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New interfaces for building hierachy and preconditioner.
This commit is contained in:
Salvatore Filippone
2016-06-09 15:38:36 +00:00
parent d989714ee9
commit 86982461ad
35 changed files with 5859 additions and 5210 deletions
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@@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html197"
<A NAME="tex2html201"
HREF="node12.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html193"
<A NAME="tex2html197"
HREF="userhtml.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html187"
<A NAME="tex2html191"
HREF="node10.html">
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<A NAME="tex2html195"
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HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html198"
<B> Next:</B> <A NAME="tex2html202"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<B> Up:</B> <A NAME="tex2html194"
<B> Up:</B> <A NAME="tex2html198"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html188"
<B> Previous:</B> <A NAME="tex2html192"
HREF="node10.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html196"
&nbsp; <B> <A NAME="tex2html200"
HREF="node2.html">Contents</A></B>
<BR>
<BR>
@@ -68,15 +68,15 @@ into subdomains, e.g. in a PDE discretization, to (approximately) solving the
subproblems corresponding to the subdomains and to building an approximate
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">23</A>].
HREF="node27.html#Cai_Widlund_92">6</A>,<A
HREF="node27.html#dd1_94">7</A>,<A
HREF="node27.html#dd2_96">23</A>].
<P>
<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
submatrices, i.e. with some common rows, to couple the local information
related to the submatrices (see, e.g., [<A
HREF="node25.html#dd2_96">23</A>]).
HREF="node27.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
@@ -95,7 +95,7 @@ correction. In this context, the one-level preconditioner is often
called `smoother'. Different two-level preconditioners are obtained by varying the
choice of the smoother and of the coarse-level correction, and the
way they are combined [<A
HREF="node25.html#dd2_96">23</A>]. The same reasoning can be applied starting
HREF="node27.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 <I>multi-level</I> preconditioners.
@@ -119,25 +119,25 @@ are considered. The algebraic approach builds coarse-space corrections using onl
information. It performs a fully automatic coarsening and enforces the interplay between
the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
interpolation [<A
HREF="node25.html#StubenGMD69_99">25</A>].
HREF="node27.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 <I>smoothed
aggregation</I> algorithm [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.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">26</A>]. In the next two subsections we provide
HREF="node27.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
HREF="node25.html#para_04">2</A>,<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#MLD2P4_TOMS">8</A>,<A
HREF="node25.html#dd2_96">23</A>].
HREF="node27.html#para_04">2</A>,<A
HREF="node27.html#aaecc_07">3</A>,<A
HREF="node27.html#apnum_07">4</A>,<A
HREF="node27.html#MLD2P4_TOMS">8</A>,<A
HREF="node27.html#dd2_96">23</A>].
<P>
<BR><HR>
@@ -145,34 +145,34 @@ is referred to [<A
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html199"
<LI><A NAME="tex2html203"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html200"
<LI><A NAME="tex2html204"
HREF="node13.html">Smoothed Aggregation</A>
</UL>
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<BR>
<B> Next:</B> <A NAME="tex2html198"
<B> Next:</B> <A NAME="tex2html202"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<B> Up:</B> <A NAME="tex2html194"
<B> Up:</B> <A NAME="tex2html198"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html188"
<B> Previous:</B> <A NAME="tex2html192"
HREF="node10.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html196"
&nbsp; <B> <A NAME="tex2html200"
HREF="node2.html">Contents</A></B>
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