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Added aggregation ordering option to docs.
This commit is contained in:
Salvatore Filippone
2016-05-09 16:04:33 +00:00
parent 875443efe7
commit c592733a8e
42 changed files with 2745 additions and 2539 deletions
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@@ -1,4 +1,4 @@
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@@ -25,31 +25,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
@@ -58,7 +57,7 @@ Multi-level Domain Decomposition Background
</H1>
<P>
<SPAN CLASS="textit">Domain Decomposition</SPAN> (DD) preconditioners, coupled with Krylov iterative
<I>Domain Decomposition</I> (DD) preconditioners, coupled with Krylov iterative
solvers, are widely used in the parallel solution of large and sparse linear systems.
These preconditioners are based on the divide and conquer technique: the matrix
to be preconditioned is divided into submatrices, a ``local'' linear system
@@ -71,13 +70,13 @@ solution of the original problem from the local solutions
[<A
HREF="node25.html#Cai_Widlund_92">6</A>,<A
HREF="node25.html#dd1_94">7</A>,<A
HREF="node25.html#dd2_96">22</A>].
HREF="node25.html#dd2_96">23</A>].
<P>
<SPAN CLASS="textit">Additive Schwarz</SPAN> preconditioners are DD preconditioners using overlapping
<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
submatrices, i.e. with some common rows, to couple the local information
related to the submatrices (see, e.g., [<A
HREF="node25.html#dd2_96">22</A>]).
HREF="node25.html#dd2_96">23</A>]).
The main motivation for choosing Additive Schwarz preconditioners is their
intrinsic parallelism. A drawback of these
preconditioners is that the number of iterations of the preconditioned solvers
@@ -90,15 +89,15 @@ in a coarse space, which globally couples the information related to the single
submatrices.
<P>
<SPAN CLASS="textit">Two-level Schwarz</SPAN> preconditioners are obtained
<I>Two-level Schwarz</I> preconditioners are obtained
by combining basic (one-level) Schwarz preconditioners with a coarse-level
correction. In this context, the one-level preconditioner is often
called `smoother'. Different two-level preconditioners are obtained by varying the
choice of the smoother and of the coarse-level correction, and the
way they are combined [<A
HREF="node25.html#dd2_96">22</A>]. The same reasoning can be applied starting
HREF="node25.html#dd2_96">23</A>]. The same reasoning can be applied starting
from the coarse-level system, i.e. a coarse-space correction can be built
from this system, thus obtaining <SPAN CLASS="textit">multi-level</SPAN> preconditioners.
from this system, thus obtaining <I>multi-level</I> preconditioners.
<P>
It is worth noting that optimal preconditioners do not necessarily correspond
@@ -120,17 +119,17 @@ are considered. The algebraic approach builds coarse-space corrections using onl
information. It performs a fully automatic coarsening and enforces the interplay between
the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
interpolation [<A
HREF="node25.html#StubenGMD69_99">24</A>].
HREF="node25.html#StubenGMD69_99">25</A>].
<P>
MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
starting from the original matrix. The algebraic approach is based on the <SPAN CLASS="textit">smoothed
aggregation</SPAN> algorithm [<A
starting from the original matrix. The algebraic approach is based on the <I>smoothed
aggregation</I> algorithm [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>]. A decoupled version
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
of this algorithm is implemented, where the smoothed aggregation is applied locally
to each submatrix [<A
HREF="node25.html#TUMINARO_TONG">25</A>]. In the next two subsections we provide
HREF="node25.html#TUMINARO_TONG">26</A>]. In the next two subsections we provide
a brief description of the multi-level Schwarz preconditioners and of the smoothed
aggregation technique as implemented in MLD2P4. For further details the reader
is referred to [<A
@@ -138,44 +137,43 @@ is referred to [<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#MLD2P4_TOMS">8</A>,<A
HREF="node25.html#dd2_96">22</A>].
HREF="node25.html#dd2_96">23</A>].
<P>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL CLASS="ChildLinks">
<LI><A NAME="tex2html197"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<UL>
<LI><A NAME="tex2html198"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html199"
HREF="node13.html">Smoothed Aggregation</A>
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