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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 >
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<BR>
@@ -295,15 +295,15 @@ ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$p,t$">) [<A
HREF="node25.html#Saad_book">22</A>, Chapter 10].
HREF="node27.html#Saad_book">22</A>, Chapter 10].
<P>
A variant of the classical AS preconditioner that outperforms it
in terms of convergence rate and of computation and communication
time on parallel distributed-memory computers is the so-called <I>Restricted AS
(RAS)</I> preconditioner&nbsp;[<A
HREF="node25.html#CAI_SARKIS">5</A>,<A
HREF="node25.html#EFSTATHIOU">15</A>]. It
HREF="node27.html#CAI_SARKIS">5</A>,<A
HREF="node27.html#EFSTATHIOU">15</A>]. It
is obtained by zeroing the components of <IMG
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img33.png"
@@ -386,8 +386,8 @@ of <IMG
WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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ALT="$W$"> increases [<A
HREF="node25.html#dd1_94">7</A>,<A
HREF="node25.html#dd2_96">23</A>]. To reduce the dependency
HREF="node27.html#dd1_94">7</A>,<A
HREF="node27.html#dd2_96">23</A>]. To reduce the dependency
of the number of iterations on the degree of parallelism we may
introduce a global coupling among the overlapping partitions by defining
a coarse-space approximation <IMG
@@ -642,12 +642,12 @@ in which the coarse-level correction is re-applied starting from the current
coarse-level system. The corresponding preconditioners, called <I>multi-level</I>
preconditioners, can significantly reduce the computational cost of preconditioning
with respect to the two-level case (see [<A
HREF="node25.html#dd2_96">23</A>, Chapter 3]).
HREF="node27.html#dd2_96">23</A>, Chapter 3]).
Additive and hybrid multilevel preconditioners
are obtained as direct extensions of the two-level counterparts.
For a detailed descrition of them, the reader is
referred to [<A
HREF="node25.html#dd2_96">23</A>, Chapter 3].
HREF="node27.html#dd2_96">23</A>, Chapter 3].
The algorithm for the application of a multi-level hybrid
post-smoothed preconditioner <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
@@ -738,26 +738,26 @@ $w = y_1$;
<P>
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HREF="node13.html">Smoothed Aggregation</A>
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<B> Up:</B> <A NAME="tex2html212"
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HREF="node2.html">Contents</A></B>
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