 
-<P>
-<TT>'ILUT'</TT> 
-<P>
-<TT>'MILU'</TT> 
-<P>
-<TT>'MUMPS'</TT> 
-<P>
-<TT>'SLU'</TT> 
-<P>
-<TT>'UMF'</TT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48>See&nbsp;Note.</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Solver for the diagonal blocks of the coarse matrix,
-                           in case the block Jacobi solver
-                           is chosen as coarsest-level solver: ILU(<IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img82.png"
- ALT="$p$">), ILU(<IMG
- WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img83.png"
- ALT="$p,t$">),
-                           MILU(<IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img82.png"
- ALT="$p$">), LU from MUMPS, SuperLU or UMFPACK 
-                          (plus triangular solve).
-                          Note that UMFPACK and SuperLU_Dist
-                          are available only in double precision.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> Defaults for <TT>COARSE_SOLVE</TT> and 
-<TT>COARSE_SUBSOLVE</TT> are chosen in the following  order:</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5>single precision version - <TT>MUMPS</TT> if installed, 
-                               then <TT>SLU</TT> if installed, 
-                               <TT>ILU</TT> otherwise;</TD>
-</TR>
-<TR><TD ALIGN="LEFT" COLSPAN=5>double precision version - <TT>UMF</TT> if installed, 
-                               then <TT>MUMPS</TT> if installed, then <TT>SLU</TT> if  
-                               installed, <TT>ILU</TT> otherwise.</TD>
-</TR>
-</TABLE>
-</DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1346"></A>
-<TABLE>
-<CAPTION><STRONG>Table 6:</STRONG>
-Parameters defining the coarse-space correction at the coarsest
-level (continued).</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>what</code></TD>
-<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><code>val</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43><SMALL>DEFAULT</SMALL></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213><SMALL>COMMENTS</SMALL></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_SWEEPS'</code></TD>
-<TD ALIGN="LEFT"><code>integer</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any integer 
-<P>
-number <IMG
- WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img75.png"
- ALT="$&gt; 0$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>10</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Number of sweeps when <code>JACOBI</code>, <code>GS</code> or <code>BJAC</code>
-                           is chosen as coarsest-level solver.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_FILLIN'</code></TD>
-<TD ALIGN="LEFT"><code>integer</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any integer 
-<P>
-number <IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img84.png"
- ALT="$\ge 0$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>0</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Fill-in level <IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img82.png"
- ALT="$p$"> of the ILU factorizations.</TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_ILUTHRS'</code></TD>
-<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any real 
-<P>
-number <IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img84.png"
- ALT="$\ge 0$"></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>0</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Drop tolerance <IMG
- WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img85.png"
- ALT="$t$"> in the ILU(<IMG
- WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img83.png"
- ALT="$p,t$">) factorization.</TD>
-</TR>
-</TABLE>
-</DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1348"></A>
-<TABLE>
-<CAPTION><STRONG>Table 7:</STRONG>
-Parameters defining the smoother or the details of the one-level preconditioner.
-</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">
-<code>what</code>              </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <SMALL>DATA TYPE</SMALL>        </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1">  <code>val</code>      </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <SMALL>DEFAULT</SMALL>  </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1">
-<SMALL>COMMENTS</SMALL> </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SMOOTHER_TYPE'</code>  </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> <code>'JACOBI'</code> </FONT>
-<P>
-<FONT SIZE="-1"><code>'GS'</code> </FONT>
-<P>
-<FONT SIZE="-1"><code>'BGS'</code> </FONT>
-<P>
-<FONT SIZE="-1"><code>'BJAC'</code>
-                            </FONT>
-<P>
-<FONT SIZE="-1"><code>'AS'</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>'FBGS'</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> Type of smoother used in the multi-level preconditioner:
-                            point-Jacobi, hybrid (forward) Gauss-Seidel,
-                            hybrid backward Gauss-Seidel, block-Jacobi, and
-                            Additive Schwarz. </FONT>
-<P>
-<FONT SIZE="-1">It is ignored by one-level preconditioners. </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SUB_SOLVE'</code>  </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> <TT>'JACOBI'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'GS'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'BGS'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'ILU'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'ILUT'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'MILU'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'MUMPS'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'SLU'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'UMF'</TT>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <TT>GS</TT> and <TT>BGS</TT> for pre- and post-smoothers
-                            of multi-level preconditioners, respectively </FONT>
-<P>
-<FONT SIZE="-1"><TT>ILU</TT> for block-Jacobi and Additive Schwarz
-                            one-level preconditioners
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> The local solver to be used with the smoother or one-level
-                            preconditioner (see Remark&nbsp;2, page&nbsp;24): point-Jacobi,
-                            hybrid (forward) Gauss-Seidel, hybrid backward
-                           Gauss-Seidel, ILU(<IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img82.png"
- ALT="$p$">),  ILU(<IMG
- WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img83.png"
- ALT="$p,t$">), MILU(<IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img82.png"
- ALT="$p$">),
-                           LU from MUMPS, SuperLU or UMFPACK
-                           (plus triangular solve). See Note for details on hybrid
-                           Gauss-Seidel. </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SMOOTHER_SWEEPS'</code>  </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> Any integer </FONT>
-<P>
-<FONT SIZE="-1">number&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img84.png"
- ALT="$\ge 0$">
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> 1
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> Number of sweeps of the smoother or one-level preconditioner.
-                            In the multi-level case, no pre-smother or
-                            post-smoother is used if this parameter is set to 0 
-                            together with <code>pos='PRE'</code> or <code>pos='POST</code>,
-                           respectively. </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SUB_OVR'</code>  </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> Any integer </FONT>
-<P>
-<FONT SIZE="-1">number&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img84.png"
- ALT="$\ge 0$">
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> 1
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> Number of overlap layers, for Additive Schwarz only. </FONT></TD>
-</TR>
-</TABLE></DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><P></P>
-<DIV ALIGN="CENTER"><A NAME="1350"></A>
-<TABLE>
-<CAPTION><STRONG>Table 8:</STRONG>
-Parameters defining the smoother or the details of the one-level preconditioner
-(continued).</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">
-<code>what</code>              </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <SMALL>DATA TYPE</SMALL>        </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1">  <code>val</code>      </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1">  <SMALL>DEFAULT</SMALL>  </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1">
-<SMALL>COMMENTS</SMALL> </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_RESTR'</code>   </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> <TT>'HALO'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'NONE'</TT>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> <TT>'HALO'</TT>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Type of restriction operator,  for Additive Schwarz only:
-                           <TT>HALO</TT> for taking into account the overlap, <TT>NONE</TT> 
-                           for neglecting it. </FONT>
-<P>
-<FONT SIZE="-1">Note that <TT>HALO</TT> must be chosen for
-                          the classical Addditive Schwarz smoother and its RAS variant.</FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_PROL'</code>   </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> <TT>'SUM'</TT> </FONT>
-<P>
-<FONT SIZE="-1"><TT>'NONE'</TT>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> <TT>'NONE'</TT>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Type of prolongation operator, for Additive Schwarz only:
-                           <TT>SUM</TT> for adding the contributions from the overlap, <TT>NONE</TT>
-                           for neglecting them.   </FONT>
-<P>
-<FONT SIZE="-1">Note that <TT>SUM</TT> must be chosen for the classical Additive
-                          Schwarz smoother, and <TT>NONE</TT> for its RAS variant. </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_FILLIN'</code>  </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> Any integer </FONT>
-<P>
-<FONT SIZE="-1">number&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img84.png"
- ALT="$\ge 0$">
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> 0
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Fill-in level <IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img82.png"
- ALT="$p$"> of the incomplete LU factorizations. </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_ILUTHRS'</code>  </FONT></TD>
-<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>real(</code><I>kind_parameter</I><code>)</code>
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> Any real number&nbsp;<IMG
- WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img84.png"
- ALT="$\ge 0$">
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> 0
-                         </FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Drop tolerance <IMG
- WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img85.png"
- ALT="$t$"> in the ILU(<IMG
- WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img83.png"
- ALT="$p,t$">) factorization. </FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  </FONT></TD>
-<TD></TD>
-<TD></TD>
-<TD></TD>
-<TD></TD>
-</TR>
-</TABLE></DIV>
-</TD></TR>
-</TABLE>
-</DIV><P></P>
-<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
@@ -884,7 +108,7 @@ Parameters defining the smoother or the details of the one-level preconditioner
   HREF="node20.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html314"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html308"
   HREF="node18.html">
@@ -894,11 +118,11 @@ Parameters defining the smoother or the details of the one-level preconditioner
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html319"
-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
 <B> Up:</B> <A NAME="tex2html315"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html309"
-  HREF="node18.html">Subroutine init</A>
+  HREF="node18.html">User Interface</A>
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 <!--End of Navigation Panel-->
diff --git a/docs/html/node2.html b/docs/html/node2.html
index a3236629..d1f05927 100644
--- a/docs/html/node2.html
+++ b/docs/html/node2.html
@@ -26,21 +26,21 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <BODY >
 <!--Navigation Panel-->
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+<A NAME="tex2html77"
   HREF="node3.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html74"
+<A NAME="tex2html75"
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-<A NAME="tex2html68"
+<A NAME="tex2html69"
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+<B> Next:</B> <A NAME="tex2html78"
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-<B> Up:</B> <A NAME="tex2html75"
+<B> Up:</B> <A NAME="tex2html76"
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-<B> Previous:</B> <A NAME="tex2html69"
+<B> Previous:</B> <A NAME="tex2html70"
   HREF="node1.html">Abstract</A>
 <BR>
 <BR>
@@ -53,72 +53,72 @@ Contents</A>
 <!--Table of Contents-->
 
 <UL>
-<LI><A NAME="tex2html78"
-  HREF="node3.html">General Overview</A>
 <LI><A NAME="tex2html79"
-  HREF="node4.html">Code Distribution</A>
+  HREF="node3.html">General Overview</A>
 <LI><A NAME="tex2html80"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
-<UL>
+  HREF="node4.html">Code Distribution</A>
 <LI><A NAME="tex2html81"
-  HREF="node6.html">Prerequisites</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
+<UL>
 <LI><A NAME="tex2html82"
-  HREF="node7.html">Optional third party libraries</A>
+  HREF="node7.html">Prerequisites</A>
 <LI><A NAME="tex2html83"
-  HREF="node8.html">Configuration options</A>
+  HREF="node8.html">Optional third party libraries</A>
 <LI><A NAME="tex2html84"
-  HREF="node9.html">Bug reporting</A>
+  HREF="node9.html">Configuration options</A>
 <LI><A NAME="tex2html85"
-  HREF="node10.html">Example and test programs</A>
+  HREF="node10.html">Bug reporting</A>
+<LI><A NAME="tex2html86"
+  HREF="node11.html">Example and test programs</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html86"
-  HREF="node11.html">Multigrid Background</A>
-<UL>
 <LI><A NAME="tex2html87"
-  HREF="node12.html">AMG preconditioners</A>
+  HREF="node12.html">Multigrid Background</A>
+<UL>
 <LI><A NAME="tex2html88"
-  HREF="node13.html">Smoothed Aggregation</A>
+  HREF="node13.html">AMG preconditioners</A>
 <LI><A NAME="tex2html89"
-  HREF="node14.html">Smoothers and coarsest-level solvers</A>
+  HREF="node14.html">Smoothed Aggregation</A>
+<LI><A NAME="tex2html90"
+  HREF="node15.html">Smoothers and coarsest-level solvers</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html90"
-  HREF="node15.html">Getting Started</A>
-<UL>
 <LI><A NAME="tex2html91"
-  HREF="node16.html">Examples</A>
+  HREF="node16.html">Getting Started</A>
+<UL>
+<LI><A NAME="tex2html92"
+  HREF="node17.html">Examples</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html92"
-  HREF="node17.html">User Interface</A>
-<UL>
 <LI><A NAME="tex2html93"
-  HREF="node18.html">Subroutine init</A>
+  HREF="node18.html">User Interface</A>
+<UL>
 <LI><A NAME="tex2html94"
-  HREF="node19.html">Subroutine set</A>
+  HREF="node19.html">Subroutine init</A>
 <LI><A NAME="tex2html95"
-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
 <LI><A NAME="tex2html96"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
 <LI><A NAME="tex2html97"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
 <LI><A NAME="tex2html98"
-  HREF="node23.html">Subroutine apply</A>
+  HREF="node23.html">Subroutine smoothers_build</A>
 <LI><A NAME="tex2html99"
-  HREF="node24.html">Subroutine free</A>
+  HREF="node24.html">Subroutine apply</A>
 <LI><A NAME="tex2html100"
-  HREF="node25.html">Subroutine descr</A>
+  HREF="node25.html">Subroutine free</A>
+<LI><A NAME="tex2html101"
+  HREF="node26.html">Subroutine descr</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html101"
-  HREF="node26.html">Adding new smoother and solver objects to MLD2P4</A>
 <LI><A NAME="tex2html102"
-  HREF="node27.html">Error Handling</A>
+  HREF="node27.html">Adding new smoother and solver objects to MLD2P4</A>
 <LI><A NAME="tex2html103"
-  HREF="node28.html">License</A>
+  HREF="node28.html">Error Handling</A>
 <LI><A NAME="tex2html104"
-  HREF="node29.html">Bibliography</A>
+  HREF="node29.html">License</A>
+<LI><A NAME="tex2html105"
+  HREF="node30.html">Bibliography</A>
 </UL>
 <!--End of Table of Contents-->
 </FONT></FONT></FONT>
diff --git a/docs/html/node20.html b/docs/html/node20.html
index 0f8f5af1..54203990 100644
--- a/docs/html/node20.html
+++ b/docs/html/node20.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine build</TITLE>
-<META NAME="description" CONTENT="Subroutine build">
+<TITLE>Subroutine set</TITLE>
+<META NAME="description" CONTENT="Subroutine set">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node21.html">
 <LINK REL="previous" HREF="node19.html">
-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
 <LINK REL="next" HREF="node21.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node21.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
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+  HREF="node18.html">
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 <A NAME="tex2html320"
   HREF="node19.html">
@@ -40,30 +40,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html331"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
 <B> Up:</B> <A NAME="tex2html327"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html321"
-  HREF="node19.html">Subroutine set</A>
+  HREF="node19.html">Subroutine init</A>
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   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00083000000000000000"></A><A NAME="sec:precbld"></A>
+<H2><A NAME="SECTION00082000000000000000"></A><A NAME="sec:precset"></A>
 <BR>
-Subroutine build
+Subroutine set
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%build(a,desc_a,info)</code>
-<BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%set(what,val,info [,ilev, ilmax, pos])</code>
+</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine builds the one-level preconditioner <code>p</code> according to the requirements
-made by the user through the routines <code>init</code> and <code>set</code>
-(see Sections&nbsp;<A HREF="node21.html#sec:hier_bld">6.4</A> and&nbsp;<A HREF="node22.html#sec:smooth_bld">6.5</A> for multi-level preconditioners).
+This routine sets the parameters defining the preconditioner <code>p</code>. More
+precisely, the parameter identified by <code>what</code> is assigned the value
+contained in <code>val</code>. 
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -71,34 +71,78 @@ made by the user through the routines <code>init</code> and <code>set</code>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-<code>a</code>  </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>. </FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>what</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=*)</code>. </FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The sparse matrix structure containing the local part of the
-                matrix to be preconditioned. Note that <I>x</I> must be chosen according
-                to the real/complex, single/double precision version of MLD2P4 under use.
-                See the PSBLAS User's Guide for details [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The parameter to be set. It can be specified through its name;
+                the string is case-insensitive. See
+                Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.</FONT></FONT></FONT></TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>desc_a</code> </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>type(psb_desc_type), intent(in)</code>. </FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">  
+<code>val </code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer</code> <I>or</I> <code>character(len=*)</code> <I>or</I>
+                <code>real(psb_spk_)</code> <I>or</I> <code>real(psb_dpk_)</code>,
+                <code>intent(in)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
-                details [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The value of the parameter to be set. The list of allowed
+                values and the corresponding data types is given in
+                Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
+                When the value is of type <code>character(len=*)</code>,
+                it is also treated as case insensitive.</FONT></FONT></FONT></TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>info</code>   </FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>info</code>   </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A>
+                for details.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>ilev</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, optional, intent(in)</code>.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> For the multi-level preconditioner, the level at which the
+                preconditioner parameter has to be set.
+                The levels are numbered in increasing
+                order starting from the finest one, i.e., level 1 is the finest level.
+                If <code>ilev</code> is not present, the parameter identified by <code>what</code>
+                is set at all the appropriate levels (see
+                Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>).</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>ilmax</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, optional, intent(in)</code>.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> For the multi-level preconditioner, when both
+                <code>ilev</code> and <code>ilmax</code> are present, the settings
+                are applied at all levels <code>ilev:ilmax</code>. When
+                <code>ilev</code> is present but <code>ilmax</code> is not, then
+                the default is <code>ilmax=ilev</code>.
+                The levels are numbered in increasing
+                order starting from the finest one, i.e., level 1 is the finest level. </FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>pos</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>charater(len=*), optional, intent(in)</code>.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Whether the other arguments apply only to the pre-smoother (<code>'PRE'</code>)
+                or to the post-smoother (<code>'POST'</code>). If <code>pos</code> is not present,
+                the other arguments are applied to both smoothers.
+                If the preconditioner is one-level or the parameter identified by <code>what</code>
+                does not concern the smoothers, <code>pos</code> is ignored.
+</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
@@ -107,13 +151,731 @@ as follows:
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precbld(p,what,val,info)</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precset(p,what,val,info)</code>
 </FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-In this case, the routine can be used to build multi-level preconditioners too.
+However, in this case the optional arguments <code>ilev</code>, <code>ilmax</code>, and <code>pos</code>
+cannot be used. 
+<BR></FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">A variety of preconditioners can be obtained
+by a suitable setting of the preconditioner parameters. These parameters
+can be logically divided into four groups, i.e., parameters defining
+</FONT></FONT></FONT>
+<OL>
+<LI>the type of multi-level cycle and how many cycles must be applied;
+</LI>
+<LI>the aggregation algorithm;
+</LI>
+<LI>the coarse-space correction at the coarsest level (for multi-level
+                 preconditioners only);
+</LI>
+<LI>the smoother of the multi-level preconditioners, or the one-level
+                  preconditioner.
+
+<P>
+</LI>
+</OL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+A list of the parameters that can be set, along with their allowed and
+default values, is given in Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
+For a description of the meaning of the parameters, please
+refer also to Section&nbsp;<A HREF="node12.html#sec:background">4</A>. 
+<BR></FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 2.</B> A smoother is usually obtained by combining two objects:
+a smoother (<code>SMOOTHER_TYPE</code>) and a local solver (<code>SUB_SOLVE</code>),
+as specified in Tables&nbsp;<A HREF="#tab:p_smoother">7</A>-<A HREF="#tab:p_smoother_1">8</A>.
+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,
+the hybrid Gauss-Seidel smoother (see Note in Table&nbsp;<A HREF="#tab:p_smoother">7</A>)
+is obtained by combining the block-Jacobi smoother object with a single sweep
+of the Gauss-Seidel solver object, while the point-Jacobi smoother is the
+result of combining the block-Jacobi smoother object with a single sweep
+of the pointwise-Jacobi solver object. However, for simplicity, shortcuts are
+provided to set point-Jacobi, hybrid (forward) Gauss-Seidel, and
+hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined
+by setting only <code>SMOOTHER_TYPE</code> to appropriate values (see
+Tables&nbsp;<A HREF="#tab:p_smoother">7</A>), i.e., without setting
+<code>SUB_SOLVE</code> too.
 </FONT></FONT></FONT>
 <P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The smoother and solver objects are arranged in a
+hierarchical manner. When specifying a smoother object, its parameters,
+including the local solver, are set to their default values, and when a solver
+object is specified, its defaults are also set, overriding in both
+cases any previous settings even if explicitly specified. Therefore if
+the user sets a smoother, and wishes to use a solver
+different from  the default one, the call to set the solver must come
+<I>after</I> the call to set the smoother. 
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">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&nbsp;<A HREF="#tab:p_coarse">5</A>). 
+<BR></FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 3.</B> In general, a coarsest-level solver cannot be used with
+both the replicated and distributed coarsest-matrix layout;
+therefore, setting the solver after the layout may change the layout.
+Similarly, setting the layout after the solver may change the solver.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">More precisely, UMFPACK and SuperLU require the coarsest-level
+matrix to be replicated, while SuperLU_Dist requires it to be distributed.
+In these cases, setting the coarsest-level solver implies that
+the layout is redefined according to the solver, ovverriding any
+previous settings. MUMPS,  point-Jacobi,
+hybrid Gauss-Seidel and block-Jacobi can be applied to
+replicated and distributed matrices, thus their choice
+does not modify any previously specified layout.
+It is worth noting that, when the matrix is replicated,
+the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers
+reduce to the corresponding local solver objects (see Remark&nbsp;2).
+For the point-Jacobi and Gauss-Seidel solvers, these objects
+correspond to a <I>single</I> point-Jacobi sweep and a <I>single</I> 
+Gauss-Seidel sweep, respectively, which are very poor solvers.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">On the other hand, the distributed layout can be used with any solver
+but UMFPACK and SuperLU; therefore, if any of these two solvers has already
+been selected, the coarsest-level solver is changed to block-Jacobi,
+with the previously chosen solver applied to the local blocks.
+Likewise, the replicated layout can be used with any solver but SuperLu_Dist;
+therefore, if SuperLu_Dist has been previously set, the coarsest-level
+solver is changed to the default sequential solver.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1337"></A>
+<TABLE>
+<CAPTION><STRONG>Table 2:</STRONG>
+Parameters defining the multi-level cycle and the number of cycles to
+be applied.
+</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>what</code></TD>
+<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><code>val</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><SMALL>DEFAULT</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204><SMALL>COMMENTS</SMALL></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>'ML_CYCLE'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'VCYCLE'</TT> 
+<P>
+<TT>'WCYCLE'</TT>   
+<P>
+<TT>'KCYCLE'</TT> 
+<P>
+<TT>'MULT'</TT> 
+<P>
+<TT>'ADD'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'VCYCLE'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204>Multi-level cycle: V-cycle, W-cycle, K-cycle, hybrid Multiplicative Schwarz,
+                           and Additive Schwarz. 
+<P>
+Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and
+                           is included for compatibility with previous versions of MLD2P4.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>'OUTER_SWEEPS'</code></TD>
+<TD ALIGN="LEFT"><TT>integer</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any integer 
+<P>
+number <IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img74.png"
+ ALT="$\ge 1$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>1</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204>Number of multi-level cycles.</TD>
+</TR>
+</TABLE>
+</DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1342"></A>
+<TABLE>
+<CAPTION><STRONG>Table 3:</STRONG>
+Parameters defining the aggregation algorithm.
+</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>what</code></TD>
+<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><code>val</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><SMALL>DEFAULT</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196><SMALL>COMMENTS</SMALL></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'MIN_COARSE_SIZE'</code></TD>
+<TD ALIGN="LEFT"><code>integer</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number 
+<P>
+<IMG
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img75.png"
+ ALT="$&gt; 0$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><!-- MATH
+ $\lfloor 40 \sqrt[3]{n} \rfloor$
+ -->
+<IMG
+ WIDTH="63" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ SRC="img76.png"
+ ALT="$\lfloor 40 \sqrt[3]{n} \rfloor$">, where <IMG
+ WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img77.png"
+ ALT="$n$"> is the dimension
+                            of the matrix at the finest level</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Coarse size threshold. The aggregation stops
+                            if  the global number of variables of the
+                            computed coarsest matrix
+                            is lower than or equal to this threshold
+                           (see Note).</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'MIN_CR_RATIO'</code></TD>
+<TD ALIGN="LEFT"><code>real</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number 
+<P>
+<IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img78.png"
+ ALT="$&gt; 1$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82>1.5</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Minimum coarsening ratio. The aggregation stops
+                            if the ratio between the matrix dimensions
+                            at two consecutive levels is lower than or equal to this
+                            threshold (see Note).</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'MAX_LEVS'</code></TD>
+<TD ALIGN="LEFT"><code>integer</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any integer 
+<P>
+number <IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img78.png"
+ ALT="$&gt; 1$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82>20</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Maximum number of levels. The aggregation stops
+                           if the number of levels reaches this value (see Note).</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'PAR_AGGR'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'DEC'</TT>, <TT>'SYMDEC'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><TT>'DEC'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Parallel aggregation algorithm. 
+<P>
+Currently, only the
+                         decoupled aggregation (<code>DEC</code>) is available; the
+                           <code>SYMDEC</code> option  applies decoupled
+                           aggregation to  the sparsity pattern
+                           of <IMG
+ WIDTH="63" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
+ SRC="img79.png"
+ ALT="$A+A^T$">.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'AGGR_TYPE'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><B><TT>'VMB'</TT></B></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><B><TT>'VMB'</TT></B></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Type of aggregation algorithm: currently, the scalar aggregation
+                             algorithm by Vanek, Mandel and Brezina is implemented
+                             [<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>].</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'AGGR_PROL'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'SMOOTHED'</TT>, <TT>'UNSMOOTHED'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><TT>'SMOOTHED'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Prolongator used by the aggregation algorithm: smoothed or unsmoothed
+                         (i.e., tentative prolongator).</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> The aggregation algorithm stops when
+at least one of the following criteria is met: 
+the coarse size threshold, the</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5>maximum coarsening ratio, or the maximum number
+of levels is reached. Therefore, the actual number of levels may be</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5>smaller than the specified maximum number
+of levels.</TD>
+</TR>
+</TABLE>
+</DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1346"></A>
+<TABLE>
+<CAPTION><STRONG>Table 4:</STRONG>
+Parameters defining the aggregation algorithm (continued).
+</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>what</code></TD>
+<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><code>val</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><SMALL>DEFAULT</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187><SMALL>COMMENTS</SMALL></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>'AGGR_ORD'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'NATURAL'</TT> 
+<P>
+<TT>'DEGREE'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'NATURAL'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>Initial ordering of indices for the aggregation
+                            algorithm: either natural ordering or sorted by
+                            descending degrees of the nodes in the
+                            matrix graph.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>'AGGR_THRESH'</code></TD>
+<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71>Any&nbsp;real 
+<P>
+number&nbsp;<IMG
+ WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ SRC="img80.png"
+ ALT="$\in [0, 1]$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>0.05</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>The threshold <IMG
+ WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img81.png"
+ ALT="$\theta$"> 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>.
+                            See also the note at the bottom of this table.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>'AGGR_FILTER'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'FILTER'</TT> 
+<P>
+<TT>'NOFILTER'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'NOFILTER'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187>Matrix used in computing the smoothed
+                           prolongator: filtered or unfiltered (see&nbsp;(<A HREF="node14.html#eq:filtered">5</A>) in Section&nbsp;<A HREF="node14.html#sec:aggregation">4.2</A>).</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> Different thresholds at different levels, such as
+those used in [<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>, Section&nbsp;5.1], can be easily set  by 
+invoking the rou-</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5>tine <TT>set</TT> with
+the parameter <TT>ilev</TT>.</TD>
+</TR>
+</TABLE>
+</DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1351"></A>
+<TABLE>
+<CAPTION><STRONG>Table 5:</STRONG>
+Parameters defining the coarse-space correction at the coarsest
+level.</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>what</code></TD>
+<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><code>val</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><SMALL>DEFAULT</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244><SMALL>COMMENTS</SMALL></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_MAT'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'DIST'</TT> 
+<P>
+<TT>'REPL'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'REPL'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Coarsest matrix layout: distributed among the processes or
+                           replicated on each of them.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_SOLVE'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'MUMPS'</TT> 
+<P>
+<TT>'UMF'</TT> 
+<P>
+<TT>'SLU'</TT> 
+<P>
+<TT>'SLUDIST'</TT> 
+<P>
+<TT>'JACOBI'</TT> 
+<P>
+<TT>'GS'</TT> 
+<P>
+<TT>'BJAC'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48>See&nbsp;Note.</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Solver used at the coarsest level: sequential
+                           LU from MUMPS, UMFPACK, or SuperLU
+                           (plus triangular solve); 
+                           distributed LU from MUMPS or SuperLU_Dist
+                           (plus triangular solve);
+                           point-Jacobi, hybrid Gauss-Seidel or block-Jacobi. 
+<P>
+Note that <TT>UMF</TT> and <TT>SLU</TT> require the coarsest
+                           matrix to be replicated, <TT>SLUDIST</TT>,  <TT>JACOBI</TT>,
+                           <TT>GS</TT> and <TT>BJAC</TT> require it to be
+                           distributed, <TT>MUMPS</TT> 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 
+                          value UMFPACK and SuperLU_Dist
+                           are available only in double precision.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_SUBSOLVE'</code></TD>
+<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'ILU'</TT> 
+<P>
+<TT>'ILUT'</TT> 
+<P>
+<TT>'MILU'</TT> 
+<P>
+<TT>'MUMPS'</TT> 
+<P>
+<TT>'SLU'</TT> 
+<P>
+<TT>'UMF'</TT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48>See&nbsp;Note.</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Solver for the diagonal blocks of the coarse matrix,
+                           in case the block Jacobi solver
+                           is chosen as coarsest-level solver: ILU(<IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img82.png"
+ ALT="$p$">), ILU(<IMG
+ WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img83.png"
+ ALT="$p,t$">),
+                           MILU(<IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img82.png"
+ ALT="$p$">), LU from MUMPS, SuperLU or UMFPACK 
+                          (plus triangular solve).
+                          Note that UMFPACK and SuperLU_Dist
+                          are available only in double precision.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> Defaults for <TT>COARSE_SOLVE</TT> and 
+<TT>COARSE_SUBSOLVE</TT> are chosen in the following  order:</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5>single precision version - <TT>MUMPS</TT> if installed, 
+                               then <TT>SLU</TT> if installed, 
+                               <TT>ILU</TT> otherwise;</TD>
+</TR>
+<TR><TD ALIGN="LEFT" COLSPAN=5>double precision version - <TT>UMF</TT> if installed, 
+                               then <TT>MUMPS</TT> if installed, then <TT>SLU</TT> if  
+                               installed, <TT>ILU</TT> otherwise.</TD>
+</TR>
+</TABLE>
+</DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1353"></A>
+<TABLE>
+<CAPTION><STRONG>Table 6:</STRONG>
+Parameters defining the coarse-space correction at the coarsest
+level (continued).</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>what</code></TD>
+<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><code>val</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43><SMALL>DEFAULT</SMALL></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213><SMALL>COMMENTS</SMALL></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_SWEEPS'</code></TD>
+<TD ALIGN="LEFT"><code>integer</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any integer 
+<P>
+number <IMG
+ WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img75.png"
+ ALT="$&gt; 0$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>10</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Number of sweeps when <code>JACOBI</code>, <code>GS</code> or <code>BJAC</code>
+                           is chosen as coarsest-level solver.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_FILLIN'</code></TD>
+<TD ALIGN="LEFT"><code>integer</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any integer 
+<P>
+number <IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img84.png"
+ ALT="$\ge 0$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>0</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Fill-in level <IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img82.png"
+ ALT="$p$"> of the ILU factorizations.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>'COARSE_ILUTHRS'</code></TD>
+<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any real 
+<P>
+number <IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img84.png"
+ ALT="$\ge 0$"></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>0</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Drop tolerance <IMG
+ WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img85.png"
+ ALT="$t$"> in the ILU(<IMG
+ WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img83.png"
+ ALT="$p,t$">) factorization.</TD>
+</TR>
+</TABLE>
+</DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1355"></A>
+<TABLE>
+<CAPTION><STRONG>Table 7:</STRONG>
+Parameters defining the smoother or the details of the one-level preconditioner.
+</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">
+<code>what</code>              </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <SMALL>DATA TYPE</SMALL>        </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1">  <code>val</code>      </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <SMALL>DEFAULT</SMALL>  </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1">
+<SMALL>COMMENTS</SMALL> </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SMOOTHER_TYPE'</code>  </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> <code>'JACOBI'</code> </FONT>
+<P>
+<FONT SIZE="-1"><code>'GS'</code> </FONT>
+<P>
+<FONT SIZE="-1"><code>'BGS'</code> </FONT>
+<P>
+<FONT SIZE="-1"><code>'BJAC'</code>
+                            </FONT>
+<P>
+<FONT SIZE="-1"><code>'AS'</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>'FBGS'</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> Type of smoother used in the multi-level preconditioner:
+                            point-Jacobi, hybrid (forward) Gauss-Seidel,
+                            hybrid backward Gauss-Seidel, block-Jacobi, and
+                            Additive Schwarz. </FONT>
+<P>
+<FONT SIZE="-1">It is ignored by one-level preconditioners. </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SUB_SOLVE'</code>  </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> <TT>'JACOBI'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'GS'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'BGS'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'ILU'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'ILUT'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'MILU'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'MUMPS'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'SLU'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'UMF'</TT>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <TT>GS</TT> and <TT>BGS</TT> for pre- and post-smoothers
+                            of multi-level preconditioners, respectively </FONT>
+<P>
+<FONT SIZE="-1"><TT>ILU</TT> for block-Jacobi and Additive Schwarz
+                            one-level preconditioners
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> The local solver to be used with the smoother or one-level
+                            preconditioner (see Remark&nbsp;2, page&nbsp;24): point-Jacobi,
+                            hybrid (forward) Gauss-Seidel, hybrid backward
+                           Gauss-Seidel, ILU(<IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img82.png"
+ ALT="$p$">),  ILU(<IMG
+ WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img83.png"
+ ALT="$p,t$">), MILU(<IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img82.png"
+ ALT="$p$">),
+                           LU from MUMPS, SuperLU or UMFPACK
+                           (plus triangular solve). See Note for details on hybrid
+                           Gauss-Seidel. </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SMOOTHER_SWEEPS'</code>  </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> Any integer </FONT>
+<P>
+<FONT SIZE="-1">number&nbsp;<IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img84.png"
+ ALT="$\ge 0$">
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> 1
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> Number of sweeps of the smoother or one-level preconditioner.
+                            In the multi-level case, no pre-smother or
+                            post-smoother is used if this parameter is set to 0 
+                            together with <code>pos='PRE'</code> or <code>pos='POST</code>,
+                           respectively. </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">  <code>'SUB_OVR'</code>  </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> Any integer </FONT>
+<P>
+<FONT SIZE="-1">number&nbsp;<IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img84.png"
+ ALT="$\ge 0$">
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> 1
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1"> Number of overlap layers, for Additive Schwarz only. </FONT></TD>
+</TR>
+</TABLE></DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><P></P>
+<DIV ALIGN="CENTER"><A NAME="1357"></A>
+<TABLE>
+<CAPTION><STRONG>Table 8:</STRONG>
+Parameters defining the smoother or the details of the one-level preconditioner
+(continued).</CAPTION>
+<TR><TD>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">
+<code>what</code>              </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <SMALL>DATA TYPE</SMALL>        </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1">  <code>val</code>      </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1">  <SMALL>DEFAULT</SMALL>  </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1">
+<SMALL>COMMENTS</SMALL> </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_RESTR'</code>   </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> <TT>'HALO'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'NONE'</TT>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> <TT>'HALO'</TT>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Type of restriction operator,  for Additive Schwarz only:
+                           <TT>HALO</TT> for taking into account the overlap, <TT>NONE</TT> 
+                           for neglecting it. </FONT>
+<P>
+<FONT SIZE="-1">Note that <TT>HALO</TT> must be chosen for
+                          the classical Addditive Schwarz smoother and its RAS variant.</FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_PROL'</code>   </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> <TT>'SUM'</TT> </FONT>
+<P>
+<FONT SIZE="-1"><TT>'NONE'</TT>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> <TT>'NONE'</TT>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Type of prolongation operator, for Additive Schwarz only:
+                           <TT>SUM</TT> for adding the contributions from the overlap, <TT>NONE</TT>
+                           for neglecting them.   </FONT>
+<P>
+<FONT SIZE="-1">Note that <TT>SUM</TT> must be chosen for the classical Additive
+                          Schwarz smoother, and <TT>NONE</TT> for its RAS variant. </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_FILLIN'</code>  </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> Any integer </FONT>
+<P>
+<FONT SIZE="-1">number&nbsp;<IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img84.png"
+ ALT="$\ge 0$">
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> 0
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Fill-in level <IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img82.png"
+ ALT="$p$"> of the incomplete LU factorizations. </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  <code>'SUB_ILUTHRS'</code>  </FONT></TD>
+<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>real(</code><I>kind_parameter</I><code>)</code>
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> Any real number&nbsp;<IMG
+ WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img84.png"
+ ALT="$\ge 0$">
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=62><FONT SIZE="-1"> 0
+                         </FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1"> Drop tolerance <IMG
+ WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img85.png"
+ ALT="$t$"> in the ILU(<IMG
+ WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img83.png"
+ ALT="$p,t$">) factorization. </FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">  </FONT></TD>
+<TD></TD>
+<TD></TD>
+<TD></TD>
+<TD></TD>
+</TR>
+</TABLE></DIV>
+</TD></TR>
+</TABLE>
+</DIV><P></P>
+<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
@@ -122,7 +884,7 @@ In this case, the routine can be used to build multi-level preconditioners too.
   HREF="node21.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html326"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html320"
   HREF="node19.html">
@@ -132,11 +894,11 @@ In this case, the routine can be used to build multi-level preconditioners too.
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html331"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
 <B> Up:</B> <A NAME="tex2html327"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html321"
-  HREF="node19.html">Subroutine set</A>
+  HREF="node19.html">Subroutine init</A>
  &nbsp; <B>  <A NAME="tex2html329"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
diff --git a/docs/html/node21.html b/docs/html/node21.html
index f1e5c65a..b998987f 100644
--- a/docs/html/node21.html
+++ b/docs/html/node21.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine hierarchy_build</TITLE>
-<META NAME="description" CONTENT="Subroutine hierarchy_build">
+<TITLE>Subroutine build</TITLE>
+<META NAME="description" CONTENT="Subroutine build">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node22.html">
 <LINK REL="previous" HREF="node20.html">
-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
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 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node22.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
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@@ -40,30 +40,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html343"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
 <B> Up:</B> <A NAME="tex2html339"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html333"
-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
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 <BR>
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-<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:hier_bld"></A>
+<H2><A NAME="SECTION00083000000000000000"></A><A NAME="sec:precbld"></A>
 <BR>
-Subroutine hierarchy_build
+Subroutine build
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%hierarchy_build(a,desc_a,info)</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%build(a,desc_a,info)</code>
 <BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine builds the hierarchy of matrices and restriction/prolongation
-operators for the multi-level preconditioner <code>p</code>, according to the requirements
-made by the user through the routines <code>init</code> and <code>set</code>.
+This routine builds the one-level preconditioner <code>p</code> according to the requirements
+made by the user through the routines <code>init</code> and <code>set</code>
+(see Sections&nbsp;<A HREF="node22.html#sec:hier_bld">6.4</A> and&nbsp;<A HREF="node23.html#sec:smooth_bld">6.5</A> for multi-level preconditioners).
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -72,17 +72,16 @@ made by the user through the routines <code>init</code> and <code>set</code>.
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-<code>a</code>      </FONT></FONT></FONT></TD>
+<code>a</code>  </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>. </FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The sparse matrix structure containing the local part of the
                 matrix to be preconditioned. Note that <I>x</I> must be chosen according
-                to the real/complex, 
-single/double precision version of MLD2P4 under use.
+                to the real/complex, single/double precision version of MLD2P4 under use.
                 See the PSBLAS User's Guide for details [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
+ HREF="node30.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
 <code>desc_a</code> </FONT></FONT></FONT></TD>
@@ -92,17 +91,29 @@ single/double precision version of MLD2P4 under use.
               </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
                 details [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
+ HREF="node30.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>info</code>   </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For compatibility with the previous versions of MLD2P4, this routine can be also invoked
+as follows:
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precbld(p,what,val,info)</code>
+</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+In this case, the routine can be used to build multi-level preconditioners too.
+</FONT></FONT></FONT>
+<P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
@@ -111,7 +122,7 @@ single/double precision version of MLD2P4 under use.
   HREF="node22.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html338"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html332"
   HREF="node20.html">
@@ -121,11 +132,11 @@ single/double precision version of MLD2P4 under use.
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html343"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
 <B> Up:</B> <A NAME="tex2html339"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html333"
-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
  &nbsp; <B>  <A NAME="tex2html341"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
diff --git a/docs/html/node22.html b/docs/html/node22.html
index 4647922a..344ae846 100644
--- a/docs/html/node22.html
+++ b/docs/html/node22.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine smoothers_build</TITLE>
-<META NAME="description" CONTENT="Subroutine smoothers_build">
+<TITLE>Subroutine hierarchy_build</TITLE>
+<META NAME="description" CONTENT="Subroutine hierarchy_build">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node23.html">
 <LINK REL="previous" HREF="node21.html">
-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
 <LINK REL="next" HREF="node23.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node23.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html350"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html344"
   HREF="node21.html">
@@ -40,32 +40,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html355"
-  HREF="node23.html">Subroutine apply</A>
+  HREF="node23.html">Subroutine smoothers_build</A>
 <B> Up:</B> <A NAME="tex2html351"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html345"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
  &nbsp; <B>  <A NAME="tex2html353"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:smooth_bld"></A>
+<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:hier_bld"></A>
 <BR>
-Subroutine smoothers_build
+Subroutine hierarchy_build
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%smoothers_build(a,desc_a,p,info)</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%hierarchy_build(a,desc_a,info)</code>
 <BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine builds the smoothers and the coarsest-level solvers for the
-multi-level preconditioner <code>p</code>, according to the requirements made by
-the user through the routines <code>init</code> and <code>set</code>, and based on the aggregation
-hierarchy produced by a previous call to <code>hierarchy_build</code>
-(see Section&nbsp;<A HREF="node21.html#sec:hier_bld">6.4</A>). 
+This routine builds the hierarchy of matrices and restriction/prolongation
+operators for the multi-level preconditioner <code>p</code>, according to the requirements
+made by the user through the routines <code>init</code> and <code>set</code>.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -81,9 +79,10 @@ hierarchy produced by a previous call to <code>hierarchy_build</code>
               </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The sparse matrix structure containing the local part of the
                 matrix to be preconditioned. Note that <I>x</I> must be chosen according
-                to the real/complex, single/double precision version of MLD2P4 under use.
+                to the real/complex, 
+single/double precision version of MLD2P4 under use.
                 See the PSBLAS User's Guide for details [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
+ HREF="node30.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
 <code>desc_a</code> </FONT></FONT></FONT></TD>
@@ -93,24 +92,26 @@ hierarchy produced by a previous call to <code>hierarchy_build</code>
               </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
                 details [<A
- HREF="node29.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
+ HREF="node30.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>info</code>   </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
 <!--Navigation Panel-->
 <A NAME="tex2html354"
   HREF="node23.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html350"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html344"
   HREF="node21.html">
@@ -120,11 +121,11 @@ hierarchy produced by a previous call to <code>hierarchy_build</code>
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html355"
-  HREF="node23.html">Subroutine apply</A>
+  HREF="node23.html">Subroutine smoothers_build</A>
 <B> Up:</B> <A NAME="tex2html351"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html345"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
  &nbsp; <B>  <A NAME="tex2html353"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
diff --git a/docs/html/node23.html b/docs/html/node23.html
index fb1abe9a..44b9e1d5 100644
--- a/docs/html/node23.html
+++ b/docs/html/node23.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine apply</TITLE>
-<META NAME="description" CONTENT="Subroutine apply">
+<TITLE>Subroutine smoothers_build</TITLE>
+<META NAME="description" CONTENT="Subroutine smoothers_build">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node24.html">
 <LINK REL="previous" HREF="node22.html">
-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
 <LINK REL="next" HREF="node24.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node24.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html362"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html356"
   HREF="node22.html">
@@ -40,46 +40,32 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html367"
-  HREF="node24.html">Subroutine free</A>
+  HREF="node24.html">Subroutine apply</A>
 <B> Up:</B> <A NAME="tex2html363"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html357"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
  &nbsp; <B>  <A NAME="tex2html365"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precapply"></A>
+<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:smooth_bld"></A>
 <BR>
-Subroutine apply
+Subroutine smoothers_build
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%apply(x,y,desc_a,info [,trans,work])</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%smoothers_build(a,desc_a,p,info)</code>
 <BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine computes <!-- MATH
- $y = op(B^{-1})\, x$
- -->
-<IMG
- WIDTH="112" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img86.png"
- ALT="$y = op(B^{-1})  x$">, where <IMG
- WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
- SRC="img24.png"
- ALT="$B$"> is a previously built
-preconditioner, stored into <code>p</code>, and <IMG
- WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img87.png"
- ALT="$op$">
-denotes the preconditioner itself or its transpose, according to
-the value of <code>trans</code>.
-Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
-<code>p%apply</code> is called within the PSBLAS routine <code>psb_krylov</code>
-and hence it is completely transparent to the user.
+This routine builds the smoothers and the coarsest-level solvers for the
+multi-level preconditioner <code>p</code>, according to the requirements made by
+the user through the routines <code>init</code> and <code>set</code>, and based on the aggregation
+hierarchy produced by a previous call to <code>hierarchy_build</code>
+(see Section&nbsp;<A HREF="node22.html#sec:hier_bld">6.4</A>). 
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -87,30 +73,17 @@ and hence it is completely transparent to the user.
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>x</code>      </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+<code>a</code>      </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>. </FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The local part of the vector <IMG
- WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
- SRC="img88.png"
- ALT="$x$">. Note that <I>type</I> and   
-                <I>kind_parameter</I> must be chosen according
-                to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>y</code>      </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The local part of the vector <IMG
- WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img89.png"
- ALT="$y$">. Note that <I>type</I> and
-                <I>kind_parameter</I> must be chosen according
-                to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The sparse matrix structure containing the local part of the
+                matrix to be preconditioned. Note that <I>x</I> must be chosen according
+                to the real/complex, single/double precision version of MLD2P4 under use.
+                See the PSBLAS User's Guide for details [<A
+ HREF="node30.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
 <code>desc_a</code> </FONT></FONT></FONT></TD>
@@ -118,82 +91,26 @@ and hence it is completely transparent to the user.
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor associated to the matrix to be
-                preconditioned.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
+                details [<A
+ HREF="node30.html#PSBLASGUIDE">13</A>].</FONT></FONT></FONT></TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>info</code>   </FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>info</code>   </FONT></FONT></FONT></TD>
 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>trans</code>  </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=1), optional, intent(in).</code></FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
- $op(B^{-1}) = B^{-1}$
- -->
-<IMG
- WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img90.png"
- ALT="$op(B^{-1}) = B^{-1}$">;
-                if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
- $op(B^{-1}) = B^{-T}$
- -->
-<IMG
- WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
- SRC="img91.png"
- ALT="$op(B^{-1}) = B^{-T}$">
-                (transpose of <IMG
- WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img92.png"
- ALT="$B^{-1})$">;  if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
- $op(B^{-1}) = B^{-C}$
- -->
-<IMG
- WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
- SRC="img93.png"
- ALT="$op(B^{-1}) = B^{-C}$">
-                (conjugate transpose of <IMG
- WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
- SRC="img92.png"
- ALT="$B^{-1})$">.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>work</code>  </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-             </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Workspace. Its size should be at
-               least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
-               Note that <I>type</I> and <I>kind_parameter</I> must be chosen according
-               to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For compatibility with the previous versions of MLD2P4, this routine can be also invoked
-as follows:
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precaply(p,what,val,info)</code>
-</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
 <!--Navigation Panel-->
 <A NAME="tex2html366"
   HREF="node24.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html362"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html356"
   HREF="node22.html">
@@ -203,11 +120,11 @@ as follows:
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html367"
-  HREF="node24.html">Subroutine free</A>
+  HREF="node24.html">Subroutine apply</A>
 <B> Up:</B> <A NAME="tex2html363"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html357"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
  &nbsp; <B>  <A NAME="tex2html365"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
diff --git a/docs/html/node24.html b/docs/html/node24.html
index 53a2959e..8364aec6 100644
--- a/docs/html/node24.html
+++ b/docs/html/node24.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine free</TITLE>
-<META NAME="description" CONTENT="Subroutine free">
+<TITLE>Subroutine apply</TITLE>
+<META NAME="description" CONTENT="Subroutine apply">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node25.html">
 <LINK REL="previous" HREF="node23.html">
-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
 <LINK REL="next" HREF="node25.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node25.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html374"
-  HREF="node17.html">
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html368"
   HREF="node23.html">
@@ -40,28 +40,46 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html379"
-  HREF="node25.html">Subroutine descr</A>
+  HREF="node25.html">Subroutine free</A>
 <B> Up:</B> <A NAME="tex2html375"
-  HREF="node17.html">User Interface</A>
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html369"
-  HREF="node23.html">Subroutine apply</A>
+  HREF="node23.html">Subroutine smoothers_build</A>
  &nbsp; <B>  <A NAME="tex2html377"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00087000000000000000"></A><A NAME="sec:precfree"></A>
+<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precapply"></A>
 <BR>
-Subroutine free
+Subroutine apply
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%free(p,info)</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%apply(x,y,desc_a,info [,trans,work])</code>
 <BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine deallocates the preconditioner data structure <code>p</code>.
+This routine computes <!-- MATH
+ $y = op(B^{-1})\, x$
+ -->
+<IMG
+ WIDTH="112" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img86.png"
+ ALT="$y = op(B^{-1})  x$">, where <IMG
+ WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img24.png"
+ ALT="$B$"> is a previously built
+preconditioner, stored into <code>p</code>, and <IMG
+ WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img87.png"
+ ALT="$op$">
+denotes the preconditioner itself or its transpose, according to
+the value of <code>trans</code>.
+Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
+<code>p%apply</code> is called within the PSBLAS routine <code>psb_krylov</code>
+and hence it is completely transparent to the user.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -69,12 +87,93 @@ This routine deallocates the preconditioner data structure <code>p</code>.
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>info</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>x</code>      </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The local part of the vector <IMG
+ WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img88.png"
+ ALT="$x$">. Note that <I>type</I> and   
+                <I>kind_parameter</I> must be chosen according
+                to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>y</code>      </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The local part of the vector <IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img89.png"
+ ALT="$y$">. Note that <I>type</I> and
+                <I>kind_parameter</I> must be chosen according
+                to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>desc_a</code> </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>type(psb_desc_type), intent(in)</code>. </FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor associated to the matrix to be
+                preconditioned.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>info</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>trans</code>  </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=1), optional, intent(in).</code></FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
+ $op(B^{-1}) = B^{-1}$
+ -->
+<IMG
+ WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img90.png"
+ ALT="$op(B^{-1}) = B^{-1}$">;
+                if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
+ $op(B^{-1}) = B^{-T}$
+ -->
+<IMG
+ WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
+ SRC="img91.png"
+ ALT="$op(B^{-1}) = B^{-T}$">
+                (transpose of <IMG
+ WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img92.png"
+ ALT="$B^{-1})$">;  if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
+ $op(B^{-1}) = B^{-C}$
+ -->
+<IMG
+ WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
+ SRC="img93.png"
+ ALT="$op(B^{-1}) = B^{-C}$">
+                (conjugate transpose of <IMG
+ WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img92.png"
+ ALT="$B^{-1})$">.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>work</code>  </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+             </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Workspace. Its size should be at
+               least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
+               Note that <I>type</I> and <I>kind_parameter</I> must be chosen according
+               to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
@@ -83,13 +182,35 @@ as follows:
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precfree(p,info)</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precaply(p,what,val,info)</code>
 </FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><HR>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
+<!--Navigation Panel-->
+<A NAME="tex2html378"
+  HREF="node25.html">
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
+<A NAME="tex2html374"
+  HREF="node18.html">
+<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
+<A NAME="tex2html368"
+  HREF="node23.html">
+<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
+<A NAME="tex2html376"
+  HREF="node2.html">
+<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
+<BR>
+<B> Next:</B> <A NAME="tex2html379"
+  HREF="node25.html">Subroutine free</A>
+<B> Up:</B> <A NAME="tex2html375"
+  HREF="node18.html">User Interface</A>
+<B> Previous:</B> <A NAME="tex2html369"
+  HREF="node23.html">Subroutine smoothers_build</A>
+ &nbsp; <B>  <A NAME="tex2html377"
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+<!--End of Navigation Panel-->
 
 </BODY>
 </HTML>
diff --git a/docs/html/node25.html b/docs/html/node25.html
index e2357c3c..7dc4fa28 100644
--- a/docs/html/node25.html
+++ b/docs/html/node25.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Subroutine descr</TITLE>
-<META NAME="description" CONTENT="Subroutine descr">
+<TITLE>Subroutine free</TITLE>
+<META NAME="description" CONTENT="Subroutine free">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -18,51 +18,50 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
 
+<LINK REL="next" HREF="node26.html">
 <LINK REL="previous" HREF="node24.html">
-<LINK REL="up" HREF="node17.html">
+<LINK REL="up" HREF="node18.html">
 <LINK REL="next" HREF="node26.html">
 </HEAD>
 
 <BODY >
 <!--Navigation Panel-->
-<A NAME="tex2html388"
+<A NAME="tex2html390"
   HREF="node26.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html384"
-  HREF="node17.html">
+<A NAME="tex2html386"
+  HREF="node18.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html380"
   HREF="node24.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html386"
+<A NAME="tex2html388"
   HREF="node2.html">
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
-<B> Next:</B> <A NAME="tex2html389"
-  HREF="node26.html">Adding new smoother and</A>
-<B> Up:</B> <A NAME="tex2html385"
-  HREF="node17.html">User Interface</A>
+<B> Next:</B> <A NAME="tex2html391"
+  HREF="node26.html">Subroutine descr</A>
+<B> Up:</B> <A NAME="tex2html387"
+  HREF="node18.html">User Interface</A>
 <B> Previous:</B> <A NAME="tex2html381"
-  HREF="node24.html">Subroutine free</A>
- &nbsp; <B>  <A NAME="tex2html387"
+  HREF="node24.html">Subroutine apply</A>
+ &nbsp; <B>  <A NAME="tex2html389"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00088000000000000000"></A><A NAME="sec:precdescr"></A>
+<H2><A NAME="SECTION00087000000000000000"></A><A NAME="sec:precfree"></A>
 <BR>
-Subroutine descr
+Subroutine free
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%descr(info, [iout])</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%free(p,info)</code>
 <BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-This routine prints a description of the preconditioner <code>p</code> to the standard output or
-to a file. It must be called after <code>hierachy_build</code> and <code>smoothers_build</code>,
-or <code>build</code>, have been called.
+This routine deallocates the preconditioner data structure <code>p</code>.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
@@ -71,20 +70,11 @@ or <code>build</code>, have been called.
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>info</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-              </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node27.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
-</TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>iout</code>   </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(in), optional</code>.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The id of the file where the preconditioner description
-                will be printed; the default is the standard output.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
 </TR>
 </TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
@@ -93,37 +83,13 @@ as follows:
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precdescr(p,info [,iout])</code>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precfree(p,info)</code>
 </FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT>
-<P>
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@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
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-<TITLE>Adding new smoother and solver objects to MLD2P4</TITLE>
-<META NAME="description" CONTENT="Adding new smoother and solver objects to MLD2P4">
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-<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:adding"></A>
+<H2><A NAME="SECTION00088000000000000000"></A><A NAME="sec:precdescr"></A>
 <BR>
-Adding new  smoother and solver objects to MLD2P4
-</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+Subroutine descr
+</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Developers can add completely new smoother and/or solver classes
-derived from the base objects in the library (see Remark&nbsp;2 in Section&nbsp;<A HREF="node19.html#sec:precset">6.2</A>),
-without recompiling the library itself. 
-</FONT></FONT></FONT>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%descr(info, [iout])</code>
+<BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">To do so, it is necessary first to select the base type to be extended.
-In our experience, it is quite likely that the new application needs
-only the definition of a ``solver'' object, which is almost
-always acting only on the local part of the distributed matrix. 
-The parallel actions required to connect the various solver objects
-are most often already provided by the block-Jacobi or the additive
-Schwarz smoothers.  To define a new solver, the developer will then
-have to define its components and methods, perhaps taking one of the
-predefined solvers as a starting point, if possible. 
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+This routine prints a description of the preconditioner <code>p</code> to the standard output or
+to a file. It must be called after <code>hierachy_build</code> and <code>smoothers_build</code>,
+or <code>build</code>, have been called.
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Once the new smoother/solver class has been developed, to use it in
-the context of the multilevel preconditioners it is necessary to:
-</FONT></FONT></FONT>
-<UL>
-<LI>declare in the application program a variable of the new type;
-</LI>
-<LI>pass that variable as the argument to the <code>set</code> routine as in the
-following:
-<DIV ALIGN="CENTER">
-<code>call p%set(smoother,info [,ilev,ilmax,pos])</code>
-<BR><code>call p%set(solver,info [,ilev,ilmax,pos])</code>
-
-</DIV>
-</LI>
-<LI>link the code implementing the various methods into the application executable.
-</LI>
-</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-The new solver object is then dynamically included in the
-preconditioner structure, and acts as a <I>mold</I> to which the 
-preconditioner will conform, even though the MLD2P4 library has not
-been modified to account for this new development. 
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">It is possible to define new values for the keyword <code>WHAT</code> in the
-<code>set</code> routine; if the library code does not recognize a keyword,
-it passes it down the composition hierarchy (levels containing
-smoothers containing in turn solvers), so that it can be eventually caught by
-the new solver. 
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">An example is provided in the source code distribution under the
-folder <code>tests/newslv</code>. In this example we are implementing a new
-incomplete factorization variant (which is simply the ILU(0)
-factorization under a new name). Because of the specifics of  this case, it is
-possible to reuse the basic structure of the ILU solver, with its
-L/D/U components and the methods needed to apply the solver; only a
-few methods, such as the description and most importantly the build,
-need to be ovverridden (rewritten). 
-</FONT></FONT></FONT>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
+<P></P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The interfaces for the calls shown above are defined using
-</FONT></FONT></FONT>
-<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-<code>smoother</code> </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>class(mld_x_base_smoother_type)</code> </FONT></FONT></FONT></TD>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>info</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The user-defined new smoother to be employed in the
-                preconditioner.</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node28.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
-<code>solver</code> </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>class(mld_x_base_solver_type)</code> </FONT></FONT></FONT></TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>iout</code>   </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(in), optional</code>.</FONT></FONT></FONT></TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
               </FONT></FONT></FONT></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The user-defined new solver to be employed in the
-                preconditioner.
-</FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The id of the file where the preconditioner description
+                will be printed; the default is the standard output.</FONT></FONT></FONT></TD>
 </TR>
-</TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-The other arguments are defined in the way described in
-Sec.&nbsp;<A HREF="node19.html#sec:precset">6.2</A>.  As an example, in  the <code>tests/newslv</code>
-code we define a new object of type <code>mld_d_tlu_solver_type</code>, and
-we pass it as follows:
-</FONT></FONT></FONT><PRE>
-  ! sparse matrix and preconditioner
-  type(psb_dspmat_type) :: a
-  type(mld_dprec_type)  :: prec
-  type(mld_d_tlu_solver_type) :: tlusv
-
-......
-  !
-  !  prepare the preconditioner: an ML with defaults, but with TLU solver at
-  !  intermediate levels. All other parameters are at default values. 
-  !  
-  call prec%init('ML',       info)
-  call prec%hierarchy_build(a,desc_a,info)
-  nlv = prec%get_nlevs()
-  call prec%set(tlusv,   info,ilev=1,ilmax=max(1,nlv-1))
-  call prec%smoothers_build(a,desc_a,info)
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-</FONT></FONT></FONT><HR>
+</TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For compatibility with the previous versions of MLD2P4, this routine can be also invoked
+as follows:
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precdescr(p,info [,iout])</code>
+</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
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@@ -172,11 +116,11 @@ we pass it as follows:
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diff --git a/docs/html/node27.html b/docs/html/node27.html
index 1be7a8f9..9c785a13 100644
--- a/docs/html/node27.html
+++ b/docs/html/node27.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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-<TITLE>Error Handling</TITLE>
-<META NAME="description" CONTENT="Error Handling">
+<TITLE>Adding new smoother and solver objects to MLD2P4</TITLE>
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@@ -40,39 +40,146 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
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-<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:errors"></A>
+<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:adding"></A>
 <BR>
-Error Handling
+Adding new  smoother and solver objects to MLD2P4
 </H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The error handling in MLD2P4 is based on the PSBLAS (version 2) error
-handling. Error conditions are signaled via an integer argument
-<code>info</code>; whenever an error condition is detected, an error trace
-stack is built by the library up to the top-level, user-callable
-routine. This routine will then decide, according to the user
-preferences, whether the error should be handled by terminating the
-program or by returning the error condition to the user code, which
-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="node29.html#PSBLASGUIDE">13</A>]. 
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Developers can add completely new smoother and/or solver classes
+derived from the base objects in the library (see Remark&nbsp;2 in Section&nbsp;<A HREF="node20.html#sec:precset">6.2</A>),
+without recompiling the library itself. 
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">To do so, it is necessary first to select the base type to be extended.
+In our experience, it is quite likely that the new application needs
+only the definition of a ``solver'' object, which is almost
+always acting only on the local part of the distributed matrix. 
+The parallel actions required to connect the various solver objects
+are most often already provided by the block-Jacobi or the additive
+Schwarz smoothers.  To define a new solver, the developer will then
+have to define its components and methods, perhaps taking one of the
+predefined solvers as a starting point, if possible. 
 </FONT></FONT></FONT>
-<BR><HR>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Once the new smoother/solver class has been developed, to use it in
+the context of the multilevel preconditioners it is necessary to:
+</FONT></FONT></FONT>
+<UL>
+<LI>declare in the application program a variable of the new type;
+</LI>
+<LI>pass that variable as the argument to the <code>set</code> routine as in the
+following:
+<DIV ALIGN="CENTER">
+<code>call p%set(smoother,info [,ilev,ilmax,pos])</code>
+<BR><code>call p%set(solver,info [,ilev,ilmax,pos])</code>
+
+</DIV>
+</LI>
+<LI>link the code implementing the various methods into the application executable.
+</LI>
+</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+The new solver object is then dynamically included in the
+preconditioner structure, and acts as a <I>mold</I> to which the 
+preconditioner will conform, even though the MLD2P4 library has not
+been modified to account for this new development. 
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">It is possible to define new values for the keyword <code>WHAT</code> in the
+<code>set</code> routine; if the library code does not recognize a keyword,
+it passes it down the composition hierarchy (levels containing
+smoothers containing in turn solvers), so that it can be eventually caught by
+the new solver. 
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">An example is provided in the source code distribution under the
+folder <code>tests/newslv</code>. In this example we are implementing a new
+incomplete factorization variant (which is simply the ILU(0)
+factorization under a new name). Because of the specifics of  this case, it is
+possible to reuse the basic structure of the ILU solver, with its
+L/D/U components and the methods needed to apply the solver; only a
+few methods, such as the description and most importantly the build,
+need to be ovverridden (rewritten). 
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The interfaces for the calls shown above are defined using
+</FONT></FONT></FONT>
+<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+<code>smoother</code> </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>class(mld_x_base_smoother_type)</code> </FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The user-defined new smoother to be employed in the
+                preconditioner.</FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+<code>solver</code> </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>class(mld_x_base_solver_type)</code> </FONT></FONT></FONT></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> 
+              </FONT></FONT></FONT></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The user-defined new solver to be employed in the
+                preconditioner.
+</FONT></FONT></FONT></TD>
+</TR>
+</TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+The other arguments are defined in the way described in
+Sec.&nbsp;<A HREF="node20.html#sec:precset">6.2</A>.  As an example, in  the <code>tests/newslv</code>
+code we define a new object of type <code>mld_d_tlu_solver_type</code>, and
+we pass it as follows:
+</FONT></FONT></FONT><PRE>
+  ! sparse matrix and preconditioner
+  type(psb_dspmat_type) :: a
+  type(mld_dprec_type)  :: prec
+  type(mld_d_tlu_solver_type) :: tlusv
+
+......
+  !
+  !  prepare the preconditioner: an ML with defaults, but with TLU solver at
+  !  intermediate levels. All other parameters are at default values. 
+  !  
+  call prec%init('ML',       info)
+  call prec%hierarchy_build(a,desc_a,info)
+  nlv = prec%get_nlevs()
+  call prec%set(tlusv,   info,ilev=1,ilmax=max(1,nlv-1))
+  call prec%smoothers_build(a,desc_a,info)
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+</FONT></FONT></FONT><HR>
+<!--Navigation Panel-->
+<A NAME="tex2html412"
+  HREF="node28.html">
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
+<A NAME="tex2html408"
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+ &nbsp; <B>  <A NAME="tex2html411"
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+<!--End of Navigation Panel-->
 
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diff --git a/docs/html/node28.html b/docs/html/node28.html
index 58e4f069..b7194cdb 100644
--- a/docs/html/node28.html
+++ b/docs/html/node28.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>License</TITLE>
-<META NAME="description" CONTENT="License">
+<TITLE>Error Handling</TITLE>
+<META NAME="description" CONTENT="Error Handling">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -40,63 +40,37 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html425"
-  HREF="node29.html">Bibliography</A>
+  HREF="node29.html">License</A>
 <B> Up:</B> <A NAME="tex2html421"
   HREF="userhtml.html">userhtml</A>
 <B> Previous:</B> <A NAME="tex2html415"
-  HREF="node27.html">Error Handling</A>
+  HREF="node27.html">Adding new smoother and</A>
  &nbsp; <B>  <A NAME="tex2html423"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H1><A NAME="SECTION000110000000000000000"></A><A NAME="sec:license"></A>
+<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:errors"></A>
 <BR>
-License
+Error Handling
 </H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The MLD2P4 is freely distributable under the following copyright
-terms: </FONT></FONT></FONT><PRE> 
-
- 
-                           MLD2P4  version 2.1
-  MultiLevel Domain Decomposition Parallel Preconditioners Package
-             based on PSBLAS (Parallel Sparse BLAS version 3.4)
-  
-  (C) Copyright 2008, 2010, 2012, 2017
-
-  Salvatore Filippone    Cranfield University, Cranfield, UK
-  Ambra Abdullahi Hassan University of Rome Tor Vergata, Rome, IT
-  Alfredo Buttari        CNRS-IRIT, Toulouse, FR
-  Pasqua D'Ambra         IAC-CNR, Naples, IT
-  Daniela di Serafino    University of Campania L. Vanvitelli, Caserta, IT
-
-  Redistribution and use in source and binary forms, with or without
-  modification, are permitted provided that the following conditions
-  are met:
-    1. Redistributions of source code must retain the above copyright
-       notice, this list of conditions and the following disclaimer.
-    2. Redistributions in binary form must reproduce the above copyright
-       notice, this list of conditions, and the following disclaimer in the
-       documentation and/or other materials provided with the distribution.
-    3. The name of the MLD2P4 group or the names of its contributors may
-       not be used to endorse or promote products derived from this
-       software without specific written permission.
- 
-  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
-  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
-  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
-  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
-  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
-  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
-  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-  POSSIBILITY OF SUCH DAMAGE.
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The error handling in MLD2P4 is based on the PSBLAS (version 2) error
+handling. Error conditions are signaled via an integer argument
+<code>info</code>; whenever an error condition is detected, an error trace
+stack is built by the library up to the top-level, user-callable
+routine. This routine will then decide, according to the user
+preferences, whether the error should be handled by terminating the
+program or by returning the error condition to the user code, which
+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="node30.html#PSBLASGUIDE">13</A>]. 
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
 </FONT></FONT></FONT>
 <BR><HR>
 
diff --git a/docs/html/node29.html b/docs/html/node29.html
index ab187489..0af35633 100644
--- a/docs/html/node29.html
+++ b/docs/html/node29.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Bibliography</TITLE>
-<META NAME="description" CONTENT="Bibliography">
+<TITLE>License</TITLE>
+<META NAME="description" CONTENT="License">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -40,140 +40,63 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html437"
-  HREF="node30.html">About this document ...</A>
+  HREF="node30.html">Bibliography</A>
 <B> Up:</B> <A NAME="tex2html433"
   HREF="userhtml.html">userhtml</A>
 <B> Previous:</B> <A NAME="tex2html427"
-  HREF="node28.html">License</A>
+  HREF="node28.html">Error Handling</A>
  &nbsp; <B>  <A NAME="tex2html435"
   HREF="node2.html">Contents</A></B> 
-<BR><BR>
+<BR>
+<BR>
 <!--End of Navigation Panel-->
- </FONT></FONT></FONT>
-<H2><A NAME="SECTION000120000000000000000">
-Bibliography</A>
-</H2><DL COMPACT><DD>
 
+<H1><A NAME="SECTION000110000000000000000"></A><A NAME="sec:license"></A>
+<BR>
+License
+</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<P></P><DT><A NAME="MUMPS">1</A>
-<DD>
-P.&nbsp;R.&nbsp;Amestoy, C.&nbsp;Ashcraft, O.&nbsp;Boiteau, A.&nbsp;Buttari, J.&nbsp;L'Excellent, C.&nbsp;Weisbecker,
-<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
-SIAM Journal on Scientific Computing, volume 37 (3), 2015, A1452-A1474.
-See also <TT>http://mumps.enseeiht.fr</TT>.
<P></P><DT><A NAME="BREZINA_VANEK">2</A>
-<DD>
-M.&nbsp;Brezina, P.&nbsp;Vanek,
-<EM>A Black-Box Iterative Solver Based on a Two-Level Schwarz Method</EM>,
-Computing, 63, 1999, 233-263.
<P></P><DT><A NAME="Briggs2000">3</A>
-<DD>
-W.&nbsp;L.&nbsp;Briggs, V.&nbsp;E.&nbsp;Henson, S.&nbsp;F.&nbsp;McCormick, 
-<EM>A Multigrid Tutorial, Second Edition</EM>,
-SIAM, 2000.
<P></P><DT><A NAME="para_04">4</A>
-<DD>
-A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di Serafino, S.&nbsp;Filippone,
-<EM>Extending PSBLAS to Build Parallel Schwarz Preconditioners</EM>,
-in J.&nbsp;Dongarra, K.&nbsp;Madsen, J.&nbsp;Wasniewski, editors,
-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">5</A>
-<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, 
-18 (3) 2007, 223-239.
<P></P><DT><A NAME="CAI_SARKIS">6</A>
-<DD>
-X.&nbsp;C.&nbsp;Cai, M.&nbsp;Sarkis,
-<EM>A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems</EM>,
-SIAM Journal on Scientific Computing, 21 (2), 1999, 792-797.
<P></P><DT><A NAME="apnum_07">7</A>
-<DD>
-P.&nbsp;D'Ambra, S.&nbsp;Filippone,  D.&nbsp;di&nbsp;Serafino,
-<EM>On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners</EM>,
-Applied Numerical Mathematics, Elsevier Science, 
-57 (11-12), 2007, 1181-1196.
<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>,  ACM Trans. Math. Softw., 37(3), 2010, art. 30.
<P></P><DT><A NAME="UMFPACK">9</A>
-<DD>
-T.&nbsp;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">10</A>
-<DD>
-J.&nbsp;W.&nbsp;Demmel, S.&nbsp;C.&nbsp;Eisenstat, J.&nbsp;R.&nbsp;Gilbert, X.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;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">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 (1) 1990, 1-17.
<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 (1) 1988, 1-17.
<P></P><DT><A NAME="PSBLASGUIDE">13</A>
-<DD>
-S.&nbsp;Filippone, A.&nbsp;Buttari, 
-<EM>PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2012,
-available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
<P></P><DT><A NAME="PSBLAS3">14</A>
-<DD>
-S.&nbsp;Filippone, A.&nbsp;Buttari,
-<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>.
-ACM Transactions on on Mathematical Software, 38 (4), 2012, art.&nbsp;23.
<P></P><DT><A NAME="psblas_00">15</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>
-<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>
-<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 (3), 1979, 308-323.
<P></P><DT><A NAME="SUPERLUDIST">18</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="Notay2008">19</A>
-<DD>
-Y.&nbsp;Notay, P.&nbsp;S.&nbsp;Vassilevski,
-<EM>Recursive Krylov-based multigrid cycles</EM>,
-Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487. 
<P></P><DT><A NAME="Saad_book">20</A>
-<DD>
-Y.&nbsp;Saad,
-<EM>Iterative methods for sparse linear systems</EM>, 2nd edition, SIAM, 2003.
<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">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="Stuben_01">23</A>
-<DD>
-K.&nbsp;St&#252;ben,
-<EM>An Introduction to Algebraic Multigrid</EM>,
-in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, Multigrid,
-Academic Press, 2001.
<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">25</A>
-<DD>
-P.&nbsp;Vanek, J.&nbsp;Mandel, M.&nbsp;Brezina,
-<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
-Computing, 56 (3) 1996, 179-196.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The MLD2P4 is freely distributable under the following copyright
+terms: </FONT></FONT></FONT><PRE> 
+
+ 
+                           MLD2P4  version 2.1
+  MultiLevel Domain Decomposition Parallel Preconditioners Package
+             based on PSBLAS (Parallel Sparse BLAS version 3.4)
+  
+  (C) Copyright 2008, 2010, 2012, 2017
+
+  Salvatore Filippone    Cranfield University, Cranfield, UK
+  Pasqua D'Ambra         IAC-CNR, Naples, IT
+  Daniela di Serafino    University of Campania L. Vanvitelli, Caserta, IT
+
+  Redistribution and use in source and binary forms, with or without
+  modification, are permitted provided that the following conditions
+  are met:
+    1. Redistributions of source code must retain the above copyright
+       notice, this list of conditions and the following disclaimer.
+    2. Redistributions in binary form must reproduce the above copyright
+       notice, this list of conditions, and the following disclaimer in the
+       documentation and/or other materials provided with the distribution.
+    3. The name of the MLD2P4 group or the names of its contributors may
+       not be used to endorse or promote products derived from this
+       software without specific written permission.
+ 
+  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
+  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+  POSSIBILITY OF SUCH DAMAGE.
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
 
-<P>
-</DL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
 </FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><BR><HR>
+<BR><HR>
 
 </BODY>
 </HTML>
diff --git a/docs/html/node3.html b/docs/html/node3.html
index 07fff983..b8c2c7a7 100644
--- a/docs/html/node3.html
+++ b/docs/html/node3.html
@@ -26,26 +26,26 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <BODY >
 <!--Navigation Panel-->
-<A NAME="tex2html115"
+<A NAME="tex2html116"
   HREF="node4.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html111"
+<A NAME="tex2html112"
   HREF="userhtml.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html105"
+<A NAME="tex2html106"
   HREF="node2.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html113"
+<A NAME="tex2html114"
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 <BR>
-<B> Next:</B> <A NAME="tex2html116"
+<B> Next:</B> <A NAME="tex2html117"
   HREF="node4.html">Code Distribution</A>
-<B> Up:</B> <A NAME="tex2html112"
+<B> Up:</B> <A NAME="tex2html113"
   HREF="userhtml.html">userhtml</A>
-<B> Previous:</B> <A NAME="tex2html106"
+<B> Previous:</B> <A NAME="tex2html107"
   HREF="node2.html">Contents</A>
- &nbsp; <B>  <A NAME="tex2html114"
+ &nbsp; <B>  <A NAME="tex2html115"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
@@ -59,9 +59,9 @@ General Overview
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">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 parallel Algebraic MultiGrid (AMG) and Domain 
 Decomposition preconditioners (see, e.g., [<A
- HREF="node29.html#Briggs2000">3</A>,<A
- HREF="node29.html#Stuben_01">23</A>,<A
- HREF="node29.html#dd2_96">21</A>]),
+ HREF="node30.html#Briggs2000">3</A>,<A
+ HREF="node30.html#Stuben_01">23</A>,<A
+ HREF="node30.html#dd2_96">21</A>]),
 to be used in the iterative solution of  linear systems,
 </FONT></FONT></FONT>
 <BR>
@@ -95,8 +95,8 @@ multi-level cycles and smoothers widely used in multigrid methods.
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The multi-level preconditioners implemented in MLD2P4 are obtained by combining
 AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and
 K-cycles&nbsp;[<A
- HREF="node29.html#Briggs2000">3</A>,<A
- HREF="node29.html#Notay2008">19</A>] are available, which allow to define
+ HREF="node30.html#Briggs2000">3</A>,<A
+ HREF="node30.html#Notay2008">19</A>] are available, which allow to define
 almost all the preconditioners in the package, including the multi-level hybrid
 Schwarz ones; a specific cycle is implemented to obtain multi-level additive
 Schwarz preconditioners. The Jacobi, hybridforward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods
@@ -104,8 +104,8 @@ are available as smoothers. An algebraic approach is used to generate a hierarch
 coarse-level matrices and operators, without explicitly using any information on the
 geometry of the original problem, e.g., the discretization of a PDE. To this end,
 the smoothed aggregation technique&nbsp;[<A
- HREF="node29.html#BREZINA_VANEK">2</A>,<A
- HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>]
+ HREF="node30.html#BREZINA_VANEK">2</A>,<A
+ HREF="node30.html#VANEK_MANDEL_BREZINA">25</A>]
 is applied. Either exact or approximate solvers can be used on the coarsest-level
 system. Specifically, different sparse LU factorizations from external
 packages, and native incomplete LU factorizations and Jacobi, hybrid Gauss-Seidel,
@@ -126,8 +126,8 @@ interface.
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">MLD2P4 has been designed to implement scalable and easy-to-use
 multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS)
 computational framework&nbsp;[<A
- HREF="node29.html#psblas_00">15</A>,<A
- HREF="node29.html#PSBLAS3">14</A>]. PSBLAS provides basic linear algebra
+ HREF="node30.html#psblas_00">15</A>,<A
+ HREF="node30.html#PSBLAS3">14</A>]. PSBLAS provides basic linear algebra
 operators and data management facilities for distributed sparse matrices,
 as well as parallel Krylov solvers which can be used with the MLD2P4 preconditioners.
 The choice of PSBLAS has been mainly motivated by the need of having
@@ -150,55 +150,55 @@ few black-box routines at the upper layer allow all users to easily
 build and apply any preconditioner available in MLD2P4;
 facilities are also available allowing  expert users to extend the set of smoothers
 and solvers for building new versions of the preconditioners (see
-Section&nbsp;<A HREF="node26.html#sec:adding">7</A>). 
+Section&nbsp;<A HREF="node27.html#sec:adding">7</A>). 
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We note that the user interface of MLD2P4 2.1 has been extended with respect to the
 previous versions in order to separate the construction of the multi-level hierarchy from
 the construction of the smoothers and solvers, and to allow for more flexibility
 at each level. The software architecture described in&nbsp;[<A
- HREF="node29.html#MLD2P4_TOMS">8</A>] has significantly
+ HREF="node30.html#MLD2P4_TOMS">8</A>] has significantly
 evolved too, in order to fully exploit the Fortran&nbsp;2003 features implemented in PSBLAS 3.
 However, compatibility with previous versions has been preserved.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">This guide is organized as follows. General information on the distribution of the source
 code is reported in Section&nbsp;<A HREF="node4.html#sec:distribution">2</A>, while details on the configuration
-and installation of the package are given in Section&nbsp;<A HREF="node5.html#sec:building">3</A>. A short description
-of the preconditioners implemented in MLD2P4 is provided in Section&nbsp;<A HREF="node11.html#sec:background">4</A>,
+and installation of the package are given in Section&nbsp;<A HREF="node6.html#sec:building">3</A>. A short description
+of the preconditioners implemented in MLD2P4 is provided in Section&nbsp;<A HREF="node12.html#sec:background">4</A>,
 to help the users in choosing among them. The basics for building and applying the
 preconditioners with the Krylov solvers implemented in PSBLAS are reported 
-in&nbsp;Section&nbsp;<A HREF="node15.html#sec:started">5</A>, where the Fortran codes of a few sample programs
+in&nbsp;Section&nbsp;<A HREF="node16.html#sec:started">5</A>, where the Fortran codes of a few sample programs
 are also shown. A reference guide for the user interface routines is provided
-in Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A>. Information on the extension of the package
-through the addition of new smoothers and solvers is reported in Section&nbsp;<A HREF="node26.html#sec:adding">7</A>. 
+in Section&nbsp;<A HREF="node18.html#sec:userinterface">6</A>. Information on the extension of the package
+through the addition of new smoothers and solvers is reported in Section&nbsp;<A HREF="node27.html#sec:adding">7</A>. 
 The error handling mechanism used by the package
-is briefly described in Section&nbsp;<A HREF="node27.html#sec:errors">8</A>. The copyright terms concerning the
-distribution and modification of MLD2P4 are reported in Appendix&nbsp;<A HREF="node28.html#sec:license">A</A>.
+is briefly described in Section&nbsp;<A HREF="node28.html#sec:errors">8</A>. The copyright terms concerning the
+distribution and modification of MLD2P4 are reported in Appendix&nbsp;<A HREF="node29.html#sec:license">A</A>.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT><HR>
 <!--Navigation Panel-->
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+<A NAME="tex2html116"
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-<A NAME="tex2html111"
+<A NAME="tex2html112"
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+<A NAME="tex2html114"
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+<B> Next:</B> <A NAME="tex2html117"
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+<B> Up:</B> <A NAME="tex2html113"
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diff --git a/docs/html/node30.html b/docs/html/node30.html
index f348d8d3..f599d623 100644
--- a/docs/html/node30.html
+++ b/docs/html/node30.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>About this document ...</TITLE>
-<META NAME="description" CONTENT="About this document ...">
+<TITLE>Bibliography</TITLE>
+<META NAME="description" CONTENT="Bibliography">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -18,53 +18,162 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
 
+<LINK REL="next" HREF="node31.html">
 <LINK REL="previous" HREF="node29.html">
 <LINK REL="up" HREF="userhtml.html">
+<LINK REL="next" HREF="node31.html">
 </HEAD>
 
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 <!--Navigation Panel-->
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-<A NAME="tex2html442"
+<A NAME="tex2html448"
+  HREF="node31.html">
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
+<A NAME="tex2html444"
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+<A NAME="tex2html446"
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+<B> Next:</B> <A NAME="tex2html449"
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+<B> Up:</B> <A NAME="tex2html445"
   HREF="userhtml.html">userhtml</A>
 <B> Previous:</B> <A NAME="tex2html439"
-  HREF="node29.html">Bibliography</A>
- &nbsp; <B>  <A NAME="tex2html445"
+  HREF="node29.html">License</A>
+ &nbsp; <B>  <A NAME="tex2html447"
   HREF="node2.html">Contents</A></B> 
-<BR>
-<BR>
+<BR><BR>
 <!--End of Navigation Panel-->
+ </FONT></FONT></FONT>
+<H2><A NAME="SECTION000120000000000000000">
+Bibliography</A>
+</H2><DL COMPACT><DD>
 
-<H1><A NAME="SECTION000130000000000000000">
-About this document ...</A>
-</H1><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
- </FONT></FONT></FONT><P>
-This document was generated using the
-<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2012 (1.2)
 <P>
-Copyright &#169; 1993, 1994, 1995, 1996,
-<A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>, 
-Computer Based Learning Unit, University of Leeds.
-<BR>
-Copyright &#169; 1997, 1998, 1999,
-<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>, 
-Mathematics Department, Macquarie University, Sydney.
+<P></P><DT><A NAME="MUMPS">1</A>
+<DD>
+P.&nbsp;R.&nbsp;Amestoy, C.&nbsp;Ashcraft, O.&nbsp;Boiteau, A.&nbsp;Buttari, J.&nbsp;L'Excellent, C.&nbsp;Weisbecker,
+<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
+SIAM Journal on Scientific Computing, volume 37 (3), 2015, A1452-A1474.
+See also <TT>http://mumps.enseeiht.fr</TT>.
<P></P><DT><A NAME="BREZINA_VANEK">2</A>
+<DD>
+M.&nbsp;Brezina, P.&nbsp;Vanek,
+<EM>A Black-Box Iterative Solver Based on a Two-Level Schwarz Method</EM>,
+Computing, 63, 1999, 233-263.
<P></P><DT><A NAME="Briggs2000">3</A>
+<DD>
+W.&nbsp;L.&nbsp;Briggs, V.&nbsp;E.&nbsp;Henson, S.&nbsp;F.&nbsp;McCormick, 
+<EM>A Multigrid Tutorial, Second Edition</EM>,
+SIAM, 2000.
<P></P><DT><A NAME="para_04">4</A>
+<DD>
+A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di Serafino, S.&nbsp;Filippone,
+<EM>Extending PSBLAS to Build Parallel Schwarz Preconditioners</EM>,
+in J.&nbsp;Dongarra, K.&nbsp;Madsen, J.&nbsp;Wasniewski, editors,
+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">5</A>
+<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, 
+18 (3) 2007, 223-239.
<P></P><DT><A NAME="CAI_SARKIS">6</A>
+<DD>
+X.&nbsp;C.&nbsp;Cai, M.&nbsp;Sarkis,
+<EM>A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems</EM>,
+SIAM Journal on Scientific Computing, 21 (2), 1999, 792-797.
<P></P><DT><A NAME="apnum_07">7</A>
+<DD>
+P.&nbsp;D'Ambra, S.&nbsp;Filippone,  D.&nbsp;di&nbsp;Serafino,
+<EM>On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners</EM>,
+Applied Numerical Mathematics, Elsevier Science, 
+57 (11-12), 2007, 1181-1196.
<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>,  ACM Trans. Math. Softw., 37(3), 2010, art. 30.
<P></P><DT><A NAME="UMFPACK">9</A>
+<DD>
+T.&nbsp;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">10</A>
+<DD>
+J.&nbsp;W.&nbsp;Demmel, S.&nbsp;C.&nbsp;Eisenstat, J.&nbsp;R.&nbsp;Gilbert, X.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;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">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 (1) 1990, 1-17.
<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 (1) 1988, 1-17.
<P></P><DT><A NAME="PSBLASGUIDE">13</A>
+<DD>
+S.&nbsp;Filippone, A.&nbsp;Buttari, 
+<EM>PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2012,
+available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
<P></P><DT><A NAME="PSBLAS3">14</A>
+<DD>
+S.&nbsp;Filippone, A.&nbsp;Buttari,
+<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>.
+ACM Transactions on on Mathematical Software, 38 (4), 2012, art.&nbsp;23.
<P></P><DT><A NAME="psblas_00">15</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>
+<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>
+<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 (3), 1979, 308-323.
<P></P><DT><A NAME="SUPERLUDIST">18</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="Notay2008">19</A>
+<DD>
+Y.&nbsp;Notay, P.&nbsp;S.&nbsp;Vassilevski,
+<EM>Recursive Krylov-based multigrid cycles</EM>,
+Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487. 
<P></P><DT><A NAME="Saad_book">20</A>
+<DD>
+Y.&nbsp;Saad,
+<EM>Iterative methods for sparse linear systems</EM>, 2nd edition, SIAM, 2003.
<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">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="Stuben_01">23</A>
+<DD>
+K.&nbsp;St&#252;ben,
+<EM>An Introduction to Algebraic Multigrid</EM>,
+in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, Multigrid,
+Academic Press, 2001.
<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">25</A>
+<DD>
+P.&nbsp;Vanek, J.&nbsp;Mandel, M.&nbsp;Brezina,
+<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
+Computing, 56 (3) 1996, 179-196.
+
 <P>
-The command line arguments were: <BR>
- <STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
+</DL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+</FONT></FONT></FONT>
 <P>
-The translation was initiated by Salvatore Filippone on 2017-07-25<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><HR>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><BR><HR>
 
 </BODY>
 </HTML>
diff --git a/docs/html/node31.html b/docs/html/node31.html
index 2f3088d1..13a02ef9 100644
--- a/docs/html/node31.html
+++ b/docs/html/node31.html
@@ -1,6 +1,6 @@
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
 
-<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
+<!--Converted with LaTeX2HTML 2012 (1.2)
 original version by:  Nikos Drakos, CBLU, University of Leeds
 * revised and updated by:  Marcus Hennecke, Ross Moore, Herb Swan
 * with significant contributions from:
@@ -13,7 +13,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
 
-<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
+<META NAME="Generator" CONTENT="LaTeX2HTML v2012">
 <META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
@@ -23,39 +23,34 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 </HEAD>
 
 <BODY >
-
-<DIV CLASS="navigation"><!--Navigation Panel-->
-<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
- SRC="file:/usr/share/latex2html/icons/next_g.png"> 
-<A NAME="tex2html435"
+<!--Navigation Panel-->
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_g.png"> 
+<A NAME="tex2html454"
   HREF="userhtml.html">
-<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
- SRC="file:/usr/share/latex2html/icons/up.png"></A> 
-<A NAME="tex2html431"
+<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
+<A NAME="tex2html450"
   HREF="node30.html">
-<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
- SRC="file:/usr/share/latex2html/icons/prev.png"></A> 
-<A NAME="tex2html437"
+<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
+<A NAME="tex2html456"
   HREF="node2.html">
-<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
- SRC="file:/usr/share/latex2html/icons/contents.png"></A>  
+<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
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+<B> Up:</B> <A NAME="tex2html455"
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-<B> Previous:</B> <A NAME="tex2html432"
+<B> Previous:</B> <A NAME="tex2html451"
   HREF="node30.html">Bibliography</A>
- &nbsp; <B>  <A NAME="tex2html438"
+ &nbsp; <B>  <A NAME="tex2html457"
   HREF="node2.html">Contents</A></B> 
 <BR>
-<BR></DIV>
+<BR>
 <!--End of Navigation Panel-->
 
-<H1><A NAME="SECTION000120000000000000000">
+<H1><A NAME="SECTION000130000000000000000">
 About this document ...</A>
-</H1>
- <P>
+</H1><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+ </FONT></FONT></FONT><P>
 This document was generated using the
-<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2002-2-1 (1.71)
+<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2012 (1.2)
 <P>
 Copyright &#169; 1993, 1994, 1995, 1996,
 <A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>, 
@@ -66,13 +61,10 @@ Copyright &#169; 1997, 1998, 1999,
 Mathematics Department, Macquarie University, Sydney.
 <P>
 The command line arguments were: <BR>
- <STRONG>latex2html</STRONG> <TT>-html_version 4.0 -dir ../../html userhtml.tex</TT>
+ <STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
 <P>
-The translation was initiated by Salvatore Filippone on 2008-07-23
+The translation was initiated by Salvatore Filippone on 2017-08-09<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <BR><HR>
-<ADDRESS>
-Salvatore Filippone
-2008-07-23
-</ADDRESS>
+
 </BODY>
 </HTML>
diff --git a/docs/html/node4.html b/docs/html/node4.html
index cb8f1623..c97dade1 100644
--- a/docs/html/node4.html
+++ b/docs/html/node4.html
@@ -18,7 +18,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
 
-<LINK REL="next" HREF="node5.html">
+<LINK REL="next" HREF="node6.html">
 <LINK REL="previous" HREF="node3.html">
 <LINK REL="up" HREF="userhtml.html">
 <LINK REL="next" HREF="node5.html">
@@ -26,26 +26,26 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <BODY >
 <!--Navigation Panel-->
-<A NAME="tex2html127"
+<A NAME="tex2html128"
   HREF="node5.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html123"
+<A NAME="tex2html124"
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 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html117"
+<A NAME="tex2html118"
   HREF="node3.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html125"
+<A NAME="tex2html126"
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 <BR>
-<B> Next:</B> <A NAME="tex2html128"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
-<B> Up:</B> <A NAME="tex2html124"
+<B> Next:</B> <A NAME="tex2html129"
+  HREF="node5.html">Contributors</A>
+<B> Up:</B> <A NAME="tex2html125"
   HREF="userhtml.html">userhtml</A>
-<B> Previous:</B> <A NAME="tex2html118"
+<B> Previous:</B> <A NAME="tex2html119"
   HREF="node3.html">General Overview</A>
- &nbsp; <B>  <A NAME="tex2html126"
+ &nbsp; <B>  <A NAME="tex2html127"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
@@ -65,7 +65,7 @@ where contact points for further information can be also found.
 </FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The software is available under a modified BSD license, as specified
-in Appendix&nbsp;<A HREF="node28.html#sec:license">A</A>; please note that some of the optional
+in Appendix&nbsp;<A HREF="node29.html#sec:license">A</A>; please note that some of the optional
 third party libraries may be licensed under a different and more
 stringent license, most notably the GPL, and this should be taken into
 account when treating derived works. 
@@ -89,8 +89,19 @@ constant
 </DIV>
 <BR CLEAR="ALL">
 <P></P><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-whose current value is <code>2.1.0</code>
+whose current value is <code>2.1.0</code>.
 </FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><HR>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
+
+<UL>
+<LI><A NAME="tex2html130"
+  HREF="node5.html">Contributors</A>
+</UL>
+<!--End of Table of Child-Links-->
 <BR><HR>
 
 </BODY>
diff --git a/docs/html/node5.html b/docs/html/node5.html
index 7a4528fb..ffcb232a 100644
--- a/docs/html/node5.html
+++ b/docs/html/node5.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Configuring and Building MLD2P4</TITLE>
-<META NAME="description" CONTENT="Configuring and Building MLD2P4">
+<TITLE>Contributors</TITLE>
+<META NAME="description" CONTENT="Contributors">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -18,9 +18,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
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-<LINK REL="next" HREF="node11.html">
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-<LINK REL="up" HREF="userhtml.html">
+<LINK REL="up" HREF="node4.html">
 <LINK REL="next" HREF="node6.html">
 </HEAD>
 
@@ -30,9 +29,9 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node6.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html135"
-  HREF="userhtml.html">
+  HREF="node4.html">
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-<A NAME="tex2html129"
+<A NAME="tex2html131"
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 <A NAME="tex2html137"
@@ -40,10 +39,10 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html140"
-  HREF="node6.html">Prerequisites</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
 <B> Up:</B> <A NAME="tex2html136"
-  HREF="userhtml.html">userhtml</A>
-<B> Previous:</B> <A NAME="tex2html130"
+  HREF="node4.html">Code Distribution</A>
+<B> Previous:</B> <A NAME="tex2html132"
   HREF="node4.html">Code Distribution</A>
  &nbsp; <B>  <A NAME="tex2html138"
   HREF="node2.html">Contents</A></B> 
@@ -51,80 +50,35 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <BR>
 <!--End of Navigation Panel-->
 
-<H1><A NAME="SECTION00050000000000000000"></A><A NAME="sec:building"></A>
-<BR>
-Configuring and Building MLD2P4
-</H1><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-
-In order to build MLD2P4 it is necessary to set up a Makefile with appropriate
-system-dependent variables; this is done by means of the <code>configure</code>
-script. The distribution also includes the autoconf and automake
-sources employed to generate the script, but usually this is not needed
-to build the software. 
+<H2><A NAME="SECTION00041000000000000000">
+Contributors</A>
+</H2><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+Contributors to version 2:
 </FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">MLD2P4 is implemented almost entirely in Fortran&nbsp;2003, with some
-interfaces to external libraries in C; the Fortran compiler
-must support the Fortran&nbsp;2003 standard plus the extension <code>MOLD=</code>
-feature, which enhances the usability of <code>ALLOCATE</code>. 
-Many compilers do this; in particular, this is
-supported by the GNU Fortran compiler, for which we 
-recommend to use at least version 4.8. 
-The software defines data types and interfaces for
-real and complex data, in both single and double precision. 
+<UL>
+<LI>Salvatore  Filippone,          Cranfield University, UK;				
+</LI>
+<LI>Pasqua     D'Ambra,            IAC-CNR, Naples, IT;				
+</LI>
+<LI>Daniela    di Serafino,        University of Campania ``L. Vanvitelli'', Caserta, IT;
+</LI>
+<LI>Ambra	 Abdullahi Hassan, University of Rome ``Tor Vergata'', IT.
+</LI>
+</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+Contributors to version 1:
 </FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Building MLD2P4 requires some base libraries (see Section&nbsp;<A HREF="node6.html#sec:prerequisites">3.1</A>);
-interfaces to optional third-party libraries, which extend the functionalities of MLD2P4
-(see Section&nbsp;<A HREF="node7.html#sec:third-party">3.2</A>), are also available.  Many Linux distributions
-(e.g., Ubuntu, Fedora, CentOS) provide precompiled packages for the prerequisite and
-optional software. In many cases these packages are split between a runtime part and a
-``developer'' part; in order to build MLD2P4 you need both. A description of the base and
-optional software used by MLD2P4 is given in the next sections.
+<UL>
+<LI>Salvatore  Filippone;
+</LI>
+<LI>Pasqua     D'Ambra;
+</LI>
+<LI>Daniela    di Serafino;
+</LI>
+<LI>Alfredo    Buttari, CNRS-IRIT, Toulouse, F. 
+</LI>
+</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
 </FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <BR><HR>
-<!--Table of Child-Links-->
-<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
-
-<UL>
-<LI><A NAME="tex2html141"
-  HREF="node6.html">Prerequisites</A>
-<LI><A NAME="tex2html142"
-  HREF="node7.html">Optional third party libraries</A>
-<LI><A NAME="tex2html143"
-  HREF="node8.html">Configuration options</A>
-<LI><A NAME="tex2html144"
-  HREF="node9.html">Bug reporting</A>
-<LI><A NAME="tex2html145"
-  HREF="node10.html">Example and test programs</A>
-</UL>
-<!--End of Table of Child-Links-->
-<HR>
-<!--Navigation Panel-->
-<A NAME="tex2html139"
-  HREF="node6.html">
-<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html135"
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-<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html129"
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-<A NAME="tex2html137"
-  HREF="node2.html">
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-<BR>
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-<B> Previous:</B> <A NAME="tex2html130"
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-<!--End of Navigation Panel-->
 
 </BODY>
 </HTML>
diff --git a/docs/html/node6.html b/docs/html/node6.html
index a5398c73..5e8fed72 100644
--- a/docs/html/node6.html
+++ b/docs/html/node6.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Prerequisites</TITLE>
-<META NAME="description" CONTENT="Prerequisites">
+<TITLE>Configuring and Building MLD2P4</TITLE>
+<META NAME="description" CONTENT="Configuring and Building MLD2P4">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -18,116 +18,111 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="STYLESHEET" HREF="userhtml.css">
 
-<LINK REL="next" HREF="node7.html">
-<LINK REL="previous" HREF="node5.html">
-<LINK REL="up" HREF="node5.html">
+<LINK REL="next" HREF="node12.html">
+<LINK REL="previous" HREF="node4.html">
+<LINK REL="up" HREF="userhtml.html">
 <LINK REL="next" HREF="node7.html">
 </HEAD>
 
 <BODY >
 <!--Navigation Panel-->
-<A NAME="tex2html156"
+<A NAME="tex2html151"
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 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html152"
-  HREF="node5.html">
+<A NAME="tex2html147"
+  HREF="userhtml.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html146"
+<A NAME="tex2html141"
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 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html154"
+<A NAME="tex2html149"
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 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
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-<B> Next:</B> <A NAME="tex2html157"
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-  HREF="node5.html">Configuring and Building MLD2P4</A>
-<B> Previous:</B> <A NAME="tex2html147"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
- &nbsp; <B>  <A NAME="tex2html155"
+<B> Next:</B> <A NAME="tex2html152"
+  HREF="node7.html">Prerequisites</A>
+<B> Up:</B> <A NAME="tex2html148"
+  HREF="userhtml.html">userhtml</A>
+<B> Previous:</B> <A NAME="tex2html142"
+  HREF="node5.html">Contributors</A>
+ &nbsp; <B>  <A NAME="tex2html150"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00051000000000000000"></A><A NAME="sec:prerequisites"></A>
+<H1><A NAME="SECTION00050000000000000000"></A><A NAME="sec:building"></A>
 <BR>
-Prerequisites
-</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+Configuring and Building MLD2P4
+</H1><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+
+In order to build MLD2P4 it is necessary to set up a Makefile with appropriate
+system-dependent variables; this is done by means of the <code>configure</code>
+script. The distribution also includes the autoconf and automake
+sources employed to generate the script, but usually this is not needed
+to build the software. 
+</FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The following base libraries are needed: 
-</FONT></FONT></FONT><DL>
-<DT><STRONG>BLAS</STRONG></DT>
-<DD>[<A
- HREF="node29.html#blas3">11</A>,<A
- HREF="node29.html#blas2">12</A>,<A
- HREF="node29.html#blas1">17</A>] Many vendors provide optimized versions
-  of BLAS; if no vendor version is
-  available for a given platform, the ATLAS software
-  (<TT><A NAME="tex2html1"
-  HREF="math-atlas.sourceforge.net">math-atlas.sourceforge.net</A></TT>)
-  may be employed.  The reference BLAS from Netlib
-  (<TT><A NAME="tex2html2"
-  HREF="www.netlib.org/blas">www.netlib.org/blas</A></TT>) are meant to define the standard
-  behaviour of the BLAS interface, so they are not optimized for any
-  particular plaftorm, and should only be used as a last
-  resort. Note that BLAS computations form a relatively small part of
-  the MLD2P4/PSBLAS computations; they are however critical when using
-  preconditioners based on MUMPS, UMFPACK or SuperLU third party
-  libraries. Note that UMFPACK requires a full LAPACK library; our
-experience is that configuring ATLAS for building full LAPACK does not
-work in the correct way. Our advice is first to download the LAPACK tarfile from
-<TT><A NAME="tex2html3"
-  HREF="www.netlib.org/lapack">www.netlib.org/lapack</A></TT> and install it independently of ATLAS. In this case,
-you need to modify the OPTS and NOOPT definitions for including -fPIC compilation option
-in the make.inc file of the LAPACK library. 
-</DD>
-<DT><STRONG>MPI</STRONG></DT>
-<DD>[<A
- HREF="node29.html#MPI2">16</A>,<A
- HREF="node29.html#MPI1">22</A>] A version of MPI is available on most
-  high-performance computing systems.
- 
-</DD>
-<DT><STRONG>PSBLAS</STRONG></DT>
-<DD>[<A
- HREF="node29.html#PSBLASGUIDE">13</A>,<A
- HREF="node29.html#psblas_00">15</A>] Parallel Sparse BLAS (PSBLAS) is
-  available from <TT><A NAME="tex2html4"
-  HREF="www.ce.uniroma2.it/psblas">www.ce.uniroma2.it/psblas</A></TT>; version
-  3.5.0  (or later) is required. Indeed, all the prerequisites
-  listed so far are also prerequisites of PSBLAS.
-</DD>
-</DL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-Please note that the four previous libraries must have Fortran
-interfaces compatible with MLD2P4;
-usually this means that they should all be built with the same
-compiler as MLD2P4.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">MLD2P4 is implemented almost entirely in Fortran&nbsp;2003, with some
+interfaces to external libraries in C; the Fortran compiler
+must support the Fortran&nbsp;2003 standard plus the extension <code>MOLD=</code>
+feature, which enhances the usability of <code>ALLOCATE</code>. 
+Many compilers do this; in particular, this is
+supported by the GNU Fortran compiler, for which we 
+recommend to use at least version 4.8. 
+The software defines data types and interfaces for
+real and complex data, in both single and double precision. 
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Building MLD2P4 requires some base libraries (see Section&nbsp;<A HREF="node7.html#sec:prerequisites">3.1</A>);
+interfaces to optional third-party libraries, which extend the functionalities of MLD2P4
+(see Section&nbsp;<A HREF="node8.html#sec:third-party">3.2</A>), are also available.  Many Linux distributions
+(e.g., Ubuntu, Fedora, CentOS) provide precompiled packages for the prerequisite and
+optional software. In many cases these packages are split between a runtime part and a
+``developer'' part; in order to build MLD2P4 you need both. A description of the base and
+optional software used by MLD2P4 is given in the next sections.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<BR><HR>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
+
+<UL>
+<LI><A NAME="tex2html153"
+  HREF="node7.html">Prerequisites</A>
+<LI><A NAME="tex2html154"
+  HREF="node8.html">Optional third party libraries</A>
+<LI><A NAME="tex2html155"
+  HREF="node9.html">Configuration options</A>
+<LI><A NAME="tex2html156"
+  HREF="node10.html">Bug reporting</A>
+<LI><A NAME="tex2html157"
+  HREF="node11.html">Example and test programs</A>
+</UL>
+<!--End of Table of Child-Links-->
+<HR>
 <!--Navigation Panel-->
-<A NAME="tex2html156"
+<A NAME="tex2html151"
   HREF="node7.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
-<A NAME="tex2html152"
-  HREF="node5.html">
+<A NAME="tex2html147"
+  HREF="userhtml.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
-<A NAME="tex2html146"
+<A NAME="tex2html141"
   HREF="node5.html">
 <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
-<A NAME="tex2html154"
+<A NAME="tex2html149"
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 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
-<B> Next:</B> <A NAME="tex2html157"
-  HREF="node7.html">Optional third party libraries</A>
-<B> Up:</B> <A NAME="tex2html153"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
-<B> Previous:</B> <A NAME="tex2html147"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
- &nbsp; <B>  <A NAME="tex2html155"
+<B> Next:</B> <A NAME="tex2html152"
+  HREF="node7.html">Prerequisites</A>
+<B> Up:</B> <A NAME="tex2html148"
+  HREF="userhtml.html">userhtml</A>
+<B> Previous:</B> <A NAME="tex2html142"
+  HREF="node5.html">Contributors</A>
+ &nbsp; <B>  <A NAME="tex2html150"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
 
diff --git a/docs/html/node7.html b/docs/html/node7.html
index f87e992d..cd53709f 100644
--- a/docs/html/node7.html
+++ b/docs/html/node7.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Optional third party libraries</TITLE>
-<META NAME="description" CONTENT="Optional third party libraries">
+<TITLE>Prerequisites</TITLE>
+<META NAME="description" CONTENT="Prerequisites">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node8.html">
 <LINK REL="previous" HREF="node6.html">
-<LINK REL="up" HREF="node5.html">
+<LINK REL="up" HREF="node6.html">
 <LINK REL="next" HREF="node8.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node8.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html164"
-  HREF="node5.html">
+  HREF="node6.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html158"
   HREF="node6.html">
@@ -40,74 +40,71 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html169"
-  HREF="node8.html">Configuration options</A>
+  HREF="node8.html">Optional third party libraries</A>
 <B> Up:</B> <A NAME="tex2html165"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
 <B> Previous:</B> <A NAME="tex2html159"
-  HREF="node6.html">Prerequisites</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
  &nbsp; <B>  <A NAME="tex2html167"
   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00052000000000000000"></A><A NAME="sec:third-party"></A>
+<H2><A NAME="SECTION00051000000000000000"></A><A NAME="sec:prerequisites"></A>
 <BR>
-Optional third party libraries
+Prerequisites
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We provide interfaces to the following third-party software libraries;
-note that these are optional, but if you enable them some defaults
-for multi-level preconditioners may change to reflect their presence. 
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><DL>
-<DT><STRONG>UMFPACK</STRONG></DT>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The following base libraries are needed: 
+</FONT></FONT></FONT><DL>
+<DT><STRONG>BLAS</STRONG></DT>
 <DD>[<A
- HREF="node29.html#UMFPACK">9</A>]
-  A sparse LU factorization package included in the SuiteSparse library, available from 
-  <TT><A NAME="tex2html5"
-  HREF="faculty.cse.tamu.edu/davis/suitesparse.html">faculty.cse.tamu.edu/davis/suitesparse.html</A></TT>; 
-  it provides sequential factorization and triangular system solution for double
-  precision real and complex data. We tested version 4.5.4 of SuiteSparse.
-  Note that for configuring SuiteSparse you should provide the right path to the BLAS
-  and LAPACK libraries in the <code>SuiteSparse_config/SuiteSparse_config.mk</code> file.
+ HREF="node30.html#blas3">11</A>,<A
+ HREF="node30.html#blas2">12</A>,<A
+ HREF="node30.html#blas1">17</A>] Many vendors provide optimized versions
+  of BLAS; if no vendor version is
+  available for a given platform, the ATLAS software
+  (<TT><A NAME="tex2html1"
+  HREF="math-atlas.sourceforge.net">math-atlas.sourceforge.net</A></TT>)
+  may be employed.  The reference BLAS from Netlib
+  (<TT><A NAME="tex2html2"
+  HREF="www.netlib.org/blas">www.netlib.org/blas</A></TT>) are meant to define the standard
+  behaviour of the BLAS interface, so they are not optimized for any
+  particular plaftorm, and should only be used as a last
+  resort. Note that BLAS computations form a relatively small part of
+  the MLD2P4/PSBLAS computations; they are however critical when using
+  preconditioners based on MUMPS, UMFPACK or SuperLU third party
+  libraries. Note that UMFPACK requires a full LAPACK library; our
+experience is that configuring ATLAS for building full LAPACK does not
+work in the correct way. Our advice is first to download the LAPACK tarfile from
+<TT><A NAME="tex2html3"
+  HREF="www.netlib.org/lapack">www.netlib.org/lapack</A></TT> and install it independently of ATLAS. In this case,
+you need to modify the OPTS and NOOPT definitions for including -fPIC compilation option
+in the make.inc file of the LAPACK library. 
 </DD>
-<DT><STRONG>MUMPS</STRONG></DT>
+<DT><STRONG>MPI</STRONG></DT>
 <DD>[<A
- HREF="node29.html#MUMPS">1</A>]
-  A sparse LU factorization package available from <TT><A NAME="tex2html6"
-  HREF="mumps.enseeiht.fr">mumps.enseeiht.fr</A></TT>;
-  it provides sequential and parallel factorizations and triangular system solution
-  for single and double precision, real and complex data.
-  We tested versions 4.10.0 and 5.0.1.
-</DD>
-<DT><STRONG>SuperLU</STRONG></DT>
-<DD>[<A
- HREF="node29.html#SUPERLU">10</A>]
-  A sparse LU factorization package available from
-  <TT><A NAME="tex2html7"
-  HREF="crd.lbl.gov/~xiaoye/SuperLU/">crd.lbl.gov/~xiaoye/SuperLU/</A></TT>; it provides sequential
-  factorization and triangular system solution for single and double precision,
-  real and complex data. We tested versions 4.3 and 5.0. If you installed BLAS from
-  ATLAS, remember to define the BLASLIB variable in the make.inc file.
+ HREF="node30.html#MPI2">16</A>,<A
+ HREF="node30.html#MPI1">22</A>] A version of MPI is available on most
+  high-performance computing systems.
  
 </DD>
-<DT><STRONG>SuperLU_Dist</STRONG></DT>
+<DT><STRONG>PSBLAS</STRONG></DT>
 <DD>[<A
- HREF="node29.html#SUPERLUDIST">18</A>]
-   A sparse LU factorization package available
-   from the same site as SuperLU; it provides parallel factorization and
-   triangular system solution for double precision real and complex data.
-   We tested versions 3.3 and 4.2. If you installed BLAS from
-   ATLAS, remember to define the BLASLIB variable in the make.inc file and
-   to add the <code>-std=c99</code> option to the C compiler options.
-   Note that this library requires the ParMETIS
-   library for parallel graph partitioning and fill-reducing matrix ordering, available from
-   <TT><A NAME="tex2html8"
-  HREF="glaros.dtc.umn.edu/gkhome/metis/parmetis/overview">glaros.dtc.umn.edu/gkhome/metis/parmetis/overview</A></TT>.
+ HREF="node30.html#PSBLASGUIDE">13</A>,<A
+ HREF="node30.html#psblas_00">15</A>] Parallel Sparse BLAS (PSBLAS) is
+  available from <TT><A NAME="tex2html4"
+  HREF="www.ce.uniroma2.it/psblas">www.ce.uniroma2.it/psblas</A></TT>; version
+  3.5.0  (or later) is required. Indeed, all the prerequisites
+  listed so far are also prerequisites of PSBLAS.
 </DD>
-</DL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+</DL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+Please note that the four previous libraries must have Fortran
+interfaces compatible with MLD2P4;
+usually this means that they should all be built with the same
+compiler as MLD2P4.
+</FONT></FONT></FONT>
 <P>
 <FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
 <!--Navigation Panel-->
@@ -115,7 +112,7 @@ for multi-level preconditioners may change to reflect their presence.
   HREF="node8.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html164"
-  HREF="node5.html">
+  HREF="node6.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html158"
   HREF="node6.html">
@@ -125,11 +122,11 @@ for multi-level preconditioners may change to reflect their presence.
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html169"
-  HREF="node8.html">Configuration options</A>
+  HREF="node8.html">Optional third party libraries</A>
 <B> Up:</B> <A NAME="tex2html165"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
 <B> Previous:</B> <A NAME="tex2html159"
-  HREF="node6.html">Prerequisites</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
  &nbsp; <B>  <A NAME="tex2html167"
   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
diff --git a/docs/html/node8.html b/docs/html/node8.html
index db0eaab4..fc7bb0fd 100644
--- a/docs/html/node8.html
+++ b/docs/html/node8.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Configuration options</TITLE>
-<META NAME="description" CONTENT="Configuration options">
+<TITLE>Optional third party libraries</TITLE>
+<META NAME="description" CONTENT="Optional third party libraries">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node9.html">
 <LINK REL="previous" HREF="node7.html">
-<LINK REL="up" HREF="node5.html">
+<LINK REL="up" HREF="node6.html">
 <LINK REL="next" HREF="node9.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node9.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
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-  HREF="node5.html">
+  HREF="node6.html">
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 <A NAME="tex2html170"
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@@ -40,231 +40,82 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html181"
-  HREF="node9.html">Bug reporting</A>
+  HREF="node9.html">Configuration options</A>
 <B> Up:</B> <A NAME="tex2html177"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
 <B> Previous:</B> <A NAME="tex2html171"
-  HREF="node7.html">Optional third party libraries</A>
+  HREF="node7.html">Prerequisites</A>
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   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00053000000000000000">
-Configuration options</A>
+<H2><A NAME="SECTION00052000000000000000"></A><A NAME="sec:third-party"></A>
+<BR>
+Optional third party libraries
 </H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to build MLD2P4, the first step is to use the <code>configure</code> script
-in the main directory to generate the necessary makefile.
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We provide interfaces to the following third-party software libraries;
+note that these are optional, but if you enable them some defaults
+for multi-level preconditioners may change to reflect their presence. 
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">As a minimal example consider the following:
-</FONT></FONT></FONT><PRE>
-./configure --with-psblas=PSB-INSTALL-DIR
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-which assumes that the various MPI compilers and support libraries are
-available in the standard directories on the system, and specifies
-only the PSBLAS install  directory (note that the latter directory must
-be specified with an <EM>absolute</EM> path).
-The full set of options may be looked at by issuing the command
-<code>./configure --help</code>, which produces:
-</FONT></FONT></FONT><PRE>
-`configure' configures MLD2P4 2.1 to adapt to many kinds of systems.
-
-Usage: ./configure [OPTION]... [VAR=VALUE]...
-
-To assign environment variables (e.g., CC, CFLAGS...), specify them as
-VAR=VALUE.  See below for descriptions of some of the useful variables.
-
-Defaults for the options are specified in brackets.
-
-Configuration:
-  -h, --help              display this help and exit
-      --help=short        display options specific to this package
-      --help=recursive    display the short help of all the included packages
-  -V, --version           display version information and exit
-  -q, --quiet, --silent   do not print `checking...' messages
-      --cache-file=FILE   cache test results in FILE [disabled]
-  -C, --config-cache      alias for `--cache-file=config.cache'
-  -n, --no-create         do not create output files
-      --srcdir=DIR        find the sources in DIR [configure dir or `..']
-
-Installation directories:
-  --prefix=PREFIX         install architecture-independent files in PREFIX
-                          [/usr/local]
-  --exec-prefix=EPREFIX   install architecture-dependent files in EPREFIX
-                          [PREFIX]
-
-By default, `make install' will install all the files in
-`/usr/local/bin', `/usr/local/lib' etc.  You can specify
-an installation prefix other than `/usr/local' using `--prefix',
-for instance `--prefix=$HOME'.
-
-For better control, use the options below.
-
-Fine tuning of the installation directories:
-  --bindir=DIR            user executables [EPREFIX/bin]
-  --sbindir=DIR           system admin executables [EPREFIX/sbin]
-  --libexecdir=DIR        program executables [EPREFIX/libexec]
-  --sysconfdir=DIR        read-only single-machine data [PREFIX/etc]
-  --sharedstatedir=DIR    modifiable architecture-independent data [PREFIX/com]
-  --localstatedir=DIR     modifiable single-machine data [PREFIX/var]
-  --libdir=DIR            object code libraries [EPREFIX/lib]
-  --includedir=DIR        C header files [PREFIX/include]
-  --oldincludedir=DIR     C header files for non-gcc [/usr/include]
-  --datarootdir=DIR       read-only arch.-independent data root [PREFIX/share]
-  --datadir=DIR           read-only architecture-independent data [DATAROOTDIR]
-  --infodir=DIR           info documentation [DATAROOTDIR/info]
-  --localedir=DIR         locale-dependent data [DATAROOTDIR/locale]
-  --mandir=DIR            man documentation [DATAROOTDIR/man]
-  --docdir=DIR            documentation root [DATAROOTDIR/doc/mld2p4]
-  --htmldir=DIR           html documentation [DOCDIR]
-  --dvidir=DIR            dvi documentation [DOCDIR]
-  --pdfdir=DIR            pdf documentation [DOCDIR]
-  --psdir=DIR             ps documentation [DOCDIR]
-
-Program names:
-  --program-prefix=PREFIX            prepend PREFIX to installed program names
-  --program-suffix=SUFFIX            append SUFFIX to installed program names
-  --program-transform-name=PROGRAM   run sed PROGRAM on installed program names
-
-Optional Features:
-  --disable-option-checking  ignore unrecognized --enable/--with options
-  --disable-FEATURE       do not include FEATURE (same as --enable-FEATURE=no)
-  --enable-FEATURE[=ARG]  include FEATURE [ARG=yes]
-  --disable-dependency-tracking  speeds up one-time build
-  --enable-dependency-tracking   do not reject slow dependency extractors
-  --enable-serial         Specify whether to enable a fake mpi library to run
-                          in serial mode.
-  --enable-long-integers  Specify usage of 64 bits integers.
-
-Optional Packages:
-  --with-PACKAGE[=ARG]    use PACKAGE [ARG=yes]
-  --without-PACKAGE       do not use PACKAGE (same as --with-PACKAGE=no)
-  --with-psblas=DIR       The install directory for PSBLAS, for example,
-                          --with-psblas=/opt/packages/psblas-3.5
-  --with-psblas-incdir=DIR
-                          Specify the directory for PSBLAS includes.
-  --with-psblas-libdir=DIR
-                          Specify the directory for PSBLAS library.
-  --with-ccopt            additional CCOPT flags to be added: will prepend
-                          to CCOPT
-  --with-fcopt            additional FCOPT flags to be added: will prepend
-                          to FCOPT
-  --with-libs             List additional link flags here. For example,
-                          --with-libs=-lspecial_system_lib or
-                          --with-libs=-L/path/to/libs
-  --with-clibs            additional CLIBS flags to be added: will prepend
-                          to CLIBS
-  --with-flibs            additional FLIBS flags to be added: will prepend
-                          to FLIBS
-  --with-library-path     additional LIBRARYPATH flags to be added: will
-                          prepend to LIBRARYPATH
-  --with-include-path     additional INCLUDEPATH flags to be added: will
-                          prepend to INCLUDEPATH
-  --with-module-path      additional MODULE_PATH flags to be added: will
-                          prepend to MODULE_PATH
-  --with-extra-libs       List additional link flags here. For example,
-                          --with-extra-libs=-lspecial_system_lib or
-                          --with-extra-libs=-L/path/to/libs
-  --with-blas=&lt;lib&gt;       use BLAS library &lt;lib&gt;
-  --with-blasdir=&lt;dir&gt;    search for BLAS library in &lt;dir&gt;
-  --with-lapack=&lt;lib&gt;     use LAPACK library &lt;lib&gt;
-  --with-mumps=LIBNAME    Specify the libname for MUMPS. Default: autodetect
-                          with minimum "-lmumps_common -lpord"
-  --with-mumpsdir=DIR     Specify the directory for MUMPS library and
-                          includes. Note: you will need to add auxiliary
-                          libraries with --extra-libs; this depends on how
-                          MUMPS was configured and installed, at a minimum you
-                          will need SCALAPACK and BLAS
-  --with-mumpsincdir=DIR  Specify the directory for MUMPS includes.
-  --with-mumpslibdir=DIR  Specify the directory for MUMPS library.
-  --with-umfpack=LIBNAME  Specify the library name for UMFPACK and its support
-                          libraries. Default: "-lumfpack -lamd"
-  --with-umfpackdir=DIR   Specify the directory for UMFPACK library and
-                          includes.
-  --with-umfpackincdir=DIR
-                          Specify the directory for UMFPACK includes.
-  --with-umfpacklibdir=DIR
-                          Specify the directory for UMFPACK library.
-  --with-superlu=LIBNAME  Specify the library name for SUPERLU library.
-                          Default: "-lsuperlu"
-  --with-superludir=DIR   Specify the directory for SUPERLU library and
-                          includes.
-  --with-superluincdir=DIR
-                          Specify the directory for SUPERLU includes.
-  --with-superlulibdir=DIR
-                          Specify the directory for SUPERLU library.
-  --with-superludist=LIBNAME
-                          Specify the libname for SUPERLUDIST library.
-                          Requires you also specify SuperLU. Default:
-                          "-lsuperlu_dist"
-  --with-superludistdir=DIR
-                          Specify the directory for SUPERLUDIST library and
-                          includes.
-  --with-superludistincdir=DIR
-                          Specify the directory for SUPERLUDIST includes.
-  --with-superludistlibdir=DIR
-                          Specify the directory for SUPERLUDIST library.
-
-Some influential environment variables:
-  FC          Fortran compiler command
-  FCFLAGS     Fortran compiler flags
-  LDFLAGS     linker flags, e.g. -L&lt;lib dir&gt; if you have libraries in a
-              nonstandard directory &lt;lib dir&gt;
-  LIBS        libraries to pass to the linker, e.g. -l&lt;library&gt;
-  CC          C compiler command
-  CFLAGS      C compiler flags
-  CPPFLAGS    C/C++/Objective C preprocessor flags, e.g. -I&lt;include dir&gt; if
-              you have headers in a nonstandard directory &lt;include dir&gt;
-  MPICC       MPI C compiler command
-  MPIFC       MPI Fortran compiler command
-  CPP         C preprocessor
-
-Use these variables to override the choices made by `configure' or to help
-it to find libraries and programs with nonstandard names/locations.
-
-Report bugs to &lt;bugreport@mld2p4.it&gt;.
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For instance, if a user has built and installed PSBLAS 3.5 under the
-<code>/opt</code> directory and is
-using the SuiteSparse package (which includes UMFPACK), then MLD2P4
-might be configured with:
-</FONT></FONT></FONT><PRE>
- ./configure --with-psblas=/opt/psblas-3.5/ \
- --with-umfpackincdir=/usr/include/suitesparse/
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-Once the configure script has completed execution, it will have
-generated the file <code>Make.inc</code> which will then be used by all
-Makefiles in the directory tree; this file will be copied in the
-install directory under the name <code>Make.inc.MLD2P4</code>.
-</FONT></FONT></FONT>
-<P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">To use the MUMPS solver package, 
-the user has to add the appropriate options to the configure script;
-by default we are looking for the libraries
-<code>-ldmumps -lsmumps</code> <code> -lzmumps -lcmumps -mumps_common -lpord</code>.
-MUMPS often uses additional packages such as ScaLAPACK, ParMETIS,
-SCOTCH, as well as enabling OpenMP; in such cases it is necessary to
-add linker options with the <code>--with-extra-libs</code> configure option.
-</FONT></FONT></FONT>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><DL>
+<DT><STRONG>UMFPACK</STRONG></DT>
+<DD>[<A
+ HREF="node30.html#UMFPACK">9</A>]
+  A sparse LU factorization package included in the SuiteSparse library, available from 
+  <TT><A NAME="tex2html5"
+  HREF="faculty.cse.tamu.edu/davis/suitesparse.html">faculty.cse.tamu.edu/davis/suitesparse.html</A></TT>; 
+  it provides sequential factorization and triangular system solution for double
+  precision real and complex data. We tested version 4.5.4 of SuiteSparse.
+  Note that for configuring SuiteSparse you should provide the right path to the BLAS
+  and LAPACK libraries in the <code>SuiteSparse_config/SuiteSparse_config.mk</code> file.
+</DD>
+<DT><STRONG>MUMPS</STRONG></DT>
+<DD>[<A
+ HREF="node30.html#MUMPS">1</A>]
+  A sparse LU factorization package available from <TT><A NAME="tex2html6"
+  HREF="mumps.enseeiht.fr">mumps.enseeiht.fr</A></TT>;
+  it provides sequential and parallel factorizations and triangular system solution
+  for single and double precision, real and complex data.
+  We tested versions 4.10.0 and 5.0.1.
+</DD>
+<DT><STRONG>SuperLU</STRONG></DT>
+<DD>[<A
+ HREF="node30.html#SUPERLU">10</A>]
+  A sparse LU factorization package available from
+  <TT><A NAME="tex2html7"
+  HREF="crd.lbl.gov/~xiaoye/SuperLU/">crd.lbl.gov/~xiaoye/SuperLU/</A></TT>; it provides sequential
+  factorization and triangular system solution for single and double precision,
+  real and complex data. We tested versions 4.3 and 5.0. If you installed BLAS from
+  ATLAS, remember to define the BLASLIB variable in the make.inc file.
+ 
+</DD>
+<DT><STRONG>SuperLU_Dist</STRONG></DT>
+<DD>[<A
+ HREF="node30.html#SUPERLUDIST">18</A>]
+   A sparse LU factorization package available
+   from the same site as SuperLU; it provides parallel factorization and
+   triangular system solution for double precision real and complex data.
+   We tested versions 3.3 and 4.2. If you installed BLAS from
+   ATLAS, remember to define the BLASLIB variable in the make.inc file and
+   to add the <code>-std=c99</code> option to the C compiler options.
+   Note that this library requires the ParMETIS
+   library for parallel graph partitioning and fill-reducing matrix ordering, available from
+   <TT><A NAME="tex2html8"
+  HREF="glaros.dtc.umn.edu/gkhome/metis/parmetis/overview">glaros.dtc.umn.edu/gkhome/metis/parmetis/overview</A></TT>.
+</DD>
+</DL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">To build the library the user will now enter 
-</FONT></FONT></FONT><PRE>
-make
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-followed (optionally) by 
-</FONT></FONT></FONT><PRE>
-make install
-</PRE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
+<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
 <!--Navigation Panel-->
 <A NAME="tex2html180"
   HREF="node9.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html176"
-  HREF="node5.html">
+  HREF="node6.html">
 <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
 <A NAME="tex2html170"
   HREF="node7.html">
@@ -274,11 +125,11 @@ make install
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html181"
-  HREF="node9.html">Bug reporting</A>
+  HREF="node9.html">Configuration options</A>
 <B> Up:</B> <A NAME="tex2html177"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
 <B> Previous:</B> <A NAME="tex2html171"
-  HREF="node7.html">Optional third party libraries</A>
+  HREF="node7.html">Prerequisites</A>
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   HREF="node2.html">Contents</A></B> 
 <!--End of Navigation Panel-->
diff --git a/docs/html/node9.html b/docs/html/node9.html
index 6a26d105..0bec52db 100644
--- a/docs/html/node9.html
+++ b/docs/html/node9.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 <HTML>
 <HEAD>
-<TITLE>Bug reporting</TITLE>
-<META NAME="description" CONTENT="Bug reporting">
+<TITLE>Configuration options</TITLE>
+<META NAME="description" CONTENT="Configuration options">
 <META NAME="keywords" CONTENT="userhtml">
 <META NAME="resource-type" CONTENT="document">
 <META NAME="distribution" CONTENT="global">
@@ -20,7 +20,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 <LINK REL="next" HREF="node10.html">
 <LINK REL="previous" HREF="node8.html">
-<LINK REL="up" HREF="node5.html">
+<LINK REL="up" HREF="node6.html">
 <LINK REL="next" HREF="node10.html">
 </HEAD>
 
@@ -30,7 +30,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   HREF="node10.html">
 <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
 <A NAME="tex2html188"
-  HREF="node5.html">
+  HREF="node6.html">
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 <A NAME="tex2html182"
   HREF="node8.html">
@@ -40,29 +40,248 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
 <BR>
 <B> Next:</B> <A NAME="tex2html193"
-  HREF="node10.html">Example and test programs</A>
+  HREF="node10.html">Bug reporting</A>
 <B> Up:</B> <A NAME="tex2html189"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
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-  HREF="node8.html">Configuration options</A>
+  HREF="node8.html">Optional third party libraries</A>
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   HREF="node2.html">Contents</A></B> 
 <BR>
 <BR>
 <!--End of Navigation Panel-->
 
-<H2><A NAME="SECTION00054000000000000000">
-Bug reporting</A>
-</H2><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
-If you find any bugs in our codes, please send an email to <BR><TT>pasqua.dambra@cnr.it</TT> 
-<BR><TT>daniela.diserafino@unicampania.it</TT> 
-<BR><TT>salvatore.filippone@cranfield.ac.uk</TT> <BR>
-You should be aware that the amount of information needed to reproduce a problem
-in a parallel program may vary quite a lot.
+<H2><A NAME="SECTION00053000000000000000">
+Configuration options</A>
+</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">In order to build MLD2P4, the first step is to use the <code>configure</code> script
+in the main directory to generate the necessary makefile.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">As a minimal example consider the following:
+</FONT></FONT></FONT><PRE>
+./configure --with-psblas=PSB-INSTALL-DIR
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+which assumes that the various MPI compilers and support libraries are
+available in the standard directories on the system, and specifies
+only the PSBLAS install  directory (note that the latter directory must
+be specified with an <EM>absolute</EM> path).
+The full set of options may be looked at by issuing the command
+<code>./configure --help</code>, which produces:
+</FONT></FONT></FONT><PRE>
+`configure' configures MLD2P4 2.1 to adapt to many kinds of systems.
+
+Usage: ./configure [OPTION]... [VAR=VALUE]...
+
+To assign environment variables (e.g., CC, CFLAGS...), specify them as
+VAR=VALUE.  See below for descriptions of some of the useful variables.
+
+Defaults for the options are specified in brackets.
+
+Configuration:
+  -h, --help              display this help and exit
+      --help=short        display options specific to this package
+      --help=recursive    display the short help of all the included packages
+  -V, --version           display version information and exit
+  -q, --quiet, --silent   do not print `checking...' messages
+      --cache-file=FILE   cache test results in FILE [disabled]
+  -C, --config-cache      alias for `--cache-file=config.cache'
+  -n, --no-create         do not create output files
+      --srcdir=DIR        find the sources in DIR [configure dir or `..']
+
+Installation directories:
+  --prefix=PREFIX         install architecture-independent files in PREFIX
+                          [/usr/local]
+  --exec-prefix=EPREFIX   install architecture-dependent files in EPREFIX
+                          [PREFIX]
+
+By default, `make install' will install all the files in
+`/usr/local/bin', `/usr/local/lib' etc.  You can specify
+an installation prefix other than `/usr/local' using `--prefix',
+for instance `--prefix=$HOME'.
+
+For better control, use the options below.
+
+Fine tuning of the installation directories:
+  --bindir=DIR            user executables [EPREFIX/bin]
+  --sbindir=DIR           system admin executables [EPREFIX/sbin]
+  --libexecdir=DIR        program executables [EPREFIX/libexec]
+  --sysconfdir=DIR        read-only single-machine data [PREFIX/etc]
+  --sharedstatedir=DIR    modifiable architecture-independent data [PREFIX/com]
+  --localstatedir=DIR     modifiable single-machine data [PREFIX/var]
+  --libdir=DIR            object code libraries [EPREFIX/lib]
+  --includedir=DIR        C header files [PREFIX/include]
+  --oldincludedir=DIR     C header files for non-gcc [/usr/include]
+  --datarootdir=DIR       read-only arch.-independent data root [PREFIX/share]
+  --datadir=DIR           read-only architecture-independent data [DATAROOTDIR]
+  --infodir=DIR           info documentation [DATAROOTDIR/info]
+  --localedir=DIR         locale-dependent data [DATAROOTDIR/locale]
+  --mandir=DIR            man documentation [DATAROOTDIR/man]
+  --docdir=DIR            documentation root [DATAROOTDIR/doc/mld2p4]
+  --htmldir=DIR           html documentation [DOCDIR]
+  --dvidir=DIR            dvi documentation [DOCDIR]
+  --pdfdir=DIR            pdf documentation [DOCDIR]
+  --psdir=DIR             ps documentation [DOCDIR]
+
+Program names:
+  --program-prefix=PREFIX            prepend PREFIX to installed program names
+  --program-suffix=SUFFIX            append SUFFIX to installed program names
+  --program-transform-name=PROGRAM   run sed PROGRAM on installed program names
+
+Optional Features:
+  --disable-option-checking  ignore unrecognized --enable/--with options
+  --disable-FEATURE       do not include FEATURE (same as --enable-FEATURE=no)
+  --enable-FEATURE[=ARG]  include FEATURE [ARG=yes]
+  --disable-dependency-tracking  speeds up one-time build
+  --enable-dependency-tracking   do not reject slow dependency extractors
+  --enable-serial         Specify whether to enable a fake mpi library to run
+                          in serial mode.
+  --enable-long-integers  Specify usage of 64 bits integers.
+
+Optional Packages:
+  --with-PACKAGE[=ARG]    use PACKAGE [ARG=yes]
+  --without-PACKAGE       do not use PACKAGE (same as --with-PACKAGE=no)
+  --with-psblas=DIR       The install directory for PSBLAS, for example,
+                          --with-psblas=/opt/packages/psblas-3.5
+  --with-psblas-incdir=DIR
+                          Specify the directory for PSBLAS includes.
+  --with-psblas-libdir=DIR
+                          Specify the directory for PSBLAS library.
+  --with-ccopt            additional CCOPT flags to be added: will prepend
+                          to CCOPT
+  --with-fcopt            additional FCOPT flags to be added: will prepend
+                          to FCOPT
+  --with-libs             List additional link flags here. For example,
+                          --with-libs=-lspecial_system_lib or
+                          --with-libs=-L/path/to/libs
+  --with-clibs            additional CLIBS flags to be added: will prepend
+                          to CLIBS
+  --with-flibs            additional FLIBS flags to be added: will prepend
+                          to FLIBS
+  --with-library-path     additional LIBRARYPATH flags to be added: will
+                          prepend to LIBRARYPATH
+  --with-include-path     additional INCLUDEPATH flags to be added: will
+                          prepend to INCLUDEPATH
+  --with-module-path      additional MODULE_PATH flags to be added: will
+                          prepend to MODULE_PATH
+  --with-extra-libs       List additional link flags here. For example,
+                          --with-extra-libs=-lspecial_system_lib or
+                          --with-extra-libs=-L/path/to/libs
+  --with-blas=&lt;lib&gt;       use BLAS library &lt;lib&gt;
+  --with-blasdir=&lt;dir&gt;    search for BLAS library in &lt;dir&gt;
+  --with-lapack=&lt;lib&gt;     use LAPACK library &lt;lib&gt;
+  --with-mumps=LIBNAME    Specify the libname for MUMPS. Default: autodetect
+                          with minimum "-lmumps_common -lpord"
+  --with-mumpsdir=DIR     Specify the directory for MUMPS library and
+                          includes. Note: you will need to add auxiliary
+                          libraries with --extra-libs; this depends on how
+                          MUMPS was configured and installed, at a minimum you
+                          will need SCALAPACK and BLAS
+  --with-mumpsincdir=DIR  Specify the directory for MUMPS includes.
+  --with-mumpslibdir=DIR  Specify the directory for MUMPS library.
+  --with-umfpack=LIBNAME  Specify the library name for UMFPACK and its support
+                          libraries. Default: "-lumfpack -lamd"
+  --with-umfpackdir=DIR   Specify the directory for UMFPACK library and
+                          includes.
+  --with-umfpackincdir=DIR
+                          Specify the directory for UMFPACK includes.
+  --with-umfpacklibdir=DIR
+                          Specify the directory for UMFPACK library.
+  --with-superlu=LIBNAME  Specify the library name for SUPERLU library.
+                          Default: "-lsuperlu"
+  --with-superludir=DIR   Specify the directory for SUPERLU library and
+                          includes.
+  --with-superluincdir=DIR
+                          Specify the directory for SUPERLU includes.
+  --with-superlulibdir=DIR
+                          Specify the directory for SUPERLU library.
+  --with-superludist=LIBNAME
+                          Specify the libname for SUPERLUDIST library.
+                          Requires you also specify SuperLU. Default:
+                          "-lsuperlu_dist"
+  --with-superludistdir=DIR
+                          Specify the directory for SUPERLUDIST library and
+                          includes.
+  --with-superludistincdir=DIR
+                          Specify the directory for SUPERLUDIST includes.
+  --with-superludistlibdir=DIR
+                          Specify the directory for SUPERLUDIST library.
+
+Some influential environment variables:
+  FC          Fortran compiler command
+  FCFLAGS     Fortran compiler flags
+  LDFLAGS     linker flags, e.g. -L&lt;lib dir&gt; if you have libraries in a
+              nonstandard directory &lt;lib dir&gt;
+  LIBS        libraries to pass to the linker, e.g. -l&lt;library&gt;
+  CC          C compiler command
+  CFLAGS      C compiler flags
+  CPPFLAGS    C/C++/Objective C preprocessor flags, e.g. -I&lt;include dir&gt; if
+              you have headers in a nonstandard directory &lt;include dir&gt;
+  MPICC       MPI C compiler command
+  MPIFC       MPI Fortran compiler command
+  CPP         C preprocessor
+
+Use these variables to override the choices made by `configure' or to help
+it to find libraries and programs with nonstandard names/locations.
+
+Report bugs to &lt;bugreport@mld2p4.it&gt;.
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For instance, if a user has built and installed PSBLAS 3.5 under the
+<code>/opt</code> directory and is
+using the SuiteSparse package (which includes UMFPACK), then MLD2P4
+might be configured with:
+</FONT></FONT></FONT><PRE>
+ ./configure --with-psblas=/opt/psblas-3.5/ \
+ --with-umfpackincdir=/usr/include/suitesparse/
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+Once the configure script has completed execution, it will have
+generated the file <code>Make.inc</code> which will then be used by all
+Makefiles in the directory tree; this file will be copied in the
+install directory under the name <code>Make.inc.MLD2P4</code>.
+</FONT></FONT></FONT>
+<P>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">To use the MUMPS solver package, 
+the user has to add the appropriate options to the configure script;
+by default we are looking for the libraries
+<code>-ldmumps -lsmumps</code> <code> -lzmumps -lcmumps -mumps_common -lpord</code>.
+MUMPS often uses additional packages such as ScaLAPACK, ParMETIS,
+SCOTCH, as well as enabling OpenMP; in such cases it is necessary to
+add linker options with the <code>--with-extra-libs</code> configure option.
 </FONT></FONT></FONT>
 <P>
-<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
-<BR><HR>
+<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">To build the library the user will now enter 
+</FONT></FONT></FONT><PRE>
+make
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
+followed (optionally) by 
+</FONT></FONT></FONT><PRE>
+make install
+</PRE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
+<!--Navigation Panel-->
+<A NAME="tex2html192"
+  HREF="node10.html">
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
+<A NAME="tex2html188"
+  HREF="node6.html">
+<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
+<A NAME="tex2html182"
+  HREF="node8.html">
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+<A NAME="tex2html190"
+  HREF="node2.html">
+<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>  
+<BR>
+<B> Next:</B> <A NAME="tex2html193"
+  HREF="node10.html">Bug reporting</A>
+<B> Up:</B> <A NAME="tex2html189"
+  HREF="node6.html">Configuring and Building MLD2P4</A>
+<B> Previous:</B> <A NAME="tex2html183"
+  HREF="node8.html">Optional third party libraries</A>
+ &nbsp; <B>  <A NAME="tex2html191"
+  HREF="node2.html">Contents</A></B> 
+<!--End of Navigation Panel-->
 
 </BODY>
 </HTML>
diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html
index 82c86e2e..dfbb0955 100644
--- a/docs/html/userhtml.html
+++ b/docs/html/userhtml.html
@@ -98,70 +98,75 @@ July 31, 2017
   HREF="node3.html">General Overview</A>
 <LI><A NAME="tex2html29"
   HREF="node4.html">Code Distribution</A>
-<LI><A NAME="tex2html30"
-  HREF="node5.html">Configuring and Building MLD2P4</A>
 <UL>
+<LI><A NAME="tex2html30"
+  HREF="node5.html">Contributors</A>
+</UL>
+<BR>
 <LI><A NAME="tex2html31"
-  HREF="node6.html">Prerequisites</A>
+  HREF="node6.html">Configuring and Building MLD2P4</A>
+<UL>
 <LI><A NAME="tex2html32"
-  HREF="node7.html">Optional third party libraries</A>
+  HREF="node7.html">Prerequisites</A>
 <LI><A NAME="tex2html33"
-  HREF="node8.html">Configuration options</A>
+  HREF="node8.html">Optional third party libraries</A>
 <LI><A NAME="tex2html34"
-  HREF="node9.html">Bug reporting</A>
+  HREF="node9.html">Configuration options</A>
 <LI><A NAME="tex2html35"
-  HREF="node10.html">Example and test programs</A>
+  HREF="node10.html">Bug reporting</A>
+<LI><A NAME="tex2html36"
+  HREF="node11.html">Example and test programs</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html36"
-  HREF="node11.html">Multigrid Background</A>
-<UL>
 <LI><A NAME="tex2html37"
-  HREF="node12.html">AMG preconditioners</A>
+  HREF="node12.html">Multigrid Background</A>
+<UL>
 <LI><A NAME="tex2html38"
-  HREF="node13.html">Smoothed Aggregation</A>
+  HREF="node13.html">AMG preconditioners</A>
 <LI><A NAME="tex2html39"
-  HREF="node14.html">Smoothers and coarsest-level solvers</A>
+  HREF="node14.html">Smoothed Aggregation</A>
+<LI><A NAME="tex2html40"
+  HREF="node15.html">Smoothers and coarsest-level solvers</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html40"
-  HREF="node15.html">Getting Started</A>
-<UL>
 <LI><A NAME="tex2html41"
-  HREF="node16.html">Examples</A>
+  HREF="node16.html">Getting Started</A>
+<UL>
+<LI><A NAME="tex2html42"
+  HREF="node17.html">Examples</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html42"
-  HREF="node17.html">User Interface</A>
-<UL>
 <LI><A NAME="tex2html43"
-  HREF="node18.html">Subroutine init</A>
+  HREF="node18.html">User Interface</A>
+<UL>
 <LI><A NAME="tex2html44"
-  HREF="node19.html">Subroutine set</A>
+  HREF="node19.html">Subroutine init</A>
 <LI><A NAME="tex2html45"
-  HREF="node20.html">Subroutine build</A>
+  HREF="node20.html">Subroutine set</A>
 <LI><A NAME="tex2html46"
-  HREF="node21.html">Subroutine hierarchy_build</A>
+  HREF="node21.html">Subroutine build</A>
 <LI><A NAME="tex2html47"
-  HREF="node22.html">Subroutine smoothers_build</A>
+  HREF="node22.html">Subroutine hierarchy_build</A>
 <LI><A NAME="tex2html48"
-  HREF="node23.html">Subroutine apply</A>
+  HREF="node23.html">Subroutine smoothers_build</A>
 <LI><A NAME="tex2html49"
-  HREF="node24.html">Subroutine free</A>
+  HREF="node24.html">Subroutine apply</A>
 <LI><A NAME="tex2html50"
-  HREF="node25.html">Subroutine descr</A>
+  HREF="node25.html">Subroutine free</A>
+<LI><A NAME="tex2html51"
+  HREF="node26.html">Subroutine descr</A>
 </UL>
 <BR>
-<LI><A NAME="tex2html51"
-  HREF="node26.html">Adding new  smoother and solver objects to MLD2P4</A>
 <LI><A NAME="tex2html52"
-  HREF="node27.html">Error Handling</A>
+  HREF="node27.html">Adding new  smoother and solver objects to MLD2P4</A>
 <LI><A NAME="tex2html53"
-  HREF="node28.html">License</A>
+  HREF="node28.html">Error Handling</A>
 <LI><A NAME="tex2html54"
-  HREF="node29.html">Bibliography</A>
+  HREF="node29.html">License</A>
 <LI><A NAME="tex2html55"
-  HREF="node30.html">About this document ...</A>
+  HREF="node30.html">Bibliography</A>
+<LI><A NAME="tex2html56"
+  HREF="node31.html">About this document ...</A>
 </UL>
 <!--End of Table of Child-Links-->
 <BR><HR>
diff --git a/docs/mld2p4-2.1-guide.pdf b/docs/mld2p4-2.1-guide.pdf
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diff --git a/docs/src/license.tex b/docs/src/license.tex
index 46f2e4cb..8f76d67c 100644
--- a/docs/src/license.tex
+++ b/docs/src/license.tex
@@ -14,8 +14,6 @@ terms: {\small
   (C) Copyright 2008, 2010, 2012, 2017
 
   Salvatore Filippone    Cranfield University, Cranfield, UK
-  Ambra Abdullahi Hassan University of Rome Tor Vergata, Rome, IT
-  Alfredo Buttari        CNRS-IRIT, Toulouse, FR
   Pasqua D'Ambra         IAC-CNR, Naples, IT
   Daniela di Serafino    University of Campania L. Vanvitelli, Caserta, IT