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Fixed docs for new smoothers/solvers, updated Makefile
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@@ -136,13 +136,15 @@ Feb. 28, 2017
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Multigrid Background
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</H1>␍␍␍Multigrid preconditioners, coupled with Krylov iterative␍solvers, are widely used in the parallel solution of large and sparse linear systems,␍because of their optimality in the solution of linear systems arising from the␍discretization of scalar elliptic Partial Differential Equations (PDEs) on regular grids.␍Optimality, also known as algorithmic scalability, is the property ␍of having a computational cost per iteration that depends linearly on␍the problem size, and a convergence rate that is independent of the problem size.␍␍Multigrid preconditioners are based on a recursive application of a two-grid process␍consisting of smoother iterations and a coarse-space (or coarse-level) correction.␍The smoothers may be either basic iterative methods, such as the Jacobi and Gauss-Seidel ones,␍or more complex subspace-correction methods, such as the Schwarz ones.␍The coarse-space correction consists of solving, in an appropriately chosen␍coarse space, the residual equation associated with the approximate solution computed␍by the smoother, and of using the solution of this equation to correct the␍previous approximation. The transfer of information between the original␍(fine) space and the coarse one is performed by using suitable restriction and␍prolongation operators. The construction of the coarse space and the corresponding␍transfer operators is carried out by applying a so-called coarsening algorithm to the system␍matrix. Two main approaches can be used to perform coarsening: the geometric approach,␍which exploits the knowledge of some physical grid associated with the matrix␍and requires the user to define transfer operators from the fine␍to the coarse level and vice versa, and the algebraic approach, which builds␍the coarse-space correction and the associate transfer operators using only matrix␍information. The first approach may be difficult when the system comes from␍discretizations on complex geometries;␍furthermore, ad hoc one-level smoothers may be required to get an efficient␍interplay between fine and coarse levels, e.g., when matrices with highly varying coefficients␍are considered. The second approach performs a fully automatic coarsening and enforces the␍interplay between fine and coarse level by suitably choosing the coarse space and␍the coarse-to-fine interpolation (see, e.g., [<A
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HREF="node26.html#Briggs2000">3</A>,<A
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HREF="node26.html#Stuben_01">23</A>,<A
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HREF="node26.html#dd2_96">21</A>] for details.)␍␍MLD2P4 uses a pure algebraic approach, based on the smoothed ␍aggregation algorithm [<A
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HREF="node26.html#BREZINA_VANEK">2</A>,<A
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HREF="node26.html#VANEK_MANDEL_BREZINA">25</A>],␍for building the sequence of coarse matrices and transfer operators,␍starting from the original one.␍A decoupled version of this algorithm is implemented, where the smoothed␍aggregation is applied locally to each submatrix [<A
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HREF="node26.html#TUMINARO_TONG">24</A>].␍A brief description of the AMG preconditioners implemented in MLD2P4 is given in ␍Sections <A HREF="node12.html#sec:multilevel">4.1</A>-<A HREF="#sec:smoothers">4.3</A>. For further details the reader␍is referred to [<A
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HREF="node26.html#aaecc_07">5</A>,<A
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HREF="node26.html#apnum_07">7</A>,<A
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HREF="node26.html#MLD2P4_TOMS">8</A>].␍␍We note that optimal multigrid preconditioners do not necessarily correspond␍to minimum execution times in a parallel setting. Indeed, to obtain effective parallel␍multigrid preconditioners, a tradeoff between the optimality and the cost of building and␍applying the smoothers and the coarse-space corrections must be achieved. Effective␍parallel preconditioners require algorithmic scalability to be coupled with implementation␍scalability, i.e., a computational cost per iteration which remains (almost) constant as␍the number of parallel processors increases.␍␍␍<BR><HR>
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HREF="node27.html#Briggs2000">3</A>,<A
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HREF="node27.html#Stuben_01">23</A>,<A
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HREF="node27.html#dd2_96">21</A>] for details.)␍␍MLD2P4 uses a pure algebraic approach, based on the smoothed ␍aggregation algorithm [<A
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HREF="node27.html#BREZINA_VANEK">2</A>,<A
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HREF="node27.html#VANEK_MANDEL_BREZINA">25</A>],␍for building the sequence of coarse matrices and transfer operators,␍starting from the original one.␍A decoupled version of this algorithm is implemented, where the smoothed␍aggregation is applied locally to each submatrix [<A
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HREF="node27.html#TUMINARO_TONG">24</A>].␍A brief description of the AMG preconditioners implemented in MLD2P4 is given in ␍Sections <A HREF="node12.html#sec:multilevel">4.1</A>-<A HREF="#sec:smoothers">4.3</A>. For further details the reader␍is referred to [<A
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HREF="node27.html#apnum_07">7</A>,<A
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HREF="node27.html#MLD2P4_TOMS">8</A>].␍␍We note that optimal multigrid preconditioners do not necessarily correspond␍to minimum execution times in a parallel setting. Indeed, to obtain effective parallel␍multigrid preconditioners, a tradeoff between the optimality and the cost of building and␍applying the smoothers and the coarse-space corrections must be achieved. Effective␍parallel preconditioners require algorithmic scalability to be coupled with implementation␍scalability, i.e., a computational cost per iteration which remains (almost) constant as␍the number of parallel processors increases.␍␍␍<BR><HR>
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<P>
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We describe the basics for building and applying MLD2P4 one-level and multi-level
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(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
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HREF="node26.html#PSBLASGUIDE">13</A>].
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The following steps are required:
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
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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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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
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<BR>
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@@ -83,7 +83,7 @@ hierarchy produced by a previous call to <code>hierarchy_build</code>
|
||||
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.
|
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See the PSBLAS User's Guide for details [<A
|
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HREF="node26.html#PSBLASGUIDE">13</A>].</TD>
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HREF="node27.html#PSBLASGUIDE">13</A>].</TD>
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</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>
|
||||
@@ -91,13 +91,13 @@ hierarchy produced by a previous call to <code>hierarchy_build</code>
|
||||
<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="node26.html#PSBLASGUIDE">13</A>].</TD>
|
||||
HREF="node27.html#PSBLASGUIDE">13</A>].</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="node24.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">8</A> for details.</TD>
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</TR>
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||||
</TABLE>
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||||
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+17
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@@ -122,7 +122,7 @@ and hence it is completely transparent to 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="node24.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">8</A> for details.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
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@@ -183,26 +183,26 @@ as follows:
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<BR>
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@@ -75,7 +75,7 @@ This routine deallocates the preconditioner data structure <code>p</code>.
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><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="node24.html#sec:errors">7</A> for details.</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>Error code. If no error, 0 is returned. See Section <A HREF="node25.html#sec:errors">8</A> for details.</TD>
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+13
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<BR>
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@@ -76,7 +76,7 @@ or <code>build</code>, have been called.
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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="node24.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">8</A> for details.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>iout</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in), optional</code>.</TD>
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@@ -99,6 +99,9 @@ as follows:
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<P>
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<P>
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<P>
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<BR><HR>
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+130
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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>
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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:adding"></A>
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<BR>
|
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Error Handling
|
||||
Adding new smoother and solver objects to MLD2P4
|
||||
</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
|
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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="node26.html#PSBLASGUIDE">13</A>].
|
||||
Developers can add completely new smoother and/or solver classes
|
||||
derived from the base objects in the library (see Remark 2 in Section <A HREF="node17.html#sec:precset">6.2</A>),
|
||||
without recompiling the library itself.
|
||||
|
||||
<P>
|
||||
To do so, it is necessary first to select the base type to be extended.
|
||||
In our experience, it is quite likely that the new application needs
|
||||
only the definition of a ``solver'' object, which is almost
|
||||
always acting only on the local part of the distributed matrix.
|
||||
The parallel actions required to connect the various solver objects
|
||||
are most often already provided by the block-Jacobi or the additive
|
||||
Schwarz smoothers. To define a new solver, the developer will then
|
||||
have to define its components and methods, perhaps taking one of the
|
||||
predefined solvers as a starting point, if possible.
|
||||
|
||||
<BR><HR>
|
||||
<P>
|
||||
Once the new smoother/solver class has been developed, to use it in
|
||||
the context of the multilevel preconditioners it is necessary to:
|
||||
|
||||
<UL>
|
||||
<LI>declare in the application program a variable of the new type;
|
||||
</LI>
|
||||
<LI>pass that variable as the argument to the <code>set</code> routine as in the
|
||||
following:
|
||||
<DIV ALIGN="CENTER">
|
||||
<code>call p%set(smoother,info [,ilev,ilmax,pos])</code>
|
||||
<BR><code>call p%set(solver,info [,ilev,ilmax,pos])</code>
|
||||
|
||||
</DIV>
|
||||
</LI>
|
||||
<LI>link the code implementing the various methods into the application executable.
|
||||
</LI>
|
||||
</UL>
|
||||
The new solver object is then dynamically included in the
|
||||
preconditioner structure, and acts as a <I>mold</I> to which the
|
||||
preconditioner will conform, even though the MLD2P4 library has not
|
||||
been modified to account for this new development.
|
||||
|
||||
<P>
|
||||
It is possible to define new values for the keyword <code>WHAT</code> in the
|
||||
<code>set</code> routine; if the library code does not recognize a keyword,
|
||||
it passes it down the composition hierarchy (levels containing
|
||||
smoothers containing in turn solvers), so that it can be eventually caught by
|
||||
the new solver.
|
||||
|
||||
<P>
|
||||
An example is provided in the source code distribution under the
|
||||
folder <code>tests/newslv</code>. In this example we are implementing a new
|
||||
incomplete factorization variant (which is simply the ILU(0)
|
||||
factorization under a new name). Because of the specifics of this case, it is
|
||||
possible to reuse the basic structure of the ILU solver, with its
|
||||
L/D/U components and the methods needed to apply the solver; only a
|
||||
few methods, such as the description and most importantly the build,
|
||||
need to be ovverridden (rewritten).
|
||||
|
||||
<P>
|
||||
The interfaces for the calls shown above are defined using
|
||||
<DIV ALIGN="CENTER">
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><code>smoother</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>class(mld_x_base_smoother_type)</code></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The user-defined new smoother to be employed in the
|
||||
preconditioner.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40><code>solver</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>class(mld_x_base_solver_type)</code></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=40> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The user-defined new solver to be employed in the
|
||||
preconditioner.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
The other arguments are defined in the way described in
|
||||
Sec. <A HREF="node17.html#sec:precset">6.2</A>. As an example, in the <code>tests/newslv</code>
|
||||
code we define a new object of type <code>mld_d_tlu_solver_type</code>, and
|
||||
we pass it as follows:
|
||||
<PRE>
|
||||
! sparse matrix and preconditioner
|
||||
type(psb_dspmat_type) :: a
|
||||
type(mld_dprec_type) :: prec
|
||||
type(mld_d_tlu_solver_type) :: tlusv
|
||||
|
||||
......
|
||||
!
|
||||
! prepare the preconditioner: an ML with defaults, but with TLU solver at
|
||||
! intermediate levels. All other parameters are at default values.
|
||||
!
|
||||
call prec%init('ML', info)
|
||||
call prec%hierarchy_build(a,desc_a,info)
|
||||
nlv = prec%get_nlevs()
|
||||
call prec%set(tlusv, info,ilev=1,ilmax=max(1,nlv-1))
|
||||
call prec%smoothers_build(a,desc_a,info)
|
||||
</PRE>
|
||||
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|
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<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:license"></A>
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<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:errors"></A>
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<BR>
|
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License
|
||||
Error Handling
|
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</H1>
|
||||
|
||||
<P>
|
||||
The MLD2P4 is freely distributable under the following copyright
|
||||
terms: <PRE>
|
||||
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">13</A>].
|
||||
|
||||
|
||||
MLD2P4 version 2.1
|
||||
MultiLevel Domain Decomposition Parallel Preconditioners Package
|
||||
based on PSBLAS (Parallel Sparse BLAS version 3.4)
|
||||
|
||||
(C) Copyright 2008, 2010, 2012, 2017
|
||||
|
||||
Salvatore Filippone Cranfield University, Cranfield, UK
|
||||
Ambra Abdullahi Hassan University of Rome Tor Vergata, Rome, IT
|
||||
Alfredo Buttari CNRS-IRIT, Toulouse, FR
|
||||
Pasqua D'Ambra IAC-CNR, Naples, IT
|
||||
Daniela di Serafino University of Campania L. Vanvitelli, Caserta, IT
|
||||
|
||||
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>
|
||||
|
||||
<BR><HR>
|
||||
|
||||
|
||||
+58
-133
@@ -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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<TITLE>Bibliography</TITLE>
|
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<H1><A NAME="SECTION000110000000000000000"></A><A NAME="sec:license"></A>
|
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<BR>
|
||||
License
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
The MLD2P4 is freely distributable under the following copyright
|
||||
terms: <PRE>
|
||||
|
||||
|
||||
<H2><A NAME="SECTION000110000000000000000">
|
||||
Bibliography</A>
|
||||
</H2><DL COMPACT><DD>
|
||||
MLD2P4 version 2.1
|
||||
MultiLevel Domain Decomposition Parallel Preconditioners Package
|
||||
based on PSBLAS (Parallel Sparse BLAS version 3.4)
|
||||
|
||||
(C) Copyright 2008, 2010, 2012, 2017
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="MUMPS">1</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 Journal on Scientific Computing, volume 37 (3), 2015, A1452-A1474.
|
||||
See also <TT>http://mumps.enseeiht.fr</TT>.␍<P></P><DT><A NAME="BREZINA_VANEK">2</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="Briggs2000">3</A>
|
||||
<DD>
|
||||
W. L. Briggs, V. E. Henson, S. F. McCormick,
|
||||
<EM>A Multigrid Tutorial, Second Edition</EM>,
|
||||
SIAM, 2000.␍<P></P><DT><A NAME="para_04">4</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">5</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="CAI_SARKIS">6</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="apnum_07">7</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><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, art. 30.␍<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><DT><A NAME="SUPERLU">10</A>
|
||||
<DD>
|
||||
J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, 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">11</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 (1) 1990, 1-17.␍<P></P><DT><A NAME="blas2">12</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 (1) 1988, 1-17.␍<P></P><DT><A NAME="PSBLASGUIDE">13</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><DT><A NAME="PSBLAS3">14</A>
|
||||
<DD>
|
||||
S. Filippone, A. Buttari,
|
||||
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>.
|
||||
ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23.␍<P></P><DT><A NAME="psblas_00">15</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">16</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">17</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 (3), 1979, 308-323.␍<P></P><DT><A NAME="SUPERLUDIST">18</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="Notay2008">19</A>
|
||||
<DD>
|
||||
Y. Notay, P. S. Vassilevski,
|
||||
<EM>Recursive Krylov-based multigrid cycles</EM>,
|
||||
Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487. ␍<P></P><DT><A NAME="Saad_book">20</A>
|
||||
<DD>
|
||||
Y. Saad,
|
||||
<EM>Iterative methods for sparse linear systems</EM>, 2nd edition, SIAM, 2003.␍<P></P><DT><A NAME="dd2_96">21</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">22</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="Stuben_01">23</A>
|
||||
<DD>
|
||||
K. Stüben,
|
||||
<EM>An Introduction to Algebraic Multigrid</EM>,
|
||||
in A. Schüller, U. Trottenberg, C. Oosterlee, Multigrid,
|
||||
Academic Press, 2001.␍<P></P><DT><A NAME="TUMINARO_TONG">24</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">25</A>
|
||||
<DD>
|
||||
P. Vanek, J. Mandel, M. Brezina,
|
||||
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
|
||||
Computing, 56 (3) 1996, 179-196.
|
||||
Salvatore Filippone Cranfield University, Cranfield, UK
|
||||
Ambra Abdullahi Hassan University of Rome Tor Vergata, Rome, IT
|
||||
Alfredo Buttari CNRS-IRIT, Toulouse, FR
|
||||
Pasqua D'Ambra IAC-CNR, Naples, IT
|
||||
Daniela di Serafino University of Campania L. Vanvitelli, Caserta, IT
|
||||
|
||||
<P>
|
||||
</DL>
|
||||
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>
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
|
||||
+137
-28
@@ -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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<HTML>
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<HEAD>
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<TITLE>About this document ...</TITLE>
|
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<META NAME="description" CONTENT="About this document ...">
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<TITLE>Bibliography</TITLE>
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<META NAME="description" CONTENT="Bibliography">
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<META NAME="resource-type" CONTENT="document">
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<META NAME="distribution" CONTENT="global">
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@@ -18,52 +18,161 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION000120000000000000000">
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Bibliography</A>
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</H2><DL COMPACT><DD>
|
||||
|
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<H1><A NAME="SECTION000120000000000000000">
|
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About this document ...</A>
|
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</H1>
|
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<P>
|
||||
This document was generated using the
|
||||
<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2012 (1.2)
|
||||
<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="MUMPS">1</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 Journal on Scientific Computing, volume 37 (3), 2015, A1452-A1474.
|
||||
See also <TT>http://mumps.enseeiht.fr</TT>.␍<P></P><DT><A NAME="BREZINA_VANEK">2</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="Briggs2000">3</A>
|
||||
<DD>
|
||||
W. L. Briggs, V. E. Henson, S. F. McCormick,
|
||||
<EM>A Multigrid Tutorial, Second Edition</EM>,
|
||||
SIAM, 2000.␍<P></P><DT><A NAME="para_04">4</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">5</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="CAI_SARKIS">6</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="apnum_07">7</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><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, art. 30.␍<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><DT><A NAME="SUPERLU">10</A>
|
||||
<DD>
|
||||
J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, 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">11</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 (1) 1990, 1-17.␍<P></P><DT><A NAME="blas2">12</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 (1) 1988, 1-17.␍<P></P><DT><A NAME="PSBLASGUIDE">13</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><DT><A NAME="PSBLAS3">14</A>
|
||||
<DD>
|
||||
S. Filippone, A. Buttari,
|
||||
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>.
|
||||
ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23.␍<P></P><DT><A NAME="psblas_00">15</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">16</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">17</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 (3), 1979, 308-323.␍<P></P><DT><A NAME="SUPERLUDIST">18</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="Notay2008">19</A>
|
||||
<DD>
|
||||
Y. Notay, P. S. Vassilevski,
|
||||
<EM>Recursive Krylov-based multigrid cycles</EM>,
|
||||
Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487. ␍<P></P><DT><A NAME="Saad_book">20</A>
|
||||
<DD>
|
||||
Y. Saad,
|
||||
<EM>Iterative methods for sparse linear systems</EM>, 2nd edition, SIAM, 2003.␍<P></P><DT><A NAME="dd2_96">21</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">22</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="Stuben_01">23</A>
|
||||
<DD>
|
||||
K. Stüben,
|
||||
<EM>An Introduction to Algebraic Multigrid</EM>,
|
||||
in A. Schüller, U. Trottenberg, C. Oosterlee, Multigrid,
|
||||
Academic Press, 2001.␍<P></P><DT><A NAME="TUMINARO_TONG">24</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">25</A>
|
||||
<DD>
|
||||
P. Vanek, J. Mandel, M. Brezina,
|
||||
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
|
||||
Computing, 56 (3) 1996, 179-196.
|
||||
|
||||
<P>
|
||||
The command line arguments were: <BR>
|
||||
<STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
The translation was initiated by Salvatore Filippone on 2017-07-17
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
|
||||
@@ -63,7 +63,7 @@ Mathematics Department, Macquarie University, Sydney.
|
||||
The command line arguments were: <BR>
|
||||
<STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
|
||||
<P>
|
||||
The translation was initiated by Salvatore Filippone on 2017-05-16
|
||||
The translation was initiated by Salvatore Filippone on 2017-07-19
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
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|
||||
+30
-30
@@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
|
||||
|
||||
<BODY >
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<!--Navigation Panel-->
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<B> Next:</B> <A NAME="tex2html109"
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<B> Up:</B> <A NAME="tex2html105"
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<B> Up:</B> <A NAME="tex2html107"
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HREF="userhtml.html">userhtml</A>
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<B> Previous:</B> <A NAME="tex2html99"
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<B> <A NAME="tex2html107"
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<B> <A NAME="tex2html109"
|
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HREF="node2.html">Contents</A></B>
|
||||
<BR>
|
||||
<BR>
|
||||
@@ -60,9 +60,9 @@ General Overview
|
||||
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 parallel Algebraic MultiGrid (AMG) and Domain
|
||||
Decomposition preconditioners (see, e.g., [<A
|
||||
HREF="node26.html#Briggs2000">3</A>,<A
|
||||
HREF="node26.html#Stuben_01">23</A>,<A
|
||||
HREF="node26.html#dd2_96">21</A>]),
|
||||
HREF="node27.html#Briggs2000">3</A>,<A
|
||||
HREF="node27.html#Stuben_01">23</A>,<A
|
||||
HREF="node27.html#dd2_96">21</A>]),
|
||||
to be used in the iterative solution of linear systems,
|
||||
<BR>
|
||||
<DIV ALIGN="RIGHT">
|
||||
@@ -95,8 +95,8 @@ multi-level cycles and smoothers widely used in multigrid methods.
|
||||
The multi-level preconditioners implemented in MLD2P4 are obtained by combining
|
||||
AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and
|
||||
K-cycles [<A
|
||||
HREF="node26.html#Briggs2000">3</A>,<A
|
||||
HREF="node26.html#Notay2008">19</A>] are available, which allow to define
|
||||
HREF="node27.html#Briggs2000">3</A>,<A
|
||||
HREF="node27.html#Notay2008">19</A>] are available, which allow to define
|
||||
almost all the preconditioners in the package, including the multi-level hybrid
|
||||
Schwarz ones; a specific cycle is implemented to obtain multi-level additive
|
||||
Schwarz preconditioners. The Jacobi, hybridforward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods
|
||||
@@ -104,8 +104,8 @@ are available as smoothers. An algebraic approach is used to generate a hierarch
|
||||
coarse-level matrices and operators, without explicitly using any information on the
|
||||
geometry of the original problem, e.g., the discretization of a PDE. To this end,
|
||||
the smoothed aggregation technique [<A
|
||||
HREF="node26.html#BREZINA_VANEK">2</A>,<A
|
||||
HREF="node26.html#VANEK_MANDEL_BREZINA">25</A>]
|
||||
HREF="node27.html#BREZINA_VANEK">2</A>,<A
|
||||
HREF="node27.html#VANEK_MANDEL_BREZINA">25</A>]
|
||||
is applied. Either exact or approximate solvers can be used on the coarsest-level
|
||||
system. Specifically, different sparse LU factorizations from external
|
||||
packages, and native incomplete LU factorizations and Jacobi, hybrid Gauss-Seidel,
|
||||
@@ -126,8 +126,8 @@ interface.
|
||||
MLD2P4 has been designed to implement scalable and easy-to-use
|
||||
multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS)
|
||||
computational framework [<A
|
||||
HREF="node26.html#psblas_00">15</A>,<A
|
||||
HREF="node26.html#PSBLAS3">14</A>]. PSBLAS provides basic linear algebra
|
||||
HREF="node27.html#psblas_00">15</A>,<A
|
||||
HREF="node27.html#PSBLAS3">14</A>]. PSBLAS provides basic linear algebra
|
||||
operators and data management facilities for distributed sparse matrices,
|
||||
as well as parallel Krylov solvers which can be used with the MLD2P4 preconditioners.
|
||||
The choice of PSBLAS has been mainly motivated by the need of having
|
||||
@@ -150,14 +150,14 @@ few black-box routines at the upper layer allow all users to easily
|
||||
build and apply any preconditioner available in MLD2P4;
|
||||
facilities are also available allowing expert users to extend the set of smoothers
|
||||
and solvers for building new versions of the preconditioners (see
|
||||
Section <A HREF="#sec:adding"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="crossref.png"></A>).
|
||||
Section <A HREF="node24.html#sec:adding">7</A>).
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<P>
|
||||
We note that the user interface of MLD2P4 2.1 has been extended with respect to the
|
||||
previous versions in order to separate the construction of the multi-level hierarchy from
|
||||
the construction of the smoothers and solvers, and to allow for more flexibility
|
||||
at each level. The software architecture described in [<A
|
||||
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|
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HREF="node27.html#MLD2P4_TOMS">8</A>] has significantly
|
||||
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|
||||
However, compatibility with previous versions has been preserved.
|
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|
||||
in Section <A HREF="node13.html#sec:started">5</A>, where the Fortran codes of a few sample programs
|
||||
are also shown. A reference guide for the user interface routines is provided
|
||||
in Section <A HREF="node15.html#sec:userinterface">6</A>. Information on the extension of the package
|
||||
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|
||||
through the addition of new smoothers and solvers is reported in Section <A HREF="node24.html#sec:adding">7</A>.
|
||||
The error handling mechanism used by the package
|
||||
is briefly described in Section <A HREF="node24.html#sec:errors">7</A>. The copyright terms concerning the
|
||||
distribution and modification of MLD2P4 are reported in Appendix <A HREF="node25.html#sec:license">A</A>.
|
||||
is briefly described in Section <A HREF="node25.html#sec:errors">8</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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The software is available under a modified BSD license, as specified
|
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in Appendix <A HREF="node25.html#sec:license">A</A>; please note that some of the optional
|
||||
in Appendix <A HREF="node26.html#sec:license">A</A>; please note that some of the optional
|
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third party libraries may be licensed under a different and more
|
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<UL>
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<LI><A NAME="tex2html134"
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<DD>[<A
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|
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|
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|
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|
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|
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|
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|
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HREF="www.ce.uniroma2.it/psblas">www.ce.uniroma2.it/psblas</A></TT>; version
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3.5.0 (or later) is required. Indeed, all the prerequisites
|
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@@ -109,26 +109,26 @@ compiler as MLD2P4.
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<DD>[<A
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|
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|
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A sparse LU factorization package available from <TT><A NAME="tex2html6"
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|
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it provides sequential and parallel factorizations and triangular system solution
|
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@@ -85,7 +85,7 @@ for multi-level preconditioners may change to reflect their presence.
|
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<DT><STRONG>SuperLU</STRONG></DT>
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<DD>[<A
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HREF="node26.html#SUPERLU">10</A>]
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A sparse LU factorization package available from
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<TT><A NAME="tex2html7"
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HREF="crd.lbl.gov/~xiaoye/SuperLU/">crd.lbl.gov/~xiaoye/SuperLU/</A></TT>; it provides sequential
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</DD>
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<DT><STRONG>SuperLU_Dist</STRONG></DT>
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<DD>[<A
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HREF="node26.html#SUPERLUDIST">18</A>]
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HREF="node27.html#SUPERLUDIST">18</A>]
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A sparse LU factorization package available
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from the same site as SuperLU; it provides parallel factorization and
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triangular system solution for double precision real and complex data.
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+16
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<BR>
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<BR>
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make install
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</PRE><HR>
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HREF="node2.html">Contents</A></B>
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@@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<BODY >
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<BR>
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<BR>
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@@ -136,13 +136,15 @@ Feb. 28, 2017
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||||
</UL>
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<BR>
|
||||
<LI><A NAME="tex2html48"
|
||||
HREF="node24.html">Error Handling</A>
|
||||
HREF="node24.html">Adding new smoother and solver objects to MLD2P4</A>
|
||||
<LI><A NAME="tex2html49"
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||||
HREF="node25.html">License</A>
|
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HREF="node25.html">Error Handling</A>
|
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<LI><A NAME="tex2html50"
|
||||
HREF="node26.html">Bibliography</A>
|
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HREF="node26.html">License</A>
|
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<LI><A NAME="tex2html51"
|
||||
HREF="node27.html">About this document ...</A>
|
||||
HREF="node27.html">Bibliography</A>
|
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<LI><A NAME="tex2html52"
|
||||
HREF="node28.html">About this document ...</A>
|
||||
</UL>
|
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<!--End of Table of Child-Links-->
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<BR><HR>
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+2674
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Load Diff
+1
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@@ -85,7 +85,7 @@
|
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|
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TOPFILE = userguide.tex
|
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HTMLFILE = userhtml.tex
|
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SECFILE = abstract.tex overview.tex distribution.tex \
|
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SECFILE = abstract.tex overview.tex distribution.tex newobjects.tex\
|
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building.tex background.tex gettingstarted.tex userinterface.tex \
|
||||
errors.tex bibliography.tex license.tex
|
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FIGDIR = figures
|
||||
|
||||
Reference in New Issue
Block a user