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<LI><A NAME="tex2html35"
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HREF="node19.html">Subroutine mld_precbld</A>
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<LI><A NAME="tex2html36"
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HREF="node20.html">Subroutine mld_precaply</A>
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HREF="node20.html">Subroutine mld_hierarchy_bld</A>
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<LI><A NAME="tex2html37"
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HREF="node21.html">Subroutine mld_precfree</A>
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HREF="node21.html">Subroutine mld_ml_prec_bld</A>
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<LI><A NAME="tex2html38"
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HREF="node22.html">Subroutine mld_precdescr</A>
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HREF="node22.html">Subroutine mld_precaply</A>
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<LI><A NAME="tex2html39"
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HREF="node23.html">Subroutine mld_precfree</A>
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<LI><A NAME="tex2html40"
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HREF="node24.html">Subroutine mld_precdescr</A>
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<BR>
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HREF="node23.html">Error Handling</A>
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@@ -88,26 +88,26 @@ the user interface of MLD2P4.
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+32
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<BODY >
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<B> Next:</B> <A NAME="tex2html198"
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<B> Next:</B> <A NAME="tex2html202"
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
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<B> Up:</B> <A NAME="tex2html194"
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HREF="node2.html">Contents</A></B>
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@@ -68,15 +68,15 @@ into subdomains, e.g. in a PDE discretization, to (approximately) solving the
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subproblems corresponding to the subdomains and to building an approximate
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solution of the original problem from the local solutions
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[<A
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HREF="node25.html#Cai_Widlund_92">6</A>,<A
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HREF="node25.html#dd1_94">7</A>,<A
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HREF="node25.html#dd2_96">23</A>].
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HREF="node27.html#Cai_Widlund_92">6</A>,<A
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HREF="node27.html#dd1_94">7</A>,<A
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HREF="node27.html#dd2_96">23</A>].
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<P>
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<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
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submatrices, i.e. with some common rows, to couple the local information
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related to the submatrices (see, e.g., [<A
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HREF="node25.html#dd2_96">23</A>]).
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HREF="node27.html#dd2_96">23</A>]).
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The main motivation for choosing Additive Schwarz preconditioners is their
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intrinsic parallelism. A drawback of these
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preconditioners is that the number of iterations of the preconditioned solvers
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@@ -95,7 +95,7 @@ correction. In this context, the one-level preconditioner is often
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called `smoother'. Different two-level preconditioners are obtained by varying the
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choice of the smoother and of the coarse-level correction, and the
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way they are combined [<A
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HREF="node25.html#dd2_96">23</A>]. The same reasoning can be applied starting
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HREF="node27.html#dd2_96">23</A>]. The same reasoning can be applied starting
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from the coarse-level system, i.e. a coarse-space correction can be built
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from this system, thus obtaining <I>multi-level</I> preconditioners.
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@@ -119,25 +119,25 @@ are considered. The algebraic approach builds coarse-space corrections using onl
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information. It performs a fully automatic coarsening and enforces the interplay between
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the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
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interpolation [<A
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HREF="node25.html#StubenGMD69_99">25</A>].
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HREF="node27.html#StubenGMD69_99">25</A>].
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<P>
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MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
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starting from the original matrix. The algebraic approach is based on the <I>smoothed
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aggregation</I> algorithm [<A
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HREF="node25.html#BREZINA_VANEK">1</A>,<A
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HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
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HREF="node27.html#BREZINA_VANEK">1</A>,<A
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HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
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of this algorithm is implemented, where the smoothed aggregation is applied locally
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to each submatrix [<A
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HREF="node25.html#TUMINARO_TONG">26</A>]. In the next two subsections we provide
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HREF="node27.html#TUMINARO_TONG">26</A>]. In the next two subsections we provide
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a brief description of the multi-level Schwarz preconditioners and of the smoothed
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aggregation technique as implemented in MLD2P4. For further details the reader
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is referred to [<A
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HREF="node25.html#para_04">2</A>,<A
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HREF="node25.html#aaecc_07">3</A>,<A
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HREF="node25.html#apnum_07">4</A>,<A
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HREF="node25.html#MLD2P4_TOMS">8</A>,<A
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HREF="node25.html#dd2_96">23</A>].
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HREF="node27.html#para_04">2</A>,<A
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HREF="node27.html#aaecc_07">3</A>,<A
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HREF="node27.html#apnum_07">4</A>,<A
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HREF="node27.html#MLD2P4_TOMS">8</A>,<A
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HREF="node27.html#dd2_96">23</A>].
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<P>
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<BR><HR>
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@@ -145,34 +145,34 @@ is referred to [<A
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html199"
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<LI><A NAME="tex2html203"
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
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+23
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR>
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@@ -295,15 +295,15 @@ ILU(<IMG
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WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img36.png"
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ALT="$p,t$">) [<A
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HREF="node25.html#Saad_book">22</A>, Chapter 10].
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HREF="node27.html#Saad_book">22</A>, Chapter 10].
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<P>
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A variant of the classical AS preconditioner that outperforms it
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in terms of convergence rate and of computation and communication
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time on parallel distributed-memory computers is the so-called <I>Restricted AS
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(RAS)</I> preconditioner [<A
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HREF="node25.html#CAI_SARKIS">5</A>,<A
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HREF="node25.html#EFSTATHIOU">15</A>]. It
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HREF="node27.html#CAI_SARKIS">5</A>,<A
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HREF="node27.html#EFSTATHIOU">15</A>]. It
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is obtained by zeroing the components of <IMG
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WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
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SRC="img33.png"
|
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@@ -386,8 +386,8 @@ of <IMG
|
||||
WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
|
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SRC="img11.png"
|
||||
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"
|
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@@ -738,26 +738,26 @@ $w = y_1$;
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@@ -65,8 +65,8 @@ the coarse-level matrix <IMG
|
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SRC="img44.png"
|
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ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I>
|
||||
algorithm described in [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>,<A
|
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HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
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HREF="node27.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>].
|
||||
The basic idea of this algorithm is to build a coarse set of vertices
|
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<IMG
|
||||
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
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@@ -114,8 +114,8 @@ Three main steps can be identified in the smoothed aggregation procedure:
|
||||
<P>
|
||||
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">27</A>], a modification of
|
||||
HREF="node27.html#apnum_07">4</A>]. According to [<A
|
||||
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>], a modification of
|
||||
this algorithm has been actually considered,
|
||||
in which each aggregate <IMG
|
||||
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
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@@ -171,9 +171,9 @@ dependent on the number of processors and on the initial partitioning of the mat
|
||||
Nevertheless, this algorithm has been chosen for the implementation in MLD2P4,
|
||||
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">26</A>].
|
||||
HREF="node27.html#aaecc_07">3</A>,<A
|
||||
HREF="node27.html#apnum_07">4</A>,<A
|
||||
HREF="node27.html#TUMINARO_TONG">26</A>].
|
||||
|
||||
<P>
|
||||
The prolongator <IMG
|
||||
@@ -251,8 +251,8 @@ P_C = S P,
|
||||
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">25</A>].
|
||||
HREF="node27.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node27.html#StubenGMD69_99">25</A>].
|
||||
A simple choice for <IMG
|
||||
WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img84.png"
|
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@@ -284,30 +284,30 @@ using some estimate of the spectral radius of <IMG
|
||||
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img87.png"
|
||||
ALT="$D^{-1}A$"> [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>].
|
||||
HREF="node27.html#BREZINA_VANEK">1</A>].
|
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@@ -59,7 +59,7 @@ Getting Started
|
||||
<P>
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We describe the basics for building and applying MLD2P4 one-level and multi-level
|
||||
Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A
|
||||
HREF="node25.html#PSBLASGUIDE">16</A>].
|
||||
HREF="node27.html#PSBLASGUIDE">16</A>].
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The following steps are required:
|
||||
|
||||
<OL>
|
||||
@@ -80,6 +80,18 @@ The following steps are required:
|
||||
Note that these strings are valid also if uppercase letters are substituted by
|
||||
corresponding lowercase ones.
|
||||
</LI>
|
||||
<LI><I>Modify the aggregation parameters.</I> This is performed by
|
||||
the routine <code>mld_precset</code>.
|
||||
This routine must be called only if the user wants to modify the default values
|
||||
of the parameters associated to the aggregation hierarchy construction.
|
||||
Examples of use of <code>mld_precset</code> are given in
|
||||
Section <A HREF="node15.html#sec:examples">5.1</A>; a complete list of all the
|
||||
preconditioner parameters and their allowed and default values is provided in
|
||||
Section <A HREF="node16.html#sec:userinterface">6</A>, Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">6</A>.
|
||||
</LI>
|
||||
<LI><I>Build the aggregation hierarchy for a given matrix.</I> This is performed by
|
||||
the routine <code>mld_hierarchy_bld</code>.
|
||||
</LI>
|
||||
<LI><I>Modify the selected preconditioner type, by properly setting
|
||||
preconditioner parameters.</I> This is performed by the routine <code>mld_precset</code>.
|
||||
This routine must be called only if the user wants to modify the default values
|
||||
@@ -90,7 +102,7 @@ The following steps are required:
|
||||
Section <A HREF="node16.html#sec:userinterface">6</A>, Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">6</A>.
|
||||
</LI>
|
||||
<LI><I>Build the preconditioner for a given matrix.</I> This is performed by
|
||||
the routine <code>mld_precbld</code>.
|
||||
the routine <code>mld_ml_prec_bld</code>.
|
||||
</LI>
|
||||
<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
|
||||
This is performed by the routine <code>mld_precaply</code>. When using the PSBLAS Krylov solvers,
|
||||
@@ -121,8 +133,8 @@ machines, it often leads to the smallest execution time when applied to
|
||||
linear systems coming from finite-difference discretizations of basic
|
||||
elliptic PDE problems, considered as standard tests for multi-level Schwarz
|
||||
preconditioners [<A
|
||||
HREF="node25.html#aaecc_07">3</A>,<A
|
||||
HREF="node25.html#apnum_07">4</A>]. However, this solver does
|
||||
HREF="node27.html#aaecc_07">3</A>,<A
|
||||
HREF="node27.html#apnum_07">4</A>]. However, this solver does
|
||||
not necessarily correspond to the smallest number of iterations of the
|
||||
preconditioned Krylov method, which is usually obtained by applying
|
||||
a direct solver to the coarsest-level system, e.g. based on the LU
|
||||
@@ -131,7 +143,7 @@ for the coarsest-level solvers available in MLD2P4).
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="943"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="949"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 1:</STRONG>
|
||||
Preconditioner types, corresponding strings and default choices.
|
||||
@@ -198,32 +210,32 @@ Preconditioner types, corresponding strings and default choices.
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL>
|
||||
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|
||||
<LI><A NAME="tex2html239"
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HREF="node2.html">Contents</A></B>
|
||||
<BR>
|
||||
<BR>
|
||||
@@ -75,7 +75,7 @@ in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
|
||||
Section <A HREF="node10.html#sec:ex_and_test">3.5</A>).
|
||||
For details on the use of the PSBLAS routines, see the PSBLAS User's
|
||||
Guide [<A
|
||||
HREF="node25.html#PSBLASGUIDE">16</A>].
|
||||
HREF="node27.html#PSBLASGUIDE">16</A>].
|
||||
|
||||
<P>
|
||||
The setup and application of the default multi-level
|
||||
@@ -86,7 +86,7 @@ the corresponding Fortran 95 codes are available in <code>examples/fileread/</co
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="946"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="952"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
|
||||
Setup and application of the default multi-level Schwarz preconditioner.
|
||||
@@ -128,7 +128,9 @@ Setup and application of the default multi-level Schwarz preconditioner.
|
||||
call mld_precinit(P,'ML',info)
|
||||
!
|
||||
! build the preconditioner
|
||||
call mld_precbld(A,desc_A,P,info)
|
||||
call mld_hierarchy_bld(A,desc_A,P,info)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
|
||||
!
|
||||
! set the solver parameters and the initial guess
|
||||
... ...
|
||||
@@ -162,12 +164,12 @@ Figure <A HREF="#fig:ex_3lh">3</A> shows how to set a three-level hybrid Sc
|
||||
preconditioner, which uses block Jacobi with ILU(0) on the
|
||||
local blocks as post-smoother, has a coarsest matrix replicated on the processors,
|
||||
and solves the coarsest-level system with the LU factorization from UMFPACK [<A
|
||||
HREF="node25.html#UMFPACK">9</A>].
|
||||
HREF="node27.html#UMFPACK">9</A>].
|
||||
Figure <A HREF="#fig:ex_3lhm">4</A> shows how to set a three-level preconditioner
|
||||
similar to the one of <A HREF="#fig:ex_3lh">3</A>, but the coarsest-level
|
||||
systems is solved with the multifrontal factorization from
|
||||
MUMPS [<A
|
||||
HREF="node25.html#UMFPACK">9</A>].
|
||||
HREF="node27.html#UMFPACK">9</A>].
|
||||
Note that MUMPS can be used on both replicated and distributed
|
||||
coarsest level matrices, as a global and local solver respectively.
|
||||
The number of levels is specified by using <code>mld_precinit</code>; the other
|
||||
@@ -202,7 +204,7 @@ boundary conditions are also available in the directory <code>examples/pdegen</c
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="948"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="954"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
|
||||
Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
@@ -216,11 +218,14 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
! block Jacobi (with ILU(0) on the blocks) as post-smoother,
|
||||
! a coarsest matrix replicated on the processors, and the
|
||||
! LU factorization from UMFPACK as coarse-level solver
|
||||
call mld_precinit(P,'ML',info,nlev=3)
|
||||
call mld_precinit(P,'ML',info)
|
||||
call mld_hierarchy_bld(A,desc_A,P,info)
|
||||
|
||||
call_mld_precset(P,'SMOOTHER_TYPE','BJAC',info)
|
||||
call_mld_precset(P,'SMOOTHER_POS,'POST'w,info)
|
||||
call mld_precset(P,'COARSE_MAT','REPL',info)
|
||||
call mld_precset(P,'COARSE_SOLVE','UMF',info)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
... ...
|
||||
</PRE>
|
||||
</TD></TR>
|
||||
@@ -235,7 +240,7 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lhm"></A><A NAME="950"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lhm"></A><A NAME="956"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
|
||||
Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
@@ -251,10 +256,12 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
! multifrontal solver in MUMPS as coarse-level solver
|
||||
|
||||
call mld_precinit(P,'ML',info,nlev=3)
|
||||
call mld_hierarchy_bld(A,desc_A,P,info)
|
||||
|
||||
call mld_precset(P,mld_smoother_type_,'BJAC',info)
|
||||
call mld_precset(P,mld_coarse_mat_,'REPL',info)
|
||||
call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
|
||||
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
... ...
|
||||
</PRE>
|
||||
</TD></TR>
|
||||
@@ -269,7 +276,7 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="952"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="958"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
|
||||
Setup of an additive three-level Schwarz preconditioner.</CAPTION>
|
||||
@@ -284,9 +291,11 @@ Setup of an additive three-level Schwarz preconditioner.</CAPTION>
|
||||
! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
|
||||
! on the blocks) as distributed coarsest-level solver
|
||||
call mld_precinit(P,'ML',info,nlev=3)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
call mld_precset(P,'ML_TYPE','ADD',info)
|
||||
call_mld_precset(P,'SMOOTHER_POS','TWOSIDE',info)
|
||||
call mld_precset(P,'COARSE_SWEEPS',5,info)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
... ...
|
||||
</PRE>
|
||||
</TD></TR>
|
||||
@@ -301,7 +310,7 @@ Setup of an additive three-level Schwarz preconditioner.</CAPTION>
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="954"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="960"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6:</STRONG>
|
||||
Setup of a one-level Schwarz preconditioner.</CAPTION>
|
||||
@@ -314,6 +323,7 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
|
||||
! set RAS with overlap 2 and ILU(0) on the local blocks
|
||||
call mld_precinit(P,'AS',info)
|
||||
call mld_precset(P,'SUB_OVR',2,info)
|
||||
call mld_precbld(A,desc_A,P,info)
|
||||
... ...
|
||||
</PRE>
|
||||
</TD></TR>
|
||||
@@ -327,26 +337,26 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
|
||||
<P>
|
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@@ -113,42 +113,46 @@ A description of each routine is given in the remainder of this section.
|
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html258"
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HREF="node17.html">Subroutine mld_precinit</A>
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<LI><A NAME="tex2html259"
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HREF="node18.html">Subroutine mld_precset</A>
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HREF="node19.html">Subroutine mld_precbld</A>
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HREF="node20.html">Subroutine mld_precaply</A>
|
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<LI><A NAME="tex2html262"
|
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HREF="node21.html">Subroutine mld_precfree</A>
|
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HREF="node17.html">Subroutine mld_precinit</A>
|
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<LI><A NAME="tex2html263"
|
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HREF="node22.html">Subroutine mld_precdescr</A>
|
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HREF="node18.html">Subroutine mld_precset</A>
|
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<LI><A NAME="tex2html264"
|
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HREF="node19.html">Subroutine mld_precbld</A>
|
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HREF="node20.html">Subroutine mld_hierarchy_bld</A>
|
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<LI><A NAME="tex2html266"
|
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HREF="node21.html">Subroutine mld_ml_prec_bld</A>
|
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<LI><A NAME="tex2html267"
|
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HREF="node22.html">Subroutine mld_precaply</A>
|
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<LI><A NAME="tex2html268"
|
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HREF="node23.html">Subroutine mld_precfree</A>
|
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|
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HREF="node24.html">Subroutine mld_precdescr</A>
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@@ -94,7 +94,7 @@ according to the preconditioner type chosen by the user.
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
|
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A> for details.</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>nlev</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, optional, intent(in)</code>.</TD>
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@@ -114,26 +114,26 @@ according to the preconditioner type chosen by the user.
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@@ -144,7 +144,7 @@ modified, and thus has no direct knowledge about the new type.
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A>
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for details.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>pos</code></TD>
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@@ -209,7 +209,7 @@ according to their needs.
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1324"></A>
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<DIV ALIGN="CENTER"><A NAME="1363"></A>
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<TABLE>
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<CAPTION><STRONG>Table 2:</STRONG>
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Parameters defining the type of multi-level preconditioner.
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1326"></A>
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<DIV ALIGN="CENTER"><A NAME="1365"></A>
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<TABLE>
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<CAPTION><STRONG>Table 3:</STRONG>
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Parameters defining the one-level preconditioner used as smoother.
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@@ -405,7 +405,7 @@ Parameters defining the one-level preconditioner used as smoother.
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1367"></A>
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<TABLE>
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<CAPTION><STRONG>Table 4:</STRONG>
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Parameters defining the aggregation algorithm.
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@@ -490,7 +490,7 @@ Parameters defining the aggregation algorithm.
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1369"></A>
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<TABLE>
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<CAPTION><STRONG>Table 5:</STRONG>
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Parameters defining the aggregation algorithm.
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@@ -602,7 +602,7 @@ Parameters defining the aggregation algorithm.
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1372"></A>
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<TABLE>
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<CAPTION><STRONG>Table 6:</STRONG>
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Parameters defining the coarse-space correction at the coarsest
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<P>
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<B> Next:</B> <A NAME="tex2html287"
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<B> Next:</B> <A NAME="tex2html293"
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HREF="node19.html">Subroutine mld_precbld</A>
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HREF="node2.html">Contents</A></B>
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HREF="node20.html">Subroutine mld_hierarchy_bld</A>
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<B> <A NAME="tex2html297"
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<B> <A NAME="tex2html303"
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR>
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@@ -67,6 +67,9 @@ This routine builds the preconditioner according to the requirements made by
|
||||
the user through the routines <code>mld_precinit</code> and <code>mld_precset</code>.
|
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<P>
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For multilevel preconditioner this routine is supported for backward
|
||||
compatibility, but we recommend to use the routines of
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Sec. <A HREF="node20.html#sec:hier_bld">6.4</A> and <A HREF="node21.html#sec:ml_prec_bld">6.5</A>.
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<FONT SIZE="+1"><B>Arguments</B></FONT>
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<P>
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@@ -80,7 +83,7 @@ the user through the routines <code>mld_precinit</code> and <code>mld_precset</c
|
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to the real/complex,
|
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single/double precision version of MLD2P4 under use.
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See the PSBLAS User's Guide for details [<A
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HREF="node25.html#PSBLASGUIDE">16</A>].</TD>
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HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
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@@ -88,7 +91,7 @@ single/double precision version of MLD2P4 under use.
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
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details [<A
|
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HREF="node25.html#PSBLASGUIDE">16</A>].</TD>
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HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
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@@ -101,34 +104,33 @@ single/double precision version of MLD2P4 under use.
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
|
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</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A> for details.</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
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</TR>
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<BR>
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<B> Next:</B> <A NAME="tex2html299"
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HREF="node20.html">Subroutine mld_precaply</A>
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<B> Up:</B> <A NAME="tex2html295"
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<B> Next:</B> <A NAME="tex2html305"
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HREF="node20.html">Subroutine mld_hierarchy_bld</A>
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<B> Up:</B> <A NAME="tex2html301"
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HREF="node16.html">User Interface</A>
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<B> Previous:</B> <A NAME="tex2html289"
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<B> Previous:</B> <A NAME="tex2html295"
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HREF="node18.html">Subroutine mld_precset</A>
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<B> <A NAME="tex2html297"
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<B> <A NAME="tex2html303"
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HREF="node2.html">Contents</A></B>
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+40
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@@ -26,21 +26,21 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -53,64 +53,68 @@ Contents</A>
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<!--Table of Contents-->
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<UL>
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<LI><A NAME="tex2html65"
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HREF="node3.html">General Overview</A>
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<LI><A NAME="tex2html66"
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HREF="node4.html">Code Distribution</A>
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<LI><A NAME="tex2html67"
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HREF="node3.html">General Overview</A>
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||||
<LI><A NAME="tex2html68"
|
||||
HREF="node4.html">Code Distribution</A>
|
||||
<LI><A NAME="tex2html69"
|
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HREF="node5.html">Configuring and Building MLD2P4</A>
|
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<UL>
|
||||
<LI><A NAME="tex2html68"
|
||||
HREF="node6.html">Prerequisites</A>
|
||||
<LI><A NAME="tex2html69"
|
||||
HREF="node7.html">Optional third party libraries</A>
|
||||
<LI><A NAME="tex2html70"
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HREF="node8.html">Configuration options</A>
|
||||
HREF="node6.html">Prerequisites</A>
|
||||
<LI><A NAME="tex2html71"
|
||||
HREF="node9.html">Bug reporting</A>
|
||||
HREF="node7.html">Optional third party libraries</A>
|
||||
<LI><A NAME="tex2html72"
|
||||
HREF="node8.html">Configuration options</A>
|
||||
<LI><A NAME="tex2html73"
|
||||
HREF="node9.html">Bug reporting</A>
|
||||
<LI><A NAME="tex2html74"
|
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HREF="node10.html">Example and test programs</A>
|
||||
</UL>
|
||||
<BR>
|
||||
<LI><A NAME="tex2html73"
|
||||
<LI><A NAME="tex2html75"
|
||||
HREF="node11.html">Multi-level Domain Decomposition Background</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html74"
|
||||
<LI><A NAME="tex2html76"
|
||||
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
||||
<LI><A NAME="tex2html75"
|
||||
<LI><A NAME="tex2html77"
|
||||
HREF="node13.html">Smoothed Aggregation</A>
|
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</UL>
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||||
<BR>
|
||||
<LI><A NAME="tex2html76"
|
||||
<LI><A NAME="tex2html78"
|
||||
HREF="node14.html">Getting Started</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html77"
|
||||
<LI><A NAME="tex2html79"
|
||||
HREF="node15.html">Examples</A>
|
||||
</UL>
|
||||
<BR>
|
||||
<LI><A NAME="tex2html78"
|
||||
<LI><A NAME="tex2html80"
|
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HREF="node16.html">User Interface</A>
|
||||
<UL>
|
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<LI><A NAME="tex2html79"
|
||||
HREF="node17.html">Subroutine mld_precinit</A>
|
||||
<LI><A NAME="tex2html80"
|
||||
HREF="node18.html">Subroutine mld_precset</A>
|
||||
<LI><A NAME="tex2html81"
|
||||
HREF="node19.html">Subroutine mld_precbld</A>
|
||||
HREF="node17.html">Subroutine mld_precinit</A>
|
||||
<LI><A NAME="tex2html82"
|
||||
HREF="node20.html">Subroutine mld_precaply</A>
|
||||
HREF="node18.html">Subroutine mld_precset</A>
|
||||
<LI><A NAME="tex2html83"
|
||||
HREF="node21.html">Subroutine mld_precfree</A>
|
||||
HREF="node19.html">Subroutine mld_precbld</A>
|
||||
<LI><A NAME="tex2html84"
|
||||
HREF="node22.html">Subroutine mld_precdescr</A>
|
||||
HREF="node20.html">Subroutine mld_hierarchy_bld</A>
|
||||
<LI><A NAME="tex2html85"
|
||||
HREF="node21.html">Subroutine mld_ml_prec_bld</A>
|
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<LI><A NAME="tex2html86"
|
||||
HREF="node22.html">Subroutine mld_precaply</A>
|
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<LI><A NAME="tex2html87"
|
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HREF="node23.html">Subroutine mld_precfree</A>
|
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<LI><A NAME="tex2html88"
|
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HREF="node24.html">Subroutine mld_precdescr</A>
|
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</UL>
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<BR>
|
||||
<LI><A NAME="tex2html85"
|
||||
HREF="node23.html">Error Handling</A>
|
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<LI><A NAME="tex2html86"
|
||||
HREF="node24.html">License</A>
|
||||
<LI><A NAME="tex2html87"
|
||||
HREF="node25.html">Bibliography</A>
|
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<LI><A NAME="tex2html89"
|
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HREF="node25.html">Error Handling</A>
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<LI><A NAME="tex2html90"
|
||||
HREF="node26.html">License</A>
|
||||
<LI><A NAME="tex2html91"
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HREF="node27.html">Bibliography</A>
|
||||
</UL>
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<!--End of Table of Contents-->
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+44
-120
@@ -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>Subroutine mld_precaply</TITLE>
|
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<TITLE>Subroutine mld_hierarchy_bld</TITLE>
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<B> <A NAME="tex2html315"
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<BR>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:precaply"></A>
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<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:hier_bld"></A>
|
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<BR>
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Subroutine mld_precaply
|
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Subroutine mld_hierarchy_bld
|
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</H2>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<code>mld_precaply(p,x,y,desc_a,info)</code>
|
||||
<BR><code>mld_precaply(p,x,y,desc_a,info,trans,work)</code>
|
||||
<code>mld_hierachy_bld(a,desc_a,p,info)</code>
|
||||
<BR>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
This routine computes <!-- MATH
|
||||
$y = op(M^{-1})\, x$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img101.png"
|
||||
ALT="$y = op(M^{-1}) x$">, where <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img60.png"
|
||||
ALT="$M$"> is a previously built
|
||||
preconditioner, stored into <code>p</code>, and <IMG
|
||||
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img102.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>mld_precaply</code> is called within the PSBLAS routine <code>psb_krylov</code>
|
||||
and hence it is completely transparent to the user.
|
||||
This routine builds the aggregation hierarchy according to the requirements made by
|
||||
the user through the routines <code>mld_precinit</code> and <code>mld_precset</code>.
|
||||
|
||||
<P>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img60.png"
|
||||
ALT="$M$">.
|
||||
Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
|
||||
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img103.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.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img104.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.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>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="node27.html#PSBLASGUIDE">16</A>].</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor associated to the matrix to be
|
||||
preconditioned.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
|
||||
details [<A
|
||||
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A> for details.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-1}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img105.png"
|
||||
ALT="$op(M^{-1}) = M^{-1}$">;
|
||||
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-T}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img106.png"
|
||||
ALT="$op(M^{-1}) = M^{-T}$">
|
||||
(transpose of <IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img107.png"
|
||||
ALT="$M^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-C}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img108.png"
|
||||
ALT="$op(M^{-1}) = M^{-C}$">
|
||||
(conjugate transpose of <IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img107.png"
|
||||
ALT="$M^{-1})$">.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>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.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
|
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<P>
|
||||
|
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|
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|
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+68
-23
@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
|
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
|
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<TITLE>Subroutine mld_precfree</TITLE>
|
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<META NAME="description" CONTENT="Subroutine mld_precfree">
|
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<TITLE>Subroutine mld_ml_prec_bld</TITLE>
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<META NAME="description" CONTENT="Subroutine mld_ml_prec_bld">
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<META NAME="keywords" CONTENT="userhtml">
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<META NAME="resource-type" CONTENT="document">
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@@ -26,69 +26,114 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> Previous:</B> <A NAME="tex2html319"
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HREF="node20.html">Subroutine mld_hierarchy_bld</A>
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<B> <A NAME="tex2html327"
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HREF="node2.html">Contents</A></B>
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|
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<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:precfree"></A>
|
||||
<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:ml_prec_bld"></A>
|
||||
<BR>
|
||||
Subroutine mld_precfree
|
||||
Subroutine mld_ml_prec_bld
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<code>mld_precfree(p,info)</code>
|
||||
<code>mld_ml_prec_bld(a,desc_a,p,info)</code>
|
||||
<BR>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
This routine deallocates the preconditioner data structure.
|
||||
This routine builds the preconditioner according to the requirements made by
|
||||
the user through the routines <code>mld_precinit</code> and
|
||||
<code>mld_precset</code>, based on the aggregation hierahy produced by a
|
||||
previous call to <code>mld_hierarchy_bld</code> (see
|
||||
Sec. <A HREF="node20.html#sec:hier_bld">6.4</A>).
|
||||
|
||||
<P>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>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="node27.html#PSBLASGUIDE">16</A>].</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
|
||||
details [<A
|
||||
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
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</TR>
|
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
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</TR>
|
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>integer, intent(out)</code>.</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
|
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A> for details.</TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
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</TR>
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||||
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HREF="node21.html">Subroutine mld_precfree</A>
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HREF="node21.html">Subroutine mld_ml_prec_bld</A>
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<B> <A NAME="tex2html339"
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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precdescr"></A>
|
||||
<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precaply"></A>
|
||||
<BR>
|
||||
Subroutine mld_precdescr
|
||||
Subroutine mld_precaply
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<code>mld_precdescr(p,info)</code>
|
||||
<BR><code>mld_precdescr(p,info,iout)</code>
|
||||
<code>mld_precaply(p,x,y,desc_a,info)</code>
|
||||
<BR><code>mld_precaply(p,x,y,desc_a,info,trans,work)</code>
|
||||
<BR>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
This routine prints a description of the preconditioner to the standard output or
|
||||
to a file. It must be called after <code>mld_precbld</code> has been called.
|
||||
This routine computes <!-- MATH
|
||||
$y = op(M^{-1})\, x$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img101.png"
|
||||
ALT="$y = op(M^{-1}) x$">, where <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img60.png"
|
||||
ALT="$M$"> is a previously built
|
||||
preconditioner, stored into <code>p</code>, and <IMG
|
||||
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img102.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>mld_precaply</code> is called within the PSBLAS routine <code>psb_krylov</code>
|
||||
and hence it is completely transparent to the user.
|
||||
|
||||
<P>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
@@ -72,29 +90,122 @@ to a file. It must be called after <code>mld_precbld</code> has been called.
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(in)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img60.png"
|
||||
ALT="$M$">.
|
||||
Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
|
||||
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img103.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.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img104.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.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor associated to the matrix to be
|
||||
preconditioned.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A> for details.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>iout</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in), optional</code>.</TD>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The id of the file where the preconditioner description
|
||||
will be printed; the default is the standard output.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-1}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img105.png"
|
||||
ALT="$op(M^{-1}) = M^{-1}$">;
|
||||
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-T}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img106.png"
|
||||
ALT="$op(M^{-1}) = M^{-T}$">
|
||||
(transpose of <IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img107.png"
|
||||
ALT="$M^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-C}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img108.png"
|
||||
ALT="$op(M^{-1}) = M^{-C}$">
|
||||
(conjugate transpose of <IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img107.png"
|
||||
ALT="$M^{-1})$">.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>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.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
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+47
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
|
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
|
||||
<H2><A NAME="SECTION00087000000000000000"></A><A NAME="sec:precfree"></A>
|
||||
<BR>
|
||||
Error Handling
|
||||
</H1>
|
||||
Subroutine mld_precfree
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
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="node25.html#PSBLASGUIDE">16</A>].
|
||||
<DIV ALIGN="CENTER">
|
||||
<code>mld_precfree(p,info)</code>
|
||||
<BR>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
This routine deallocates the preconditioner data structure.
|
||||
|
||||
<P>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>integer, intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
|
||||
+52
-56
@@ -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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<HEAD>
|
||||
<TITLE>License</TITLE>
|
||||
<META NAME="description" CONTENT="License">
|
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<TITLE>Subroutine mld_precdescr</TITLE>
|
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<B> <A NAME="tex2html361"
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<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:license"></A>
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<H2><A NAME="SECTION00088000000000000000"></A><A NAME="sec:precdescr"></A>
|
||||
<BR>
|
||||
License
|
||||
</H1>
|
||||
Subroutine mld_precdescr
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
The MLD2P4 is freely distributable under the following copyright
|
||||
terms: <PRE>
|
||||
<DIV ALIGN="CENTER">
|
||||
<code>mld_precdescr(p,info)</code>
|
||||
<BR><code>mld_precdescr(p,info,iout)</code>
|
||||
<BR>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
This routine prints a description of the preconditioner to the standard output or
|
||||
to a file. It must be called after <code>mld_precbld</code> has been called.
|
||||
|
||||
MLD2P4 version 2.0
|
||||
MultiLevel Domain Decomposition Parallel Preconditioners Package
|
||||
based on PSBLAS (Parallel Sparse BLAS version 3.3)
|
||||
<P>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
(C) Copyright 2008, 2010, 2012, 2015
|
||||
|
||||
Salvatore Filippone University of Rome Tor Vergata
|
||||
Alfredo Buttari CNRS-IRIT, Toulouse
|
||||
Pasqua D'Ambra ICAR-CNR, Naples
|
||||
Daniela di Serafino Second University of Naples
|
||||
|
||||
|
||||
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>
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">7</A> for details.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>iout</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in), optional</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The id of the file where the preconditioner description
|
||||
will be printed; the default is the standard output.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
|
||||
+31
-157
@@ -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>Error Handling</TITLE>
|
||||
<META NAME="description" CONTENT="Error Handling">
|
||||
<META NAME="keywords" CONTENT="userhtml">
|
||||
<META NAME="resource-type" CONTENT="document">
|
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<META NAME="distribution" CONTENT="global">
|
||||
@@ -19,185 +19,59 @@ original version by: Nikos Drakos, CBLU, University of Leeds
|
||||
<LINK REL="STYLESHEET" HREF="userhtml.css">
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|
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HREF="node24.html">Subroutine mld_precdescr</A>
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<B> <A NAME="tex2html373"
|
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HREF="node2.html">Contents</A></B>
|
||||
<BR><BR>
|
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<BR>
|
||||
<BR>
|
||||
<!--End of Navigation Panel-->
|
||||
|
||||
<H2><A NAME="SECTION000110000000000000000">
|
||||
Bibliography</A>
|
||||
</H2><DL COMPACT><DD>
|
||||
<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
|
||||
<BR>
|
||||
Error Handling
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="BREZINA_VANEK">1</A>
|
||||
<DD>
|
||||
M. Brezina, P. 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="para_04">2</A>
|
||||
<DD>
|
||||
A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone,
|
||||
<EM>Extending PSBLAS to Build Parallel Schwarz Preconditioners</EM>,
|
||||
in , J. Dongarra, K. Madsen, J. Wasniewski, editors,
|
||||
Proceedings of PARA 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">3</A>
|
||||
<DD>
|
||||
A. Buttari, P. D'Ambra, D. di Serafino, S. 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="apnum_07">4</A>
|
||||
<DD> P. D'Ambra, S. Filippone, D. di 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></P><DT><A NAME="CAI_SARKIS">5</A>
|
||||
<DD>
|
||||
X. C. Cai, M. 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="Cai_Widlund_92">6</A>
|
||||
<DD>
|
||||
X. C. Cai, O. B. Widlund,
|
||||
<EM>Domain Decomposition Algorithms for Indefinite Elliptic Problems</EM>,
|
||||
SIAM Journal on Scientific and Statistical Computing, 13, 1, 1992, 243-258.<P></P><DT><A NAME="dd1_94">7</A>
|
||||
<DD>
|
||||
T. Chan and T. Mathew,
|
||||
<EM>Domain Decomposition Algorithms</EM>,
|
||||
in A. Iserles, editor, Acta Numerica 1994, 61-143.
|
||||
Cambridge University Press.<P></P><DT><A NAME="MLD2P4_TOMS">8</A>
|
||||
<DD>
|
||||
P. D'Ambra, D. di Serafino, S. Filippone,
|
||||
<I>MLD2P4: a Package of Parallel Multilevel
|
||||
Algebraic Domain Decomposition Preconditioners
|
||||
in Fortran 95</I>, ACM Trans. Math. Softw., 37(3), 2010.<P></P><DT><A NAME="UMFPACK">9</A>
|
||||
<DD>
|
||||
T.A. 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/ davis/</TT>)
|
||||
<P>
|
||||
<P></P><DT><A NAME="MUMPS">10</A>
|
||||
<DD>
|
||||
P.R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L'Excellent, C. Weisbecker
|
||||
<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
|
||||
SIAM SISC, volume 37, number 3, pages A1452-A1474.
|
||||
(See also <TT>http://mumps.enseeiht.fr</TT>)
|
||||
<P>
|
||||
<P></P><DT><A NAME="SUPERLU">11</A>
|
||||
<DD>
|
||||
J.W. Demmel, S.C. Eisenstat, J.R. Gilbert, X.S. Li and J.W.H. 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">12</A>
|
||||
<DD>
|
||||
J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling,
|
||||
<I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
|
||||
ACM Transactions on Mathematical Software, 16, 1990, 1-17.<P></P><DT><A NAME="blas2">13</A>
|
||||
<DD>
|
||||
J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson,
|
||||
<I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
|
||||
ACM Transactions on Mathematical Software, 14, 1988, 1-17.<P></P><DT><A NAME="BLACS">14</A>
|
||||
<DD>
|
||||
J. J. Dongarra and R. C. Whaley,
|
||||
<EM>A User's Guide to the BLACS v. 1.1</EM>,
|
||||
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
|
||||
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="EFSTATHIOU">15</A>
|
||||
<DD>
|
||||
E. Efstathiou, J. G. Gander,
|
||||
<EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
|
||||
BIT Numerical Mathematics, 43, 2003, 945-959.<P></P><DT><A NAME="PSBLASGUIDE">16</A>
|
||||
<DD>
|
||||
S. Filippone, A. 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>.
|
||||
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="node27.html#PSBLASGUIDE">16</A>].
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="PSBLAS3">17</A>
|
||||
<DD>
|
||||
Salvatore Filippone and Alfredo Buttari.
|
||||
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran
|
||||
2003.</EM>
|
||||
ACM Trans. on Math Software, 38(4), 2012.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="psblas_00">18</A>
|
||||
<DD>
|
||||
S. Filippone, M. 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">19</A>
|
||||
<DD>
|
||||
W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, M. Snir,
|
||||
<EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
|
||||
MIT Press, 1998.<P></P><DT><A NAME="blas1">20</A>
|
||||
<DD>
|
||||
C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh,
|
||||
<I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
|
||||
ACM Transactions on Mathematical Software, 5, 1979, 308-323.<P></P><DT><A NAME="SUPERLUDIST">21</A>
|
||||
<DD>
|
||||
X. S. Li, J. W. 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="Saad_book">22</A>
|
||||
<DD>
|
||||
Y. Saad,
|
||||
<I>Iterative methods for sparse linear systems</I>, 2nd edition,
|
||||
SIAM, 2003
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="dd2_96">23</A>
|
||||
<DD>
|
||||
B. Smith, P. Bjorstad, W. Gropp,
|
||||
<EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
|
||||
Partial Differential Equations</EM>,
|
||||
Cambridge University Press, 1996.<P></P><DT><A NAME="MPI1">24</A>
|
||||
<DD>
|
||||
M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra,
|
||||
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
|
||||
MIT Press, 1998.<P></P><DT><A NAME="StubenGMD69_99">25</A>
|
||||
<DD>
|
||||
K. Stüben,
|
||||
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
|
||||
in A. Schüller, U. Trottenberg, C. Oosterlee, editors, Multigrid,
|
||||
Academic Press, 2000.<P></P><DT><A NAME="TUMINARO_TONG">26</A>
|
||||
<DD>
|
||||
R. S. Tuminaro, C. 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">27</A>
|
||||
<DD>
|
||||
P. Vanek, J. Mandel and M. Brezina,
|
||||
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
|
||||
Computing, 56, 1996, 179-196.
|
||||
<P>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
|
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</BODY>
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|
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+61
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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Copyright © 1993, 1994, 1995, 1996,
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<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:license"></A>
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<BR>
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Copyright © 1997, 1998, 1999,
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The translation was initiated by Salvatore Filippone on 2016-05-23
|
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The MLD2P4 is freely distributable under the following copyright
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|
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|
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MLD2P4 version 2.0
|
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MultiLevel Domain Decomposition Parallel Preconditioners Package
|
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based on PSBLAS (Parallel Sparse BLAS version 3.3)
|
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|
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(C) Copyright 2008, 2010, 2012, 2015
|
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Salvatore Filippone University of Rome Tor Vergata
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Alfredo Buttari CNRS-IRIT, Toulouse
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Pasqua D'Ambra ICAR-CNR, Naples
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Daniela di Serafino Second University of Naples
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Redistribution and use in source and binary forms, with or without
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<H2><A NAME="SECTION000110000000000000000">
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</H2><DL COMPACT><DD>
|
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<P>
|
||||
This document was generated using the
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<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2002-2-1 (1.71)
|
||||
<P></P><DT><A NAME="BREZINA_VANEK">1</A>
|
||||
<DD>
|
||||
M. Brezina, P. 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="para_04">2</A>
|
||||
<DD>
|
||||
A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone,
|
||||
<EM>Extending PSBLAS to Build Parallel Schwarz Preconditioners</EM>,
|
||||
in , J. Dongarra, K. Madsen, J. Wasniewski, editors,
|
||||
Proceedings of PARA 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">3</A>
|
||||
<DD>
|
||||
A. Buttari, P. D'Ambra, D. di Serafino, S. 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="apnum_07">4</A>
|
||||
<DD> P. D'Ambra, S. Filippone, D. di 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>
|
||||
Copyright © 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 © 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="CAI_SARKIS">5</A>
|
||||
<DD>
|
||||
X. C. Cai, M. 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="Cai_Widlund_92">6</A>
|
||||
<DD>
|
||||
X. C. Cai, O. B. Widlund,
|
||||
<EM>Domain Decomposition Algorithms for Indefinite Elliptic Problems</EM>,
|
||||
SIAM Journal on Scientific and Statistical Computing, 13, 1, 1992, 243-258.<P></P><DT><A NAME="dd1_94">7</A>
|
||||
<DD>
|
||||
T. Chan and T. Mathew,
|
||||
<EM>Domain Decomposition Algorithms</EM>,
|
||||
in A. Iserles, editor, Acta Numerica 1994, 61-143.
|
||||
Cambridge University Press.<P></P><DT><A NAME="MLD2P4_TOMS">8</A>
|
||||
<DD>
|
||||
P. D'Ambra, D. di Serafino, S. Filippone,
|
||||
<I>MLD2P4: a Package of Parallel Multilevel
|
||||
Algebraic Domain Decomposition Preconditioners
|
||||
in Fortran 95</I>, ACM Trans. Math. Softw., 37(3), 2010.<P></P><DT><A NAME="UMFPACK">9</A>
|
||||
<DD>
|
||||
T.A. 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/ davis/</TT>)
|
||||
<P>
|
||||
The command line arguments were: <BR>
|
||||
<STRONG>latex2html</STRONG> <TT>-noaddress -dir ../../html userhtml.tex</TT>
|
||||
<P></P><DT><A NAME="MUMPS">10</A>
|
||||
<DD>
|
||||
P.R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L'Excellent, C. Weisbecker
|
||||
<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
|
||||
SIAM SISC, volume 37, number 3, pages A1452-A1474.
|
||||
(See also <TT>http://mumps.enseeiht.fr</TT>)
|
||||
<P>
|
||||
<P></P><DT><A NAME="SUPERLU">11</A>
|
||||
<DD>
|
||||
J.W. Demmel, S.C. Eisenstat, J.R. Gilbert, X.S. Li and J.W.H. 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">12</A>
|
||||
<DD>
|
||||
J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling,
|
||||
<I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
|
||||
ACM Transactions on Mathematical Software, 16, 1990, 1-17.<P></P><DT><A NAME="blas2">13</A>
|
||||
<DD>
|
||||
J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson,
|
||||
<I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
|
||||
ACM Transactions on Mathematical Software, 14, 1988, 1-17.<P></P><DT><A NAME="BLACS">14</A>
|
||||
<DD>
|
||||
J. J. Dongarra and R. C. Whaley,
|
||||
<EM>A User's Guide to the BLACS v. 1.1</EM>,
|
||||
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
|
||||
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="EFSTATHIOU">15</A>
|
||||
<DD>
|
||||
E. Efstathiou, J. G. Gander,
|
||||
<EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
|
||||
BIT Numerical Mathematics, 43, 2003, 945-959.<P></P><DT><A NAME="PSBLASGUIDE">16</A>
|
||||
<DD>
|
||||
S. Filippone, A. 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></P><DT><A NAME="PSBLAS3">17</A>
|
||||
<DD>
|
||||
Salvatore Filippone and Alfredo Buttari.
|
||||
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran
|
||||
2003.</EM>
|
||||
ACM Trans. on Math Software, 38(4), 2012.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="psblas_00">18</A>
|
||||
<DD>
|
||||
S. Filippone, M. 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">19</A>
|
||||
<DD>
|
||||
W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, M. Snir,
|
||||
<EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
|
||||
MIT Press, 1998.<P></P><DT><A NAME="blas1">20</A>
|
||||
<DD>
|
||||
C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh,
|
||||
<I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
|
||||
ACM Transactions on Mathematical Software, 5, 1979, 308-323.<P></P><DT><A NAME="SUPERLUDIST">21</A>
|
||||
<DD>
|
||||
X. S. Li, J. W. 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="Saad_book">22</A>
|
||||
<DD>
|
||||
Y. Saad,
|
||||
<I>Iterative methods for sparse linear systems</I>, 2nd edition,
|
||||
SIAM, 2003
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="dd2_96">23</A>
|
||||
<DD>
|
||||
B. Smith, P. Bjorstad, W. Gropp,
|
||||
<EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
|
||||
Partial Differential Equations</EM>,
|
||||
Cambridge University Press, 1996.<P></P><DT><A NAME="MPI1">24</A>
|
||||
<DD>
|
||||
M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra,
|
||||
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
|
||||
MIT Press, 1998.<P></P><DT><A NAME="StubenGMD69_99">25</A>
|
||||
<DD>
|
||||
K. Stüben,
|
||||
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
|
||||
in A. Schüller, U. Trottenberg, C. Oosterlee, editors, Multigrid,
|
||||
Academic Press, 2000.<P></P><DT><A NAME="TUMINARO_TONG">26</A>
|
||||
<DD>
|
||||
R. S. Tuminaro, C. 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">27</A>
|
||||
<DD>
|
||||
P. Vanek, J. Mandel and M. Brezina,
|
||||
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
|
||||
Computing, 56, 1996, 179-196.
|
||||
<P>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
The translation was initiated by Salvatore Filippone on 2008-09-12
|
||||
<BR><HR>
|
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</BODY>
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<!--Converted with LaTeX2HTML 2012 (1.2)
|
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original version by: Nikos Drakos, CBLU, University of Leeds
|
||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
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* with significant contributions from:
|
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
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|
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<TITLE>Error Handling</TITLE>
|
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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
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<BR>
|
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Error Handling
|
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<H1><A NAME="SECTION000120000000000000000">
|
||||
About this document ...</A>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
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">14</A>].
|
||||
|
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This document was generated using the
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<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2012 (1.2)
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<P>
|
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Copyright © 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 © 1997, 1998, 1999,
|
||||
<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>,
|
||||
Mathematics Department, Macquarie University, Sydney.
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<P>
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The command line arguments were: <BR>
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<STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
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<P>
|
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The translation was initiated by Salvatore Filippone on 2016-06-09
|
||||
<BR><HR>
|
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<ADDRESS>
|
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Salvatore Filippone
|
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2008-07-23
|
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+25
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@@ -59,7 +59,7 @@ General Overview
|
||||
<P>
|
||||
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 <I>multi-level Schwarz preconditioners</I> [<A
|
||||
HREF="node25.html#dd2_96">23</A>],
|
||||
HREF="node27.html#dd2_96">23</A>],
|
||||
to be used in the iterative solutions of sparse linear systems:
|
||||
<BR>
|
||||
<DIV ALIGN="RIGHT">
|
||||
@@ -97,8 +97,8 @@ generate a sequence of coarse-level corrections to a basic AS preconditioner, wi
|
||||
explicitly using any information on the geometry of the original problem (e.g. the
|
||||
discretization of a PDE). The <I>smoothed aggregation</I> technique is applied
|
||||
as algebraic coarsening strategy [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
|
||||
HREF="node27.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>].
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
@@ -116,8 +116,8 @@ interface.
|
||||
MLD2P4 has been designed to implement scalable and easy-to-use
|
||||
multilevel preconditioners in the context of the <I>PSBLAS
|
||||
(Parallel Sparse BLAS) computational framework</I> [<A
|
||||
HREF="node25.html#psblas_00">18</A>,<A
|
||||
HREF="node25.html#PSBLAS3">17</A>].
|
||||
HREF="node27.html#psblas_00">18</A>,<A
|
||||
HREF="node27.html#PSBLAS3">17</A>].
|
||||
PSBLAS is a library originally developed to address the parallel implementation of
|
||||
iterative solvers for sparse linear system, by providing basic linear algebra
|
||||
operators and data management facilities for distributed sparse matrices; it
|
||||
@@ -130,10 +130,10 @@ portability, modularity ed extensibility in the development of the preconditione
|
||||
package. On the other hand, the implementation of MLD2P4 has led to some
|
||||
revisions and extentions of the PSBLAS kernels, leading to the
|
||||
PSBLAS 2.0 version [<A
|
||||
HREF="node25.html#PSBLASGUIDE">16</A>]. The inter-process comunication required
|
||||
HREF="node27.html#PSBLASGUIDE">16</A>]. The inter-process comunication required
|
||||
by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
|
||||
MPI [<A
|
||||
HREF="node25.html#MPI1">24</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
|
||||
HREF="node27.html#MPI1">24</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
|
||||
machine where PSBLAS and MPI implementations are available.
|
||||
|
||||
<P>
|
||||
@@ -167,32 +167,32 @@ with the Krylov solvers implemented in PSBLAS are reported in Section <A HR
|
||||
Fortran codes of a few sample programs are also shown. A reference guide for
|
||||
the upper-layer routines of MLD2P4, that are the user interface, is provided
|
||||
in Section <A HREF="node16.html#sec:userinterface">6</A>. The error handling mechanism used by the package is briefly described
|
||||
in Section <A HREF="node23.html#sec:errors">7</A>. The copyright terms concerning the distribution and modification
|
||||
of MLD2P4 are reported in Appendix <A HREF="node24.html#sec:license">A</A>.
|
||||
in Section <A HREF="node25.html#sec:errors">7</A>. The copyright terms concerning the distribution and modification
|
||||
of MLD2P4 are reported in Appendix <A HREF="node26.html#sec:license">A</A>.
|
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@@ -66,7 +66,7 @@ where contact points for further information can be also found.
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The software is available under a modified BSD license, as specified
|
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|
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<DD>[<A
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HREF="node25.html#MPI2">19</A>,<A
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HREF="node27.html#MPI1">24</A>] A version of MPI is available on most
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high-performance computing systems;
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HREF="node27.html#PSBLASGUIDE">16</A>,<A
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HREF="node27.html#psblas_00">18</A>] Parallel Sparse BLAS is
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available from
|
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<BR><code>http://www.ce.uniroma2.it/psblas</code>; version
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3.4.0 (or later) is required. Indeed, all the prerequisites
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<DT><STRONG>UMFPACK</STRONG></DT>
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<DD>[<A
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HREF="node25.html#UMFPACK">9</A>]
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HREF="node27.html#UMFPACK">9</A>]
|
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A sparse direct factorization package available from
|
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<BR> <code>http://www.cise.ufl.edu/research/sparse/umfpack/</code>;
|
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provides serial factorization and triangular system solution for double
|
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<DT><STRONG>SuperLU</STRONG></DT>
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<DD>[<A
|
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HREF="node25.html#SUPERLU">11</A>]
|
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HREF="node27.html#SUPERLU">11</A>]
|
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A sparse direct factorization package available from
|
||||
<BR> <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial
|
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factorization and triangular system solution for single and double precision,
|
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<DT><STRONG>SuperLU_Dist</STRONG></DT>
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<DD>[<A
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HREF="node25.html#SUPERLUDIST">21</A>]
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HREF="node27.html#SUPERLUDIST">21</A>]
|
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A sparse direct factorization package available
|
||||
from the same site as SuperLU; provides parallel factorization and
|
||||
triangular system solution for double precision real and complex data.
|
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<DT><STRONG>MUMPS</STRONG></DT>
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<DD>[<A
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HREF="node25.html#MUMPS">10</A>]
|
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HREF="node27.html#MUMPS">10</A>]
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MUMPS (“MUltifrontal Massively Parallel Solver”) is a sparse, direct factorization
|
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package available from
|
||||
<BR> <code>http://mumps.enseeiht.fr/</code>.
|
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+13
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<LI><A NAME="tex2html35"
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HREF="node19.html">Subroutine mld_precbld</A>
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<LI><A NAME="tex2html36"
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HREF="node20.html">Subroutine mld_precaply</A>
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HREF="node20.html">Subroutine mld_hierarchy_bld</A>
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<LI><A NAME="tex2html38"
|
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HREF="node22.html">Subroutine mld_precdescr</A>
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HREF="node22.html">Subroutine mld_precaply</A>
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HREF="node23.html">Subroutine mld_precfree</A>
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HREF="node24.html">Subroutine mld_precdescr</A>
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<LI><A NAME="tex2html41"
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|
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HREF="node25.html">Error Handling</A>
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<LI><A NAME="tex2html42"
|
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HREF="node26.html">About this document ...</A>
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|
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<LI><A NAME="tex2html43"
|
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HREF="node27.html">Bibliography</A>
|
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<LI><A NAME="tex2html44"
|
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HREF="node28.html">About this document ...</A>
|
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</UL>
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<BR><HR>
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+4680
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Load Diff
@@ -21,6 +21,16 @@ The following steps are required:
|
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\verb|mld_precinit| to identify the preconditioner types are also given.
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Note that these strings are valid also if uppercase letters are substituted by
|
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corresponding lowercase ones.
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\item \emph{Modify the aggregation parameters.} This is performed by
|
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the routine \verb|mld_precset|.
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This routine must be called only if the user wants to modify the default values
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of the parameters associated to the aggregation hierarchy construction.
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Examples of use of \verb|mld_precset| are given in
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Section~\ref{sec:examples}; a complete list of all the
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preconditioner parameters and their allowed and default values is provided in
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Section~\ref{sec:userinterface}, Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
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\item \emph{Build the aggregation hierarchy for a given matrix.} This is performed by
|
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the routine \verb|mld_hierarchy_bld|.
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\item \emph{Modify the selected preconditioner type, by properly setting
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preconditioner parameters.} This is performed by the routine \verb|mld_precset|.
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This routine must be called only if the user wants to modify the default values
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@@ -30,7 +40,7 @@ The following steps are required:
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preconditioner parameters and their allowed and default values is provided in
|
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Section~\ref{sec:userinterface}, Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
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\item \emph{Build the preconditioner for a given matrix.} This is performed by
|
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the routine \verb|mld_precbld|.
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the routine \verb|mld_ml_prec_bld|.
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\item \emph{Apply the preconditioner at each iteration of a Krylov solver.}
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This is performed by the routine \verb|mld_precaply|. When using the PSBLAS Krylov solvers,
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this step is completely transparent to the user, since \verb|mld_precaply| is called
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@@ -172,7 +182,9 @@ the corresponding Fortran 95 codes are available in \verb|examples/fileread/|.
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call mld_precinit(P,'ML',info)
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!
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! build the preconditioner
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call mld_precbld(A,desc_A,P,info)
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call mld_hierarchy_bld(A,desc_A,P,info)
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call mld_ml_prec_bld(A,desc_A,P,info)
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|
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!
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! set the solver parameters and the initial guess
|
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... ...
|
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@@ -257,11 +269,14 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
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! block Jacobi (with ILU(0) on the blocks) as post-smoother,
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! a coarsest matrix replicated on the processors, and the
|
||||
! LU factorization from UMFPACK as coarse-level solver
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call mld_precinit(P,'ML',info,nlev=3)
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call mld_precinit(P,'ML',info)
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call mld_hierarchy_bld(A,desc_A,P,info)
|
||||
|
||||
call_mld_precset(P,'SMOOTHER_TYPE','BJAC',info)
|
||||
call_mld_precset(P,'SMOOTHER_POS,'POST'w,info)
|
||||
call mld_precset(P,'COARSE_MAT','REPL',info)
|
||||
call mld_precset(P,'COARSE_SOLVE','UMF',info)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
... ...
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||||
\end{verbatim}
|
||||
}
|
||||
@@ -283,10 +298,12 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
|
||||
! multifrontal solver in MUMPS as coarse-level solver
|
||||
|
||||
call mld_precinit(P,'ML',info,nlev=3)
|
||||
call mld_hierarchy_bld(A,desc_A,P,info)
|
||||
|
||||
call mld_precset(P,mld_smoother_type_,'BJAC',info)
|
||||
call mld_precset(P,mld_coarse_mat_,'REPL',info)
|
||||
call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
|
||||
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
... ...
|
||||
\end{verbatim}
|
||||
}
|
||||
@@ -308,9 +325,11 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
|
||||
! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
|
||||
! on the blocks) as distributed coarsest-level solver
|
||||
call mld_precinit(P,'ML',info,nlev=3)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
call mld_precset(P,'ML_TYPE','ADD',info)
|
||||
call_mld_precset(P,'SMOOTHER_POS','TWOSIDE',info)
|
||||
call mld_precset(P,'COARSE_SWEEPS',5,info)
|
||||
call mld_ml_prec_bld(A,desc_A,P,info)
|
||||
... ...
|
||||
\end{verbatim}
|
||||
}
|
||||
@@ -329,6 +348,7 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
|
||||
! set RAS with overlap 2 and ILU(0) on the local blocks
|
||||
call mld_precinit(P,'AS',info)
|
||||
call mld_precset(P,'SUB_OVR',2,info)
|
||||
call mld_precbld(A,desc_A,P,info)
|
||||
... ...
|
||||
\end{verbatim}
|
||||
}
|
||||
|
||||
@@ -492,6 +492,71 @@ level.\label{tab:p_coarse}}
|
||||
This routine builds the preconditioner according to the requirements made by
|
||||
the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
|
||||
|
||||
For multilevel preconditioner this routine is supported for backward
|
||||
compatibility, but we recommend to use the routines of
|
||||
Sec.~\ref{sec:hier_bld} and~\ref{sec:ml_prec_bld}.
|
||||
{\vskip2\baselineskip\noindent\large\bfseries Arguments}
|
||||
|
||||
\begin{tabular}{p{1.2cm}p{12cm}}
|
||||
\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\
|
||||
& The sparse matrix structure containing the local part of the
|
||||
matrix to be preconditioned. Note that \emph{x} must be chosen according
|
||||
to the real/complex,
|
||||
single/double precision version of MLD2P4 under use.
|
||||
See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\
|
||||
\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
|
||||
& The communication descriptor of \verb|a|. See the PSBLAS User's Guide for
|
||||
details \cite{PSBLASGUIDE}.\\
|
||||
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
|
||||
& The preconditioner data structure. Note that \emph{x} must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.\\
|
||||
\verb|info| & \verb|integer, intent(out)|.\\
|
||||
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
|
||||
\end{tabular}
|
||||
|
||||
\subsection{Subroutine mld\_hierarchy\_bld\label{sec:hier_bld}}
|
||||
|
||||
\begin{center}
|
||||
\verb|mld_hierachy_bld(a,desc_a,p,info)|\\
|
||||
\end{center}
|
||||
|
||||
\noindent
|
||||
This routine builds the aggregation hierarchy according to the requirements made by
|
||||
the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
|
||||
|
||||
{\vskip2\baselineskip\noindent\large\bfseries Arguments}
|
||||
|
||||
\begin{tabular}{p{1.2cm}p{12cm}}
|
||||
\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\
|
||||
& The sparse matrix structure containing the local part of the
|
||||
matrix to be preconditioned. Note that \emph{x} must be chosen according
|
||||
to the real/complex,
|
||||
single/double precision version of MLD2P4 under use.
|
||||
See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\
|
||||
\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
|
||||
& The communication descriptor of \verb|a|. See the PSBLAS User's Guide for
|
||||
details \cite{PSBLASGUIDE}.\\
|
||||
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
|
||||
& The preconditioner data structure. Note that \emph{x} must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.\\
|
||||
\verb|info| & \verb|integer, intent(out)|.\\
|
||||
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
|
||||
\end{tabular}
|
||||
|
||||
|
||||
\subsection{Subroutine mld\_ml\_prec\_bld\label{sec:ml_prec_bld}}
|
||||
|
||||
\begin{center}
|
||||
\verb|mld_ml_prec_bld(a,desc_a,p,info)|\\
|
||||
\end{center}
|
||||
|
||||
\noindent
|
||||
This routine builds the preconditioner according to the requirements made by
|
||||
the user through the routines \verb|mld_precinit| and
|
||||
\verb|mld_precset|, based on the aggregation hierahy produced by a
|
||||
previous call to \verb|mld_hierarchy_bld| (see
|
||||
Sec.~\ref{sec:hier_bld}).
|
||||
|
||||
{\vskip2\baselineskip\noindent\large\bfseries Arguments}
|
||||
|
||||
\begin{tabular}{p{1.2cm}p{12cm}}
|
||||
|
||||
Reference in New Issue
Block a user