fdurastante/amg4psblas
1
0
Fork 0
mirror of https://github.com/sfilippone/amg4psblas.git synced 2026-10-19 04:12:11 +00:00
Code Issues Packages Projects Releases Wiki Activity

mld2p4: final fixes for 1.1 release.

Browse Source
This commit is contained in:
Salvatore Filippone
2009-03-16 08:47:03 +00:00
parent 5e0cfebc6d
commit 73dac6d963
56 changed files with 1275 additions and 1325 deletions
Download Patch File Download Diff File Expand all files Collapse all files
docs/html/node13.html
+7 -7
View File
@@ -70,7 +70,7 @@ the coarse-level matrix <IMG
ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I>
algorithm described in [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>].
HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>].
The basic idea of this algorithm is to build a coarse set of vertices
<IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -120,7 +120,7 @@ Three main steps can be identified in the smoothed aggregation procedure:
To perform the coarsening step, we have implemented the aggregation algorithm sketched
in [<A
HREF="node25.html#apnum_07">4</A>]. According to [<A
HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>], a modification of
HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>], a modification of
this algorithm has been actually considered,
in which each aggregate <IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -159,7 +159,7 @@ for a given <!-- MATH
ALT="$\theta \in [0,1]$">.
Since this algorithm has a sequential nature, a <I>decoupled</I> version of
it has been chosen, where each processor <IMG
WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
WIDTH="10" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img74.png"
ALT="$i$"> independently applies the algorithm to
the set of vertices <IMG
@@ -178,7 +178,7 @@ since it has been shown to produce good results in practice
[<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#TUMINARO_TONG">23</A>].
HREF="node25.html#TUMINARO_TONG">24</A>].
<P>
The prolongator <IMG
@@ -189,7 +189,7 @@ The prolongator <IMG
$P \in \Re^{n \times n_C}$
-->
<IMG
WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="img77.png"
ALT="$P \in \Re^{n \times n_C}$">, defined as
<BR>
@@ -257,7 +257,7 @@ in order to remove oscillatory components from the range of the prolongator
and hence to improve the convergence properties of the multi-level
Schwarz method [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#StubenGMD69_99">22</A>].
HREF="node25.html#StubenGMD69_99">23</A>].
A simple choice for <IMG
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img83.png"
@@ -286,7 +286,7 @@ where the value of <IMG
SRC="img85.png"
ALT="$\omega$"> can be chosen
using some estimate of the spectral radius of <IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$D^{-1}A$"> [<A
HREF="node25.html#BREZINA_VANEK">1</A>].