From 06f8f83114cca17e7d88f19c0dfd176221791d28 Mon Sep 17 00:00:00 2001 From: sfilippone Date: Tue, 23 Dec 2025 11:21:53 +0100 Subject: [PATCH] Update documentation for release --- docs/amg4psblas_1.2-guide.pdf | Bin 1878092 -> 1878728 bytes docs/html/index.html | 2 +- docs/html/userhtml.html | 2 +- docs/html/userhtmlli1.html | 34 +- docs/html/userhtmlse1.html | 66 +- docs/html/userhtmlse3.html | 92 +-- docs/html/userhtmlse4.html | 132 ++-- docs/html/userhtmlse5.html | 1199 ++++++++++++++++----------------- docs/html/userhtmlse7.html | 4 + docs/html/userhtmlse8.html | 73 +- docs/src/abstract.tex | 42 +- docs/src/building.tex | 17 +- docs/src/gettingstarted.tex | 20 +- docs/src/license.tex | 69 +- docs/src/overview.tex | 68 +- docs/src/userguide.tex | 2 +- docs/src/userhtml.tex | 2 +- docs/src/userinterface.tex | 73 +- 18 files changed, 975 insertions(+), 922 deletions(-) diff --git a/docs/amg4psblas_1.2-guide.pdf b/docs/amg4psblas_1.2-guide.pdf index 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class="cmr-12">University of Rome Tor-Vergata and IAC-CNR
Software version: 1.2
December 31st, 2025 +class="cmr-12">December 23rd, 2025 diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index 05e3ea7c..4ed148b0 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -31,7 +31,7 @@ class="cmr-12">University of Rome Tor-Vergata and IAC-CNR
Software version: 1.2
December 31st, 2025 +class="cmr-12">December 23rd, 2025 diff --git a/docs/html/userhtmlli1.html b/docs/html/userhtmlli1.html index 328c05e6..43007b4d 100644 --- a/docs/html/userhtmlli1.html +++ b/docs/html/userhtmlli1.html @@ -72,32 +72,34 @@ class="small-caps">n class="cmcsc-10x-x-120">PSBLAS) is a package of parallel algebraic multilevel preconditioners included in the PSCToolkit (Parallel Sparse Computation Toolkit) software framework. It is a progress +class="cmr-12">PSCToolkit (Parallel Sparse Computation Toolkit) software framework. It of a software development project started in 2007, named MLD2P4, which originally +class="cmr-12">is an evolutiuon of a software development project started in 2007, named implemented a multilevel version of some domain decomposition preconditioners of +class="cmr-12">MLD2P4, which originally implemented a multilevel version of some domain additive-Schwarz type, and was based on a parallel decoupled version of the well known +class="cmr-12">decomposition preconditioners of additive-Schwarz type, and was based on a parallel smoothed aggregation method to generate the multilevel hierarchy of coarser +class="cmr-12">decoupled version of the well known smoothed aggregation method to generate the matrices. In the last years, within the context of the EU-H2020 EoCoE project +class="cmr-12">multilevel hierarchy of coarser matrices. In the last few years the package (Energy Oriented Center of Excellence), the package was extended for including +class="cmr-12">was extended for including new algorithms and functionalities for the setup new algorithms and functionalities for the setup and application new AMG +class="cmr-12">and application new AMG preconditioners with the final aims of improving preconditioners with the final aims of improving efficiency and scalability when tens of +class="cmr-12">efficiency and scalability when tens of thousands cores are used, and of boosting thousands cores are used, and of boosting reliability in dealing with general +class="cmr-12">reliability in dealing with general symmetric positive definite linear systems; these symmetric positive definite linear systems. Due to the significant number +class="cmr-12">developments have been supported in the context of the EU-H2020 EoCoE +project (Energy Oriented Center of Excellence). Due to the significant number of changes and the increase in scope, we decided to rename the package as AMG4PSBLAS. -

AMG4PSBLAS has been designed to provide scalable and easy-to-use preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra @@ -111,14 +113,14 @@ class="cmr-12">algebraic approach; therefore users level interfaces assume that class="cmr-12">and preconditioners are represented as PSBLAS distributed sparse matrices. AMG4PSBLAS enables the user to easily specify different features of an algebraic -multilevel preconditioner, thus allowing to experiment with different preconditioners for +multilevel preconditioner, thus allowing to experiment with different preconditioners for the problem and parallel computers at hand. -

The package employs object-oriented design techniques in Fortran 2003, with parallel implementation is based on a Single Program Multiple Dat class="cmr-12">paradigm; the inter-process communication is based on MPI and is managed mainly through PSBLAS. -

This guide provides a brief description of the functionalities and the user interface of AMG4PSBLAS. diff --git a/docs/html/userhtmlse1.html b/docs/html/userhtmlse1.html index ae661559..f42c44aa 100644 --- a/docs/html/userhtmlse1.html +++ b/docs/html/userhtmlse1.html @@ -100,18 +100,18 @@ src="userhtml0x.png" alt="Ax = b, id="x4-3001r1"> (1) -

where A is a square, real or complex, sparse symmetric positive definite (s.p.d) matrix. -

The preconditioners implemented in AMG4PSBLAS are obtained by combining 3 different types of AMG cycles with smoothers and coarsest-level solvers. Available +class="cmr-12">different types of AMG cycles with smoothers and coarsest-level solvers. We provide a multigrid cycles include the V-, W-, and a version of a Krylov-type cycle +class="cmr-12">number of multigrid cycles, including the V-, W-, and a version of a Krylov-type cycle (K-cycle) 14]. -

An algebraic approach is used to generate a hierarchy of coarse-level matrices and operators, without explicitly using any information on the geometry of the original @@ -150,7 +150,7 @@ class="cmr-12">problem, e.g., the discretization of a PDE. To this end, two diff class="cmr-12">strategies, based on aggregation, are available:

-

Either exact or approximate solvers can be used on the coarsest-level system. We provide interfaces to various parallel and sequential sparse LU factorizations from external @@ -210,7 +210,7 @@ class="cmr-12">parallel weighted Jacobi, hybrid Gauss-Seidel, block-Jacobi solve class="cmr-12">preconditioned Krylov methods; all smoothers can be also exploited as one-level preconditioners. -

AMG4PSBLAS is written in Fortran 2003, following an object-oriented design Single and double precision implementations of AMG4PSBLAS are ava class="cmr-12">for both the real and the complex case, which can be used through a single interface. -

AMG4PSBLAS has been designed to implement scalable and easy-to-use +

AMG4PSBLAS has been designed to implement scalable and easy-to-use multilevel multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS) +class="cmr-12">preconditioners in the context of the PSBLAS (Parallel Sparse BLAS) computational computational frameworkframework [ 22]. PSBLAS provides basic linear algebra operators +class="cmr-12">. PSBLAS provides basic linear algebra operators and data and data management facilities for distributed sparse matrices, kernels for +class="cmr-12">management facilities for distributed sparse matrices, kernels for sequential incomplete sequential incomplete factorizations needed for the parallel block-Jacobi and +class="cmr-12">factorizations needed for the parallel block-Jacobi and additive Schwarz smoothers, and additive Schwarz smoothers, and parallel Krylov solvers which can be used with +class="cmr-12">parallel Krylov solvers which can be used with the AMG4PSBLAS preconditioners. the AMG4PSBLAS preconditioners. The choice of PSBLAS has been mainly +class="cmr-12">The choice of PSBLAS has been mainly motivated by the need of having a portable motivated by the need of having a portable and efficient software infrastructure +class="cmr-12">and efficient software infrastructure implementing “de facto” standard parallel sparse implementing “de facto” standard parallel sparse linear algebra kernels, to +class="cmr-12">linear algebra kernels, to pursue goals such as performance, portability, modularity pursue goals such as performance, portability, modularity ed extensibility +class="cmr-12">ed extensibility in the development of the preconditioner package. On the in the development of the preconditioner package. On the other hand, the +class="cmr-12">other hand, the implementation of AMG4PSBLAS, which was driven by the implementation of AMG4PSBLAS, which was driven by the need to face the exascale +class="cmr-12">need to face the exascale challenge, has led to some important revisions and challenge, has led to some important revisions and extentions of the PSBLAS +class="cmr-12">extentions of the PSBLAS infrastructure. The inter-process comunication infrastructure. The inter-process comunication required by AMG4PSBLAS +class="cmr-12">required by AMG4PSBLAS is encapsulated in the PSBLAS routines; therefore, is encapsulated in the PSBLAS routines; therefore, AMG4PSBLAS can be +class="cmr-12">AMG4PSBLAS can be run on any parallel machine where PSBLAS implementations run on any parallel machine where PSBLAS implementations are available. +class="cmr-12">are available. The most recent version of PSBLAS (release 3.9) includes a plug-in for In the most recent version of PSBLAS (release 3.7), a plug-in for GPU is -included; it includes CUDA versions of main vector operations and of sparse +class="cmr-12">GPU; it contains CUDA versions of main vector operations and of sparse matrix-vector multiplication, so that Krylov methods coupled with AMG4PSBLAS preconditioners relying on Jacobi and block-Jacobi smoothers with class="cmr-12">approximate inverses on the blocks can be efficiently executed on cluster of GPUs. -

AMG4PSBLAS has a layered and modular software architecture where three main layers can be identified. The lower layer consists of the PSBLAS kernels, the middle one implements the construction and application phases of the preconditioners, and the +upper one provides a uniform interface to all the preconditioners. This architecture -upper one provides a uniform interface to all the preconditioners. This architecture allows for different levels of use of the package: few black-box routines at the upper  6). -

This guide is organized as follows. General information on the distribution of the source code is reported in Section. Most Fortran compilers provide this feature; in particular, thi supported by the GNU Fortran compiler, for which we recommend to use at least version 4.8. The software defines data types and interfaces for real and complex data, +class="cmr-12">version 12. The software defines data types and interfaces for real and complex data, in in both single and double precision. +class="cmr-12">both single and double precision.

Building AMG4PSBLAS requires some base libraries (see Section “developer” part; in order to build AMG4PSBLAS you ne class="cmr-12">the base and optional software used by AMG4PSBLAS is given in the next sections. -

+

3.1 Prerequisites

-

The following base libraries are needed:

-

+

BLAS

-

[18for including -fPIC compilation option in the make.inc file of th library.

-

+

MPI

-

[25A version of MPI is available on most high-performance computing< systems.

-

+

PSBLAS

-

[21; version class="cmr-12">3.9.0 (or later) is required. Indeed, all the prerequisites listed so far are also prerequisites of PSBLAS.

-

Please note that the four previous libraries must have Fortran interfaces compatible with AMG4PSBLAS; usually this means that they should all be built with the same compiler being used for AMG4PSBLAS. -

If you want to use the PSBLAS support for NVIDIA GPUs, you will also need a working version of the CUDA Toolkit that is compatible with the @@ -214,7 +214,7 @@ class="cmr-12">options: 

 ./configure --enable-cuda --with-cudadir=${CUDA_HOME} --with-cudacc=xx,yy,zz
-

Previous versions required you to have the auxiliary libraries SPGPU and PSBLAS-EXT compiled, this is no longer necessary because they have been integrated @@ -226,24 +226,24 @@ class="cmr-12"> 4.2. -

+

3.2 Optional third party libraries

-

We provide interfaces to the following third-party software libraries; note that these are optional, but if you enable them some defaults for multilevel preconditioners may change to reflect their presence. -

+

-

+

UMFPACK

-

[16provide the right path to the BLAS and LAPACK libraries class="cmtt-12">SuiteSparse_config/SuiteSparse_config.mk file.

-

+

MUMPS

-

[2solution for single and double precision, real and complex data. versions 4.10.0 and 5.0.1.

-

+

SuperLU

-

[17data. We tested versions 4.3 and 5.0. If you installed BLAS from remember to define the BLASLIB variable in the make.inc file.

-

+

SuperLU_Dist

-

[28parallel graph partitioning and fill-reducing matrix ordering, av href="glaros.dtc.umn.edu/gkhome/metis/parmetis/overview" class="url" >glaros.dtc.umn.edu/gkhome/metis/parmetis/overview.

-

+

3.3 Configuration options

-

In order to build AMG4PSBLAS, the first step is to use the configure script in the main directory to generate the necessary makefile. -

As a minimal example consider the following: @@ -360,7 +360,7 @@ class="cmr-12">As a minimal example consider the following: 

 ./configure --with-psblas=PSB-INSTALL-DIR
-

which assumes that the various MPI compilers and support libraries are available in the standard directories on the system, and specifies only the PSBLAS install directory @@ -374,7 +374,7 @@ class="cmtt-12">./configure --help, which produces: 

produces:  
‘configure/issues>.
    

-
For instance, if a user has built and installed PSBLAS 3.7 under the 
For instance, if a user has built and installed PSBLAS 3.9 under the /opt directory and is
 might be configured with:
 
                                                                                
    
-./configure --with-psblas=/opt/psblas-3.7/ \
+./configure --with-psblas=/opt/psblas-3.9/ \
 --with-umfpackincdir=/usr/include/suitesparse/
 

-
 
 Once the configure script has completed execution, it will have generated the file
 Make.inc which will then be used by all Makefiles in the directory tree; t
 class="cmr-12">copied in the install directory under the name Make.inc.AMG4PSBLAS.
-
   
   To use the MUMPS solver package, the user has to add the appropriate options to
 the configure script; by default we are looking for the libraries --with-extra-libs configure
 option.
-
   
   To build the library the user will now enter
                                                                                
 
@@ -3962,7 +3962,7 @@ class="cmr-12">To build the library the user will now enter
    
 make
 

-
 
 followed (optionally) by
                                                                                
 
@@ -3970,12 +3970,12 @@ class="cmr-12">followed (optionally) by
    
 make install
 

-

+

    
3.4    Bug reporting

-
If you find any bugs in our codes, please report them through our issues page
 on
 https://github.com/psctoolkit/psctoolkit/issues

-
   
   To enable us to track the bug, please provide a log from the failing application, the
 test conditions, and ideally a self-contained test program reproducing the
 issue.
-

+

    
3.5    Example and test programs

-
The package contains a samples directory, divided in two subdirs subdirectories.
 Their purpose is as follows:
      

-     

+     

 simple 

-     
contains  a  set  of  simple  example  programs  with  a  predefined  choice  of
      preconditioners,  selectable  via  integer  values.  These  are  intended  to  get
      acquainted with the multilevel preconditioners available in AMG4PSBLAS.
      

-     

+     

 advanced 

-     
contains a set of more sophisticated examples that will allow the user, via
      the input files in the runs subdirectories, to experiment with the full range
      of preconditioners implemented in the package.

-
The fileread directories contain sample programs that read sparse matrices from files,
diff --git a/docs/html/userhtmlse4.html b/docs/html/userhtmlse4.html
index 286b0483..493821fa 100644
--- a/docs/html/userhtmlse4.html
+++ b/docs/html/userhtmlse4.html
@@ -351,7 +351,7 @@ class="content">Preconditioner types, corresponding strings and default choices.
                                                                                
    

    
-
   
   Note that the module amg_prec_mod, containing the definition of the preconditioner
 4.1).
 

-
   
   Remark 1. Coarsest-level solvers based on the LU factorization, such as those
 problems. However, this does not necessarily correspond to the sh
 on parallel computers.
+
   Remark 2. Memory allocation on GPUs is a costly operation implying a
+synchronization; therefore, it is convenient to preallocate internal preconditioner
+workspace with the method prec%allocate_wrk(info) before invoking an iterative
+method, and release it upon exit with prec%deallocate_wrk(info).
    
4.1    Examples

-
The code reported in Figure and ps
 class="cmr-12">must be used by the example
 program.
-
   
   The part of the code dealing with reading and assembling the sparse matrix and the
 right-hand side vector and the deallocation of the relevant data structures, performed
@@ -451,7 +464,7 @@ href="userhtmlli3.html#XPSBLASGUIDE">21].
-
   
   The setup and application of the default multilevel preconditioner for the real single
 precision and the complex, single and double precision, versions are obtained
@@ -461,6 +474,9 @@ class="cmr-12"> 5 for
+                                                                               
+
+                                                                               
 details). If these versions are installed, the corresponding codes are available in
 .
                                                                                
 
                                                                                
-
   
   

                                                                                
@@ -478,7 +494,7 @@ class="cmr-12">.
                                                                                
 

-

+

                                                                                
 
                                                                                
@@ -535,7 +551,7 @@ class="cmr-12">.
   call psb_exit(ctxt)
   stop
-

+

@@ -548,7 +564,7 @@ class="content">setup and application of the default multilevel preconditioner (

-

Different versions of the multilevel preconditioner can be obtained by changing the default values of the preconditioner parameters. The code reported in Figure2 shows how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- +class="cmr-12">how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and and post-smoother, and solves the coarsest-level system with 8 block-Jacobi +class="cmr-12">post-smoother, and solves the coarsest-level system with 8 block-Jacobi sweeps. Note sweeps. Note that the ILU(0) factorization (plus triangular solve) is used as +class="cmr-12">that the ILU(0) factorization (plus triangular solve) is used as local solver for the local solver for the block-Jacobi sweeps, since this is the default associated +class="cmr-12">block-Jacobi sweeps, since this is the default associated with block-Jacobi and set with block-Jacobi and set byby P%init. Furthermore, specifying block-Jacobi as -coarsest-level solver implies that the coarsest-level matrix is distributed among +class="cmr-12">. Furthermore, specifying block-Jacobi as coarsest-level solver implies that the processes. Figurethe coarsest-level matrix is distributed among the processes. Figure 3 shows how to set a W-cycle preconditioner using the +class="cmr-12">shows how Coarsening based on Compatible Weighted Matching, aggregates of size at +class="cmr-12">to set a W-cycle preconditioner using the Coarsening based on Compatible most 8 and smoothed prolongators. It applies 2 hybrid Gauss-Seidel sweeps as +class="cmr-12">Weighted Matching, aggregates of size at most 8 and smoothed prolongators. It pre- and post-smoother, and solves the coarsest-level system with the parallel +class="cmr-12">applies 2 hybrid Gauss-Seidel sweeps as pre- and post-smoother, and solves the flexible Conjugate Gradient method (KRM) coupled with the block-Jacobi +class="cmr-12">coarsest-level system with the parallel flexible Conjugate Gradient method (KRM) preconditioner having ILU(0) on the blocks. Default parameters are used for stopping +class="cmr-12">coupled with the block-Jacobi preconditioner having ILU(0) on the blocks, with criterion of the coarsest solver. Note that, also in this case, specifying KRM as +class="cmr-12">default parameters used for the coarsest solver. Note that specifying KRM as coarsest-level solver implies that the coarsest-level matrix is distributed among the processes. -

The code fragments shown in Figures are included in the example program class="cmr-12">file amg_dexample_ml.f90 too. -

Finally, Figure nonsymmetric. The corresponding example program is available in t amg_dexample_1lev.f90. -

For all the previous preconditioners, example programs where the sparse matrix and the right-hand side are generated by discretizing a PDE with Dirichlet @@ -631,7 +645,7 @@ class="cmr-12">. -

@@ -639,7 +653,7 @@ class="cmr-12">.
-

+

 ... ...
 ! build a V-cycle preconditioner with 1 block-Jacobi sweep (with
@@ -653,7 +667,7 @@ class="cmr-12">.
   call P%smoothers_build(A,desc_A,info)
 ... ...
-

+


Listing 2: setup of a multilevel preconditioner based on the default decoupled coarsening
@@ -664,7 +678,7 @@ class="content">setup of a multilevel preconditioner based on the default decoup -

@@ -672,7 +686,7 @@ class="content">setup of a multilevel preconditioner based on the default decoup
-

+

 ... ...
 ! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
@@ -692,7 +706,7 @@ class="content">setup of a multilevel preconditioner based on the default decoup
   call P%smoothers_build(A,desc_A,info)
 ... ...
-

+


Listing 3: setup of a multilevel preconditioner based on the coupled coarsening using @@ -704,7 +718,7 @@ weighted matching
-

@@ -712,7 +726,7 @@ weighted matching
-

+

 ... ...
 ! set RAS with overlap 2 and ILU(0) on the local blocks
@@ -723,7 +737,7 @@ weighted matching
! solve Ax=b with preconditioned BiCGSTAB   call psb_krylov(’BICGSTAB’,A,P,b,x,tol,desc_A,info) -

+


Listing 4: setup of a one-level Schwarz preconditioner.
@@ -735,7 +749,7 @@ class="content">setup of a one-level Schwarz preconditioner.

The code discussed here shows how to set up a program exploiting the combined GPU capabilities of PSBLAS and AMG4PSBLAS. The code example is available in the @@ -743,14 +757,14 @@ class="cmr-12">capabilities of PSBLAS and AMG4PSBLAS. The code example is availa class="cmr-12">source distribution directory amg4psblas/examples/gpu. -

First of all, we need to include the appropriate modules and declare some auxiliary variables: -

@@ -758,7 +772,7 @@ class="cmr-12">variables:
-

+

 program amg_dexample_gpu
   use psb_base_mod
@@ -777,7 +791,7 @@ program amg_dexample_gpu
 
  
-

+


Listing 5: setup of a GPU-enabled test program part one.
@@ -785,7 +799,7 @@ class="content">setup of a GPU-enabled test program part one.

In this particular example we are choosing to employ a HLG data structure for @@ -793,14 +807,14 @@ class="cmr-12">data structure for class="cmr-12">sparse matrices on GPUs; for more information please refer to the PSBLAS users’ guide. -

We then have to initialize the GPU environment, and pass the appropriate MOLD variables to the build methods (see also the PSBLAS users’ guide). -

@@ -808,7 +822,7 @@ class="cmr-12">variables to the build methods (see also the PSBLAS users’
-

+

   call psb_init(ctxt)
   call psb_info(ctxt,iam,np)
@@ -823,7 +837,7 @@ class="cmr-12">variables to the build methods (see also the PSBLAS users’
 
  
-

+


Listing 6: setup of a GPU-enabled test program part two.
@@ -831,7 +845,7 @@ class="content">setup of a GPU-enabled test program part two.

Finally, we convert the input matrix, the descriptor and the vectors to use a GPU-enabled internal storage format. We then preallocate the preconditioner @@ -842,7 +856,7 @@ class="cmr-12">GPU environment -

@@ -850,7 +864,7 @@ class="cmr-12">GPU environment
-

+

   call desc_a%cnv(mold=igmold)
   call a%cscnv(info,mold=agmold)
@@ -877,7 +891,7 @@ class="cmr-12">GPU environment
 
  
-

+


Listing 7: setup of a GPU-enabled test program part three.
@@ -885,7 +899,7 @@ class="content">setup of a GPU-enabled test program part three.

It is very important to employ smoothers and coarsest solvers that are suited to the GPU, i.e. methods that do NOT employ triangular system solve kernels. Methods that @@ -893,30 +907,30 @@ class="cmr-12">GPU, i.e. methods that do NOT employ triangular system solve kern class="cmr-12">satisfy this constraint include:

  • -

    JACOBI

  • -

    BJAC with the following methods on the local blocks:

    • -

      INVK

    • -

      INVT

    • -

      AINV

  • -

    POLY

-

and their ℓ1 point-Jacobi, hybrid (forward) Gauss-Seidel, and hybrid backward class="cmr-12">the previous smoothers can be defined just by setting ’SMOOTHER_TYPE’ to certain specific values (see Tablescertain specific values (see Table 7accelerated using the specified polynomial smoothing technique. B ℓ1-Jacobi smoother serves as the base smoother, offering theoretical guarantees on the +class="cmr-12">-Jacobi smoother serves as the base smoother, offering theoretical guarantees resulting convergence factoron the resulting convergence factor [ 27]. Alternative combinations are experimental and +class="cmr-12">. Alternative combinations are lack established guarantees.
experimental.
-

Remark 4. Many of the coarsest-level solvers apply to a specific coarsest-matrix layout; therefore, setting the solver after the layout may change the layout to either distributed or replicated. Similarly, setting the layout after the solver may change the +class="cmr-12">distributed or replicated, and similarly, setting the layout after the solver may solver. -

More precisely, UMFPACK and SuperLU require the coarsest-level matrix to be +class="cmr-12">change the solver. More specifically, UMFPACK and SuperLU require the replicated, while SuperLU_Dist and KRM require it to be distributed. In these cases, +class="cmr-12">coarsest-level matrix to be replicated, while SuperLU_Dist and KRM require it to setting the coarsest-level solver implies that the layout is redefined according to the +class="cmr-12">be distributed; therefore, setting the coarsest-level solver implies that the solver, ovverriding any previous settings. MUMPS, point-Jacobi, hybrid Gauss-Seidel +class="cmr-12">layout is redefined according to the solver, ovverriding any previous settings. and block-Jacobi can be applied to replicated and distributed matrices, thus their +class="cmr-12">MUMPS, point-Jacobi, hybrid Gauss-Seidel and block-Jacobi can be applied to choice does not modify any previously specified layout. It is worth noting that, when +class="cmr-12">replicated and distributed matrices, thus their choice does not modify any the matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers +class="cmr-12">previously specified layout. It is worth noting that, when the matrix is replicated, and their the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers and their ℓ1- - +versions reduce to the corresponding local solver objects (see Remark 2). +class="cmr-12"> 2). For the For the point-Jacobi and Gauss-Seidel solvers, these objects correspond to a point-Jacobi and Gauss-Seidel solvers, these objects correspond to a single point-Jacobi sweep and a single Gauss-Seidel sweep, respectively, which are very poor solvers. -

On the other hand, the distributed layout can be used with any solver but +

On the other hand, the distributed layout can be used with any solver except and UMFPACK and SuperLU; therefore, if any of these two solvers has already been +class="cmr-12">SuperLU; therefore, if any of these two solvers has already been selected, the selected, the coarsest-level solver is changed to block-Jacobi, with the previously chosen +class="cmr-12">coarsest-level solver is changed to block-Jacobi, with the previously chosen solver solver applied to the local blocks. Likewise, the replicated layout can be used with any +class="cmr-12">applied to the local blocks. Likewise, the replicated layout can be used with any solver solver but SuperLubut SuperLu_Dist and KRM; therefore, if SuperLu_Dist or KRM have been previously set, the coarsest-level solver is changed to the default sequential solver. -

In a parallel setting with many cores, we suggest to the users to change the default coarsest solver for using the KRM choice, i.e. a parallel distributed iterative solution of @@ -615,7 +614,7 @@ class="cmr-12">the coarsest system based on Krylov methods. -

Remark 4. The argument idx can be used to allow finer control for those solvers; @@ -635,7 +634,7 @@ class="cmr-12">. -

@@ -643,7 +642,7 @@ class="cmr-12">.
-

+

+class="td11">

1

Parameters defining the aggregation algorithm.

@@ -948,7 +947,7 @@ class="content">Parameters defining the aggregation algorithm.

+

what

what

dtype

val

val

deault

cots

’ML_CYCLE’

character(len=*)

’VCYCLE’ -

’WCYCLE’ -

’KCYCLE’ -

’ADD’

’VCYCLE’

Multilevel cycle: V-cycle, W-cycle, K-cycle, +class="td11">

’ML_CYCLE’

character(len=*)

’VCYCLE’ +

’WCYCLE’ +

’KCYCLE’ +

’ADD’

’VCYCLE’

Multilevel cycle: V-cycle, W-cycle, K-cycle, and additive composition.

’CYCLE_SWEEPS’

integer

Any integer -

number

’CYCLE_SWEEPS’

integer

Any integer +

number ≥ 1

1

Number of multilevel cycles.

Number of multilevel cycles.

-

@@ -731,7 +730,7 @@ applied.
-

+

@@ -745,7 +744,7 @@ id="TBL-5-4">

what

what

dtype

val

val

deault

cots

’MIN_COARSE_SIZE_PER_PROCESS’

integer

Any number -

’MIN_COARSE_SIZE_PER_PROCESS’

integer

Any number +

> 0

200

Coarse size threshold per process. The +class="td11">

200

Coarse size threshold per process. The aggregation stops if the global number of variables of the computed coarsest matrix is lower than or equal to this @@ -793,13 +792,13 @@ processes (see Note).

’MIN_COARSE_SIZE’

integer

Any number -

’MIN_COARSE_SIZE’

integer

Any number +

> 0

-1

Coarse size threshold. The aggregation +class="td11">

-1

Coarse size threshold. The aggregation stops if the global number of variables of the computed coarsest matrix is lower than or equal to this @@ -809,13 +808,13 @@ ignored in favour of the default for

’MIN_CR_RATIO’

real

Any number -

’MIN_CR_RATIO’

real

Any number +

> 1

1.5

Minimum coarsening ratio. The +class="td11">

1.5

Minimum coarsening ratio. The aggregation stops if the ratio between the global matrix dimensions at two consecutive levels is lower than or @@ -823,30 +822,30 @@ equal to this threshold (see Note).

’MAX_LEVS’

integer

Any integer -

number

’MAX_LEVS’

integer

Any integer +

number > 1

20

Maximum number of levels. The +class="td11">

20

Maximum number of levels. The aggregation stops if the number of levels reaches this value (see Note).

’PAR_AGGR_ALG’

character(len=*)

’PAR_AGGR_ALG’

character(len=*)

’DECOUPLED’, ’SYMDEC’, ’COUPLED’

’DECOUPLED’

Parallel aggregation algorithm. -

the SYMDEC option applies decoupled +class="td11">

Parallel aggregation algorithm. +

the SYMDEC option applies decoupled aggregation to the sparsity pattern of A + T .

’AGGR_TYPE’

character(len=*)

’SOC1’, +class="td11">

’AGGR_TYPE’

character(len=*)

’SOC1’, ’SOC2’, ’MATCHBOXP’

’SOC1’

Type +class="td11">

’SOC1’

Type of aggregation algorithm: currently, for the decoupled aggregation we implement two measures of strength @@ -878,18 +877,18 @@ href="userhtmlli3.html#XMatchBoxP">9].

’AGGR_SIZE’

integer

Any integer -

power of 2, +class="td11">

’AGGR_SIZE’

integer

Any integer +

power of 2, with aggr_size ≥ 2

4

Maximum size of aggregates when +class="td11">

4

Maximum size of aggregates when the coupled aggregation based on matching is applied. For aggressive coarsening with size of aggregate @@ -901,12 +900,12 @@ class="cmtt-10x-x-109">’MATCHBOXP’

’AGGR_PROL’

character(len=*)

’SMOOTHED’, +class="td11">

’AGGR_PROL’

character(len=*)

’SMOOTHED’, ’UNSMOOTHED’

’SMOOTHED’

Prolongator used by the aggregation +class="td11">

’SMOOTHED’

Prolongator used by the aggregation algorithm: smoothed or unsmoothed (i.e., tentative prolongator).

Parameters defining the aggregation algorithm (continued).

@@ -1068,7 +1067,7 @@ class="content">Parameters defining the aggregation algorithm (continued). -

+

@@ -1082,7 +1081,7 @@ id="TBL-7-4">

@@ -1332,7 +1331,7 @@ class="content">Parameters defining the solver at the coarsest level (continued) -

@@ -1340,7 +1339,7 @@ class="content">Parameters defining the solver at the coarsest level (continued)
-

+

@@ -1354,7 +1353,7 @@ id="TBL-8-4">

+class="td11">

The stopping tolerance.

Additional parameters defining the solver at the coarsest level. -

@@ -1639,7 +1638,7 @@ class="content">Additional parameters defining the solver at the coarsest level.
-

+

what

what

dtype

val

val

deault

cots

’AGGR_ORD’

character(len=*)

’AGGR_ORD’

character(len=*)

’NATURAL’ -

’DEGREE’

’NATURAL’

Initial ordering of indices for +class="td11">

Initial ordering of indices for the decoupled aggregation algorithm: either natural ordering or sorted by descending degrees of the nodes in the @@ -1008,30 +1007,30 @@ matrix graph.

’AGGR_THRESH’

real(kind_parameter)

Any real -

number 

’AGGR_THRESH’

real(kind_parameter)

Any real +

number ∈ [0,1]

0.01

The threshold

0.01

The threshold θ in the strength of connection algorithm. See also the note at the bottom of this table.

’AGGR_FILTER’

character(len=*)

’AGGR_FILTER’

character(len=*)

’FILTER’ -

’NOFILTER’

’NOFILTER’

Matrix used in computing the smoothed +class="td11">

Matrix used in computing the smoothed prolongator: filtered or unfiltered.

what

what

dtype

val

val

deault

cots

’COARSE_MAT’

character(len=*)

’DIST’ -

’REPL’

’REPL’

Coarsest matrix layout: distributed among the +class="td11">

’COARSE_MAT’

character(len=*)

’DIST’ +

’REPL’

’REPL’

Coarsest matrix layout: distributed among the processes or replicated on each of them.

’COARSE_SOLVE’

character(len=*)

’MUMPS’ -

’UMF’ -

’SLU’ -

’SLUDIST’ -

’ILU’ -

’JACOBI’ -

’GS’ -

’BJAC’ -

’KRM’ -

’L1-JACOBI’ -

’L1-BJAC’ -

’L1-FBGS’

See Note.

Solver used at the coarsest level: sequential +class="td11">

’COARSE_SOLVE’

character(len=*)

’MUMPS’ +

’UMF’ +

’SLU’ +

’SLUDIST’ +

’ILU’ +

’JACOBI’ +

’GS’ +

’BJAC’ +

’KRM’ +

’L1-JACOBI’ +

’L1-BJAC’ +

’L1-FBGS’

See Note.

Solver used at the coarsest level: sequential LU from MUMPS, UMFPACK, or SuperLU (plus triangular solve); distributed LU from MUMPS or SuperLU_Dist (plus triangular solve); @@ -1170,20 +1169,20 @@ double precision.

’COARSE_SUBSOLVE’

character(len=*)

’ILU’ -

’ILUT’ -

’MILU’ -

’MUMPS’ -

’SLU’ -

’SLUDIST’ -

’UMF’ -

’INVT’ -

’INVK’ -

’AINV’

See Note.

Solver for the diagonal blocks of the coarsest +class="td11">

’COARSE_SUBSOLVE’

character(len=*)

’ILU’ +

’ILUT’ +

’MILU’ +

’MUMPS’ +

’SLU’ +

’SLUDIST’ +

’UMF’ +

’INVT’ +

’INVK’ +

’AINV’

See Note.

Solver for the diagonal blocks of the coarsest matrix, in case the block Jacobi solver is chosen as coarsest-level solver: ILU(p), ILU(ILU otherwise.

what

what

dtype

val

val

deault

cos

’COARSE_SWEEPS’

integer

Any +class="td11">

’COARSE_SWEEPS’

integer

Any integer number > 0

10

Number of sweeps when JACOBI, GS or BJAC is +class="td11">

10

Number of sweeps when JACOBI, GS or BJAC is chosen as coarsest-level solver.

’COARSE_FILLIN’

integer

Any +class="td11">

’COARSE_FILLIN’

integer

Any integer number ≥ 0

0

Fill-in level

0

Fill-in level p of the ILU factorizations and first fill-in for the approximate inverses.

’COARSE_ILUTHRS’

real(kind_parameter)

Any real +class="td11">

’COARSE_ILUTHRS’

real(kind_parameter)

Any real number ≥ 0

0

Drop tolerance

0

Drop tolerance t in the ILU(p,t) factorization and first drop-tolerance for the approximate inverses.

what

what

dtype

val

val

deault

cots

’BJAC_STOP’

character(len=*)

’FALSE’ -

’TRUE’

’FALSE’

Select whether to use a stopping criterion for +class="td11">

’BJAC_STOP’

character(len=*)

’FALSE’ +

’TRUE’

’FALSE’

Select whether to use a stopping criterion for the Block-Jacobi method used as a coarse solver.

’BJAC_TRACE’

character(len=*)

’FALSE’ -

’TRUE’

’FALSE’

Select whether to print a trace for the +class="td11">

’BJAC_TRACE’

character(len=*)

’FALSE’ +

’TRUE’

’FALSE’

Select whether to print a trace for the calculated residual for the Block-Jacobi method used as a coarse solver.

’BJAC_ITRACE’

integer

Any integer -

’BJAC_ITRACE’

integer

Any integer +

> 0

-1

Number of iterations after which a trace is to +class="td11">

-1

Number of iterations after which a trace is to be printed.

’BJAC_RESCHECK’

integer

Any integer -

’BJAC_RESCHECK’

integer

Any integer +

> 0

-1

Number of iterations after which a residual is +class="td11">

-1

Number of iterations after which a residual is to be calculated.

’BJAC_STOPTOL’

real(kind_parameter)

Any real -

’BJAC_STOPTOL’

real(kind_parameter)

Any real +

< 1

0

Tolerance for the stopping criterion on the +class="td11">

0

Tolerance for the stopping criterion on the residual.

’KRM_METHOD’

character(len=*)

’CG’ -

’FCG’ -

’CGS’ -

’CGR’ -

’BICG’ -

’BICGSTAB’ -

’BICGSTABL’ -

’RGMRES’

’FCG’

A string that defines the iterative method to +class="td11">

’KRM_METHOD’

character(len=*)

’CG’ +

’FCG’ +

’CGS’ +

’CGR’ +

’BICG’ +

’BICGSTAB’ +

’BICGSTABL’ +

’RGMRES’

’FCG’

A string that defines the iterative method to be used when employing a Krylov method ’KRM’ as a coarse solver. CG the Conjugate @@ -1482,24 +1481,24 @@ information.

’KRM_KPREC’

character(len=*)

Table 

’KRM_KPREC’

character(len=*)

Table 1

’BJAC’

The one-level +class="td11">

’BJAC’

The one-level preconditioners from the Table 1 can be used for the coarse Krylov solver.

’KRM_SUB_SOLVE’

character(len=*)

Table 

’KRM_SUB_SOLVE’

character(len=*)

Table 5

’ILU’

Solver for the diagonal blocks of the coarsest +class="td11">

’ILU’

Solver for the diagonal blocks of the coarsest matrix preconditioner, in case the block Jacobi solver is chosen as ’KRM_KPREC’: ILU(5 applies here.

’KRM_GLOBAL’

character(len=*)

’TRUE’, +class="td11">

’KRM_GLOBAL’

character(len=*)

’TRUE’, ’FALSE’

’FALSE’

Choose between a global Krylov solver, all +class="td11">

’FALSE’

Choose between a global Krylov solver, all unknowns on a single node, or a distributed one. The default choice is the distributed solver.

’KRM_EPS’

real(kind_parameter)

Real

’KRM_EPS’

real(kind_parameter)

Real < 1

10

10-6

The stopping tolerance.

’KRM_IRST’

integer

Integer -

’KRM_IRST’

integer

Integer +

≥ 1

30

An integer specifying the restart parameter. +class="td11">

30

An integer specifying the restart parameter. This is employed for the BiCGSTABL or RGMRES @@ -1560,12 +1559,12 @@ methods, otherwise it is ignored.

’KRM_ISTOPC’

integer

Integers +class="td11">

’KRM_ISTOPC’

integer

Integers 1,2,3

2

If

2

If 1 then the method uses the normwise backward error in the infinity norm; if 2, the @@ -1578,24 +1577,24 @@ for the details.

’KRM_ITMAX’

integer

Integer -

’KRM_ITMAX’

integer

Integer +

≥ 1

40

The maximum number of iterations to +class="td11">

40

The maximum number of iterations to perform.

’KRM_ITRACE’

integer

Integer -

’KRM_ITRACE’

integer

Integer +

≥ 0

-1

If

-1

If > 0 print out an informational message about convergence every ’KRM_ITRACE’ iterations. If = 0 print a @@ -1603,13 +1602,13 @@ message in case of convergence failure.

’KRM_FILLIN’

integer

Integer -

’KRM_FILLIN’

integer

Integer +

≥ 0

0

Fill-in level

0

Fill-in level p of the ILU factorizations and first fill-in for the approximate inverses.

what

what

dtype

val

val

deault

cots

’SMOOTHER_TYPE’

character(len=*)

’JACOBI’ -

’GS’ -

’BGS’ -

’BJAC’ -

’AS’ -

’L1-JACOBI’ -

’L1-BJAC’ -

’L1-FBGS’ -

’POLY’

’FBGS’

’SMOOTHER_TYPE’

character(len=*)

’JACOBI’ +

’GS’ +

’BGS’ +

’BJAC’ +

’AS’ +

’L1-JACOBI’ +

’L1-BJAC’ +

’L1-FBGS’ +

’POLY’

’FBGS’

Type of smoother used in the multilevel preconditioner: point-Jacobi, hybrid @@ -1726,26 +1725,26 @@ class="cmr-10">] class="cmr-10">and Remark 3 (p. 21). -

It is ignored by one-level preconditioners.

’SUB_SOLVE’

character(len=*)

’JACOBI’ +class="td11">

’SUB_SOLVE’

character(len=*)

’JACOBI’ ’GS’ -

’BGS’ -

’ILU’ -

’ILUT’ -

’MILU’ -

’MUMPS’ -

’SLU’ -

’UMF’ -

’INVT’ -

’INVK’ -

’AINV’

’BGS’ +

’ILU’ +

’ILUT’ +

’MILU’ +

’MUMPS’ +

’SLU’ +

’UMF’ +

’INVT’ +

’INVK’ +

’AINV’

GS and BGS multilevel class="cmr-10">preconditioners, respectively -

ILU for block-Jacobi and Additive Schwarz class="cmr-10">one-level preconditioners

The local solver to be used with the smoother or one-level preconditioner (see @@ -1823,18 +1822,18 @@ class="cmr-10">Note for details on hybrid Gauss-Seidel.

’SMOOTHER_SWEEPS’

integer

’SMOOTHER_SWEEPS’

integer

Any integer -

number ≥ 0

1

Number of sweeps of the smoother or one-level preconditioner. In the multilevel @@ -1852,11 +1851,11 @@ class="cmr-10">respectively. Is ignored if the smoother is

’POLY_DEGREE’

integer

’POLY_DEGREE’

integer

Any integer -

number ≥ and ≤ 30

1

Degree of the polynomial accelerator, is equal to the number of matrix-vector @@ -1893,7 +1892,7 @@ preconditioner. -

@@ -1901,7 +1900,7 @@ preconditioner.
-

+

what

what

dtype

val

val

deault

cots

’SUB_OVR’

integer

’SUB_OVR’

integer

Any integer -

number ≥ 0

1

Number of overlap layers, for Additive Schwarz only.

’SUB_RESTR’

character(len=*)

’HALO’ -

’NONE’

’HALO’

’SUB_RESTR’

character(len=*)

’HALO’ +

’NONE’

’HALO’

Type of restriction operator, for Additive Schwarz only: for taking into account the overlap, ’NONE’ for neglecting it. -

Note that HALO must be chosen for the @@ -1987,12 +1986,12 @@ class="cmr-10">its RAS variant.

’SUB_PROL’

character(len=*)

’SUM’ -

’NONE’

’NONE’

’SUB_PROL’

character(len=*)

’SUM’ +

’NONE’

’NONE’

Type of prolongation operator, for Additive Schwarz only: ’SUM’ contributions from the overlap, for neglecting them. -

Note that ’SUM’ must be chosen for the for its RAS variant.

’SUB_FILLIN’

integer

’SUB_FILLIN’

integer

Any integer -

number ≥ 0

0

Fill-in level p of the incomplete LU @@ -2032,18 +2031,18 @@ class="cmr-10">factorizations.

’SUB_ILUTHRS’

real(kind_parameter)

’SUB_ILUTHRS’

real(kind_parameter)

Any real number ≥ 0

0

Drop tolerance t in the ILU(factorization.

’MUMPS_LOC_GLOB’

character(len=*)

’LOCAL_SOLVER’ -

’GLOBAL_SOLVER’

’GLOBAL_SOLVER’

’MUMPS_LOC_GLOB’

character(len=*)

’LOCAL_SOLVER’ +

’GLOBAL_SOLVER’

’GLOBAL_SOLVER’

Whether MUMPS should be used as a distributed solver, or as a serial solver acting @@ -2070,15 +2069,15 @@ class="cmr-10">process.

’MUMPS_IPAR_ENTRY’

integer

’MUMPS_IPAR_ENTRY’

integer

Any integer number

0

Set an entry in the MUMPS integer control array, as chosen via the idx argument.

’MUMPS_RPAR_ENTRY’

real

’MUMPS_RPAR_ENTRY’

real

Any real number

0

Set an entry in the MUMPS real control array, as chosen via the idx Parameters defining the smoother or the details of the one-level -

@@ -2126,7 +2125,7 @@ class="content">Parameters defining the smoother or the details of the one-level
-

+

what

what

dtype

val

val

deault

cots

’POLY_VARIANT’

character(len=*)

’CHEB_4’ -

’CHEB_4_OPT’ -

’CHEB_1_OPT’

’CHEB_4’

’POLY_VARIANT’

character(len=*)

’CHEB_4’ +

’CHEB_4_OPT’ +

’CHEB_1_OPT’

’CHEB_4’

Select the type of polynomial accelerator. @@ -2226,11 +2225,11 @@ class="cmr-10">-kind.

’POLY_RHO_ESTIMATE’

character(len=*)

’POLY_RHO_EST_POWER’

’POLY_RHO_EST_POWER’

’POLY_RHO_ESTIMATE’

character(len=*)

’POLY_RHO_EST_POWER’

’POLY_RHO_EST_POWER’

Algorithm for estimating the spectral @@ -2253,17 +2252,17 @@ class="cmr-10">two following options.

’POLY_RHO_ESTIMATE_ITERATIONS’

integer

’POLY_RHO_ESTIMATE_ITERATIONS’

integer

Any integer -

number ≥ 1

20

Number of iterations for the spectral radius @@ -2272,19 +2271,19 @@ class="cmr-10">estimate.

’POLY_RHO_BA’

real(kind_parameter)

’POLY_RHO_BA’

real(kind_parameter)

Any real -

number ∈ (0,1]

1

Sets an estimate of the spectral radius of @@ -2317,10 +2316,10 @@ class="cmr-12">Method hierarchy_build

-

-

call p%hierarchy_build(a,desc_a,info)
+

+

call p%hierarchy_build(a,desc_a,info)

-

This method builds the hierarchy of matrices and restriction/prolongation operators for the multilevel preconditioner p, according to the requirements made by the user class="cmr-12">through the methods init and set. -

Arguments

Arguments id="TBL-12-1">

a

type(psb_

a

type(psb_xspmat_type), intent(in).

The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that ].

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor of a. See the PSBLAS User’s Guide ].

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section Method smoothers_build

-

-

call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])
+

+

call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])

-

This method builds the smoothers and the coarsest-level solvers for the multilevel preconditioner p 5.3). -

Arguments

Arguments id="TBL-13-1"> @@ -2542,10 +2541,10 @@ class="cmr-12">5.5 Method build
-

-

call p%build(a,desc_a,info[,amold,vmold,imold])
+

+

call p%build(a,desc_a,info[,amold,vmold,imold])

-

This method builds the preconditioner p according to the requirements made by the and class="cmr-12">, whose nomenclature would however be somewhat unnatural when dealing with simple one-level preconditioners. -

Arguments

a

type(psb_

a

type(psb_xspmat_type), intent(in).

The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that ].

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor of a. See the PSBLAS User’s Guide ].

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

amold

class(psb_

amold

class(psb_x_base_sparse_mat), intent(in), optional.

The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same on all @@ -2507,26 +2506,26 @@ class="cmr-12">].

vmold

class(psb_

vmold

class(psb_x_base_vect_type), intent(in), optional.

The desired dynamic type for internal vector components; this allows e.g. running on GPUs.

imold

class(psb_i_base_vect_type), intent(in), optional

imold

class(psb_i_base_vect_type), intent(in), optional.

The desired dynamic type for internal integer vector components; this allows e.g. running on GPUs.

Arguments id="TBL-14-1">

a

type(psb_

a

type(psb_xspmat_type), intent(in).

The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that ].

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor of a. See the PSBLAS User’s Guide ].

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

amold

class(psb_

amold

class(psb_x_base_sparse_mat), intent(in), optional.

The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same on all @@ -2654,33 +2653,33 @@ class="cmr-12">].

vmold

class(psb_

vmold

class(psb_x_base_vect_type), intent(in), optional.

The desired dynamic type for internal vector components; this allows e.g. running on GPUs.

imold

class(psb_i_base_vect_type), intent(in), optional

imold

class(psb_i_base_vect_type), intent(in), optional.

The desired dynamic type for internal integer vector components; this allows e.g. running on GPUs.

-

The method can be used to build multilevel preconditioners too. @@ -2691,10 +2690,10 @@ class="cmr-12">5.6 Method apply

-

-

call p%apply(x,y,desc_a,info [,trans,work])
+

+

call p%apply(x,y,desc_a,info [,trans,work])

-

This method computes y = and class="cmr-12">hence it is completely transparent to the user, who will almost never invoke it directly. -

Arguments

Arguments id="TBL-15-1"> +class="td11">

trans

x

x

type(kind_parameter), dimension(:), intent(in)—.

The local part of the vector x. Note that , single/double class="cmr-12">precision version of AMG4PSBLAS under use.

y

y

type(kind_parameter), dimension(:), intent(out)—.

The local part of the vector y. Note that , single/double class="cmr-12">precision version of AMG4PSBLAS under use.

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor associated to the matrix to be preconditioned.

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

trans

character(len=1), optional, intent(in).

character(len=1), optional, intent(in).

If trans = ’N’,’n’ then 1).

work

work

type(kind_parameter), dimension(:), optional, target—.

Workspace. Its size should be at least 4 * psb_cd_get_local_ cols(desc_a) (see the PSBLAS User’s Guide). Note that 5.7 Method free

-

-

call p%free(p,info)
+

+

call p%free(p,info)

-

This method deallocates the preconditioner data structure p. -

Arguments

Arguments id="TBL-16-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 5.8 Method descr

-

-

call p%descr(info, [iout, root, verbosity])
+

+

call p%descr(info, [iout, root, verbosity])

-

This method prints a description of the preconditioner p to the standard output or to a , or b class="cmr-12">, have been called. -

Arguments

Arguments id="TBL-17-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

iout

integer, intent(in), optional

iout

integer, intent(in), optional.

The id of the file where the preconditioner description will be printed; the default is the standard output.

root

integer, intent(in), optional

root

integer, intent(in), optional.

The id of the process where the preconditioner description will be printed; the default is psb_root_.

verbosity

integer, intent(in), optional

verbosity

integer, intent(in), optional.

The verbosity level of the description. Default value is 0. For values higher than 0, it prints out further information, e.g., for @@ -3009,31 +3008,31 @@ class="cmr-12">matrices on every process.

-

+

5.9 Auxiliary Methods

-

Various functionalities are implemented as additional methods of the preconditioner object. -

+

5.9.1 Method: dump
-

-

call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])
+

+

call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])

-

Dump on file.

Dump on file. +

Arguments

Arguments id="TBL-18-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

amold

class(psb_

amold

class(psb_x_base_sparse_mat), intent(in), optional.

The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same on all @@ -3076,19 +3075,19 @@ class="cmr-12">.

-

+

5.9.2 Method: clone
-

-

call p%clone(pout,info)
+

+

call p%clone(pout,info)

-

Create a (deep) copy of the preconditioner object.

Create a (deep) copy of the preconditioner object. +

Arguments

Arguments id="TBL-19-1">

pout

type(amg_

pout

type(amg_xprec_type), intent(out).

The copy of the preconditioner data structure. Note that x must @@ -3115,13 +3114,13 @@ class="cmr-12">, single/double precision class="cmr-12">version of AMG4PSBLAS under use.

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section for details.

-

+

5.9.3 Method: sizeof
-

-

sz = p%sizeof([global])
+

+

sz = p%sizeof([global])

Method: sizeof id="TBL-20-1">

global

logical, optional

global

logical, optional.

Whether the global or local preconditioner memory occupation is desired. Default: .false.Return memory footprint in bytes. -

+

5.9.4 Method: allocate_wrk
-

-

call p%allocate_wrk(info[, vmold])
+

+

call p%allocate_wrk(info[, vmold])

-

Allocate internal work vectors. Each application of the preconditioner uses a number of work vectors which are allocated internally as necessary; therefore allocation and @@ -3202,7 +3201,7 @@ class="cmr-12">taken care of based on the dynamic type of the argument to the apply method. -

Arguments

Arguments id="TBL-21-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

vmold

class(psb_

vmold

class(psb_x_base_vect_type), intent(in), optional.

The desired dynamic type for internal vector components; this allows e.g. running on GPUs.

-

+

5.9.5 Method: deallocate_wrk
-

-

call p%deallocate_wrk(info)
+

+

call p%deallocate_wrk(info)
call p%free_wrk(info)

-

Deallocate internal work vectors.

Deallocate internal work vectors. +

Arguments

Arguments id="TBL-22-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section . +

+ + + diff --git a/docs/html/userhtmlse8.html b/docs/html/userhtmlse8.html index 0b786932..67408b51 100644 --- a/docs/html/userhtmlse8.html +++ b/docs/html/userhtmlse8.html @@ -38,46 +38,47 @@ class="cmr-12">AMG4PSBLAS is freely distributable under the following copyright 

 
-                           AMG4PSBLAS  version 1.0
-              Algebraic MultiGrid Preconditioners Package
-             based on PSBLAS (Parallel Sparse BLAS version 3.7)
 
-  (C) Copyright 2021
-
-  Pasqua D’Ambra         IAC-CNR, IT
-  Fabio Durastante       University of Pisa and IAC-CNR, IT
-  Salvatore Filippone    University of Rome Tor-Vergata and IAC-CNR, 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.
+                             AMG4PSBLAS version 1.2
+    Algebraic Multigrid Package
+               based on PSBLAS (Parallel Sparse BLAS version 3.9)
+
+    (C) Copyright 2025
+
+        Salvatore Filippone
+        Pasqua D’Ambra
+        Fabio Durastante
+
+    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 AMG4PSBLAS 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 AMG4PSBLAS 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.
-

+

-

AMG4PSBLAS is an evolution of MLD2P4, whose license we reproduce here to abide by its terms: @@ -123,7 +124,7 @@ class="cmr-12">abide by its terms:   POSSIBILITY OF SUCH DAMAGE. -

AMG4PSBLAS is distributed together with (a small part of) the graph-matching @@ -183,7 +184,7 @@ class="cmr-12">here. // // ************************************************************************ -

+

diff --git a/docs/src/abstract.tex b/docs/src/abstract.tex index 74e85b80..d074fa1e 100644 --- a/docs/src/abstract.tex +++ b/docs/src/abstract.tex @@ -4,30 +4,42 @@ \fi \textsc{AMG4PSBLAS (Algebraic MultiGrid Preconditioners Package -based on PSBLAS}) is a package of parallel algebraic multilevel preconditioners included in the PSCToolkit (Parallel Sparse Computation Toolkit) software framework. -It is a progress of a software development project started in 2007, named MLD2P4, which originally implemented a -multilevel version of some domain decomposition preconditioners of additive-Schwarz type, and was based on a parallel decoupled version of the well known smoothed +based on PSBLAS}) is a package of parallel algebraic multilevel +preconditioners included in the PSCToolkit (Parallel Sparse +Computation Toolkit) software framework. +It is an evolutiuon of a software development project started in 2007, +named MLD2P4, which originally implemented a +multilevel version of some domain decomposition preconditioners of +additive-Schwarz type, and was based on a parallel decoupled version +of the well known smoothed aggregation method to generate the multilevel hierarchy of coarser matrices. -In the last years, within the context of the EU-H2020 EoCoE project (Energy Oriented Center of Excellence), the package was extended for including new algorithms and -functionalities for the setup and application new AMG preconditioners with the final aims of improving efficiency and scalability when tens of thousands cores are -used, and of boosting reliability in dealing with general symmetric positive definite linear systems. -Due to the significant number of changes and the increase in scope, we decided to rename the package as AMG4PSBLAS. +In the last few years the package was extended for +including new algorithms and +functionalities for the setup and application new AMG preconditioners +with the final aims of improving efficiency and scalability when tens +of thousands cores are used, and of boosting reliability in dealing +with general symmetric positive definite linear systems; these +developments have been supported in the context of the EU-H2020 EoCoE +project (Energy Oriented Center of Excellence). +Due to the significant number of changes and the increase in scope, we +decided to rename the package as AMG4PSBLAS. -AMG4PSBLAS has been designed to provide scalable and easy-to-use preconditioners -in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) -computational framework and can be used in conjuction with the Krylov solvers -available in this framework. +AMG4PSBLAS has been designed to provide scalable and easy-to-use +preconditioners in the context of the PSBLAS (Parallel Sparse Basic +Linear Algebra Subprograms) computational framework and can be used in +conjuction with the Krylov solvers available in this framework. Our package is based on a completely algebraic approach; therefore users level interfaces assume that the system matrix and preconditioners are represented as PSBLAS distributed sparse matrices. AMG4PSBLAS enables the user to easily specify different -features of an algebraic multilevel preconditioner, thus allowing to experiment -with different preconditioners for the problem and parallel computers at hand. +features of an algebraic multilevel preconditioner, thus allowing to +experiment with different preconditioners for the problem and parallel +computers at hand. The package employs object-oriented design techniques in -Fortran~2003, with interfaces to additional third party libraries +Fortran~2003, with interfaces to additional third party libraries such as MUMPS, UMFPACK, SuperLU, and SuperLU\_Dist, which -can be exploited in building multilevel preconditioners. The parallel +can be exploited in building multilevel preconditioners. The parallel implementation is based on a Single Program Multiple Data (SPMD) paradigm; the inter-process communication is based on MPI and is managed mainly through PSBLAS. diff --git a/docs/src/building.tex b/docs/src/building.tex index a4b6aba5..f3a15583 100644 --- a/docs/src/building.tex +++ b/docs/src/building.tex @@ -13,19 +13,20 @@ must support the Fortran~2003 standard plus the extension \verb|MOLD=| feature, which enhances the usability of \verb|ALLOCATE|. Most Fortran compilers provide this feature; in particular, this is supported by the GNU Fortran compiler, for which we -recommend to use at least version 4.8. +recommend to use at least version 12. The software defines data types and interfaces for real and complex data, in both single and double precision. Building AMG4PSBLAS requires some base libraries (see -Section~\ref{sec:prerequisites}); interfaces to optional third-party +Section~\ref{sec:prerequisites}); interfaces to optional third-party libraries, which extend the functionalities of AMG4PSBLAS (see -Section~\ref{sec:third-party}), are also available. A number of Linux -distributions (e.g., Ubuntu, Fedora, CentOS) provide precompiled +Section~\ref{sec:third-party}), are also available. A number of Linux +distributions (e.g., Ubuntu, Fedora, CentOS) provide precompiled packages for the prerequisite and optional software. In many cases these packages are split between a runtime part and a ``developer'' part; in order to build AMG4PSBLAS you need both. A description of the -base and optional software used by AMG4PSBLAS is given in the next sections. +base and optional software used by AMG4PSBLAS is given in the next +sections. \subsection{Prerequisites\label{sec:prerequisites}} @@ -157,17 +158,17 @@ The full set of options may be looked at by issuing the command \else \lstinputlisting{../configureout.txt} \fi -For instance, if a user has built and installed PSBLAS 3.7 under the +For instance, if a user has built and installed PSBLAS 3.9 under the \verb|/opt| directory and is using the SuiteSparse package (which includes UMFPACK), then AMG4PSBLAS might be configured with: \ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{console} -./configure --with-psblas=/opt/psblas-3.7/ --with-umfpackincdir=/usr/include/suitesparse/ +./configure --with-psblas=/opt/psblas-3.9/ --with-umfpackincdir=/usr/include/suitesparse/ \end{minted} \else \begin{verbatim} -./configure --with-psblas=/opt/psblas-3.7/ \ +./configure --with-psblas=/opt/psblas-3.9/ \ --with-umfpackincdir=/usr/include/suitesparse/ \end{verbatim} \fi diff --git a/docs/src/gettingstarted.tex b/docs/src/gettingstarted.tex index 4e1678a2..52b34a3d 100644 --- a/docs/src/gettingstarted.tex +++ b/docs/src/gettingstarted.tex @@ -94,7 +94,6 @@ Multilevel &\fortinline|'ML'| & V-cycle with one hybrid forward Gauss- \label{tab:precinit}} \end{center} \end{table} - Note that the module \fortinline|amg_prec_mod|, containing the definition of the preconditioner data type and the interfaces to the routines of AMG4PSBLAS, must be used in any program calling such routines. @@ -110,6 +109,12 @@ a standard discretization of basic scalar elliptic PDE problems. However, this does not necessarily correspond to the shortest execution time on parallel~computers. +\textbf{Remark 2.} Memory allocation on GPUs is a costly operation +implying a synchronization; therefore, it is convenient to preallocate +internal preconditioner workspace with the method +\verb|prec%allocate_wrk(info)| before invoking an iterative method, +and release it upon exit with \verb|prec%deallocate_wrk(info)|. + \subsection{Examples\label{sec:examples}} @@ -140,7 +145,6 @@ for the real single precision and the complex, single and double precision, versions are obtained with straightforward modifications of the previous example (see Section~\ref{sec:userinterface} for details). If these versions are installed, the corresponding codes are available in \verb|samples/simple/file|\-\verb|read|. - \begin{listing}[tbp] \begin{center} \begin{minipage}{.90\textwidth} @@ -260,7 +264,6 @@ stop \label{fig:ex1}} \end{center} \end{listing} - Different versions of the multilevel preconditioner can be obtained by changing the default values of the preconditioner parameters. The code reported in Figure~\ref{fig:ex2} shows how to set a V-cycle preconditioner @@ -272,10 +275,15 @@ with block-Jacobi and set by~\fortinline|P%init|. Furthermore, specifying block-Jacobi as coarsest-level solver implies that the coarsest-level matrix is distributed among the processes. -Figure~\ref{fig:ex3} shows how to set a W-cycle preconditioner using the Coarsening based on Compatible Weighted Matching, aggregates of size at most $8$ and smoothed prolongators. It applies +Figure~\ref{fig:ex3} shows how to set a W-cycle preconditioner using +the Coarsening based on Compatible Weighted Matching, aggregates of +size at most $8$ and smoothed prolongators. It applies 2 hybrid Gauss-Seidel sweeps as pre- and post-smoother, -and solves the coarsest-level system with the parallel flexible Conjugate Gradient method (KRM) coupled with the block-Jacobi preconditioner having ILU(0) on the blocks. Default parameters are used for stopping criterion of the coarsest solver. -Note that, also in this case, specifying KRM as coarsest-level +and solves the coarsest-level system with the parallel flexible +Conjugate Gradient method (KRM) coupled with the block-Jacobi +preconditioner having ILU(0) on the blocks, with default parameters +used for the coarsest solver. +Note that specifying KRM as coarsest-level solver implies that the coarsest-level matrix is distributed among the processes. %It is specified that the coarsest-level diff --git a/docs/src/license.tex b/docs/src/license.tex index a1d6574c..9662ea3a 100644 --- a/docs/src/license.tex +++ b/docs/src/license.tex @@ -6,40 +6,41 @@ AMG4PSBLAS is freely distributable under the following copyright terms: {\small \begin{verbatim} - - AMG4PSBLAS version 1.0 - Algebraic MultiGrid Preconditioners Package - based on PSBLAS (Parallel Sparse BLAS version 3.7) - - (C) Copyright 2021 - - Pasqua D'Ambra IAC-CNR, IT - Fabio Durastante University of Pisa and IAC-CNR, IT - Salvatore Filippone University of Rome Tor-Vergata and IAC-CNR, 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. + + + AMG4PSBLAS version 1.2 + Algebraic Multigrid Package + based on PSBLAS (Parallel Sparse BLAS version 3.9) + + (C) Copyright 2025 + + Salvatore Filippone + Pasqua D'Ambra + Fabio Durastante + + 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 AMG4PSBLAS 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 AMG4PSBLAS 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. \end{verbatim} } diff --git a/docs/src/overview.tex b/docs/src/overview.tex index ef31a157..c3c3fd16 100644 --- a/docs/src/overview.tex +++ b/docs/src/overview.tex @@ -3,7 +3,9 @@ {\textsc{\ref{sec:overview} General Overview}} The \textsc{Algebraic MultiGrid Preconditioners Package based on -PSBLAS} (\textsc{AMG\-4\-PSBLAS}) provides parallel Algebraic MultiGrid (AMG) preconditioners (see, e.g., \cite{Briggs2000,Stuben_01}), +PSBLAS} (\textsc{AMG\-4\-PSBLAS}) provides parallel Algebraic +MultiGrid (AMG) preconditioners (see, e.g., +\cite{Briggs2000,Stuben_01}), to be used in the iterative solution of linear systems, \begin{equation} Ax=b, @@ -18,12 +20,14 @@ where $A$ is a square, real or complex, sparse symmetric positive definite (s.p. The preconditioners implemented in AMG4PSBLAS are obtained by combining 3 different types of AMG cycles with smoothers and coarsest-level -solvers. Available multigrid cycles include the V-, W-, and a version of a Krylov-type cycle +solvers. We provide a number of multigrid cycles, including the V-, +W-, and a version of a Krylov-type cycle (K-cycle)~\cite{Briggs2000,Notay2008}; they can be combined with Jacobi, hybrid %\footnote{see Note 2 in Table~\ref{tab:p_coarse}, p.~28.} forward/backward Gauss-Seidel, block-Jacobi and additive Schwarz -smoothers with various versions of local incomplete factorizations and approximate inverses +smoothers with various versions of local incomplete factorizations and +approximate inverses on the blocks. The Jacobi, block-Jacobi and Gauss-Seidel smoothers are also available in the $\ell_1$ version~\cite{DDF2020}. @@ -41,7 +45,8 @@ two different coarsening strategies, based on aggregation, are available: and described in detail in~\cite{DDF2020}; \end{itemize} Either exact or approximate solvers can be used on the coarsest-level -system. We provide interfaces to various parallel and sequential sparse LU factorizations from external +system. We provide interfaces to various parallel and sequential +sparse LU factorizations from external packages, sequential native incomplete LU and approximate inverse factorizations, parallel weighted Jacobi, hybrid Gauss-Seidel, block-Jacobi solvers and calls to preconditioned Krylov methods; all @@ -74,36 +79,41 @@ important revisions and extentions of the PSBLAS infrastructure. The inter-process comunication required by AMG4PSBLAS is encapsulated in the PSBLAS routines; therefore, AMG4PSBLAS can be run on any parallel machine where PSBLAS -implementations are available. In the most recent version of PSBLAS -(release 3.7), a plug-in for GPU is included; it includes CUDA +implementations are available. The most recent version of PSBLAS +(release 3.9) includes a plug-in for GPU; it contains CUDA versions of main vector operations and of sparse matrix-vector multiplication, so that Krylov methods coupled with AMG4PSBLAS -preconditioners relying on Jacobi and block-Jacobi smoothers with -sparse approximate inverses on the blocks can be efficiently executed +preconditioners relying on Jacobi and block-Jacobi smoothers with +sparse approximate inverses on the blocks can be efficiently executed on cluster of GPUs. -AMG4PSBLAS has a layered and modular software architecture where three main layers can be -identified. The lower layer consists of the PSBLAS kernels, the middle one implements -the construction and application phases of the preconditioners, and the upper one -provides a uniform interface to all the preconditioners. -This architecture allows for different levels of use of the package: -few black-box routines at the upper layer allow all users to easily -build and apply any preconditioner available in AMG4PSBLAS; -facilities are also available allowing expert users to extend the set of smoothers -and solvers for building new versions of the preconditioners (see -Section~\ref{sec:adding}). +AMG4PSBLAS has a layered and modular software architecture where three +main layers can be identified. The lower layer consists of the PSBLAS +kernels, the middle one implements the construction and application +phases of the preconditioners, and the upper one provides a uniform +interface to all the preconditioners. This architecture allows for +different levels of use of the package: few black-box routines at the +upper layer allow all users to easily build and apply any +preconditioner available in AMG4PSBLAS; facilities are also available +allowing expert users to extend the set of smoothers and solvers for +building new versions of the preconditioners (see +Section~\ref{sec:adding}). -This guide is organized as follows. General information on the distribution of the source -code is reported in Section~\ref{sec:distribution}, while details on the configuration -and installation of the package are given in Section~\ref{sec:building}. The basics for building and applying the -preconditioners with the Krylov solvers implemented in PSBLAS are reported -in~Section~\ref{sec:started}, where the Fortran codes of a few sample programs -are also shown. A reference guide for the user interface routines is provided -in Section~\ref{sec:userinterface}. Information on the extension of the package -through the addition of new smoothers and solvers is reported in Section~\ref{sec:adding}. -The error handling mechanism used by the package -is briefly described in Section~\ref{sec:errors}. The copyright terms concerning the -distribution and modification of AMG4PSBLAS are reported in Appendix~\ref{sec:license}. +This guide is organized as follows. General information on the +distribution of the source code is reported in +Section~\ref{sec:distribution}, while details on the configuration and +installation of the package are given in +Section~\ref{sec:building}. The basics for building and applying the +preconditioners with the Krylov solvers implemented in PSBLAS are +reported in~Section~\ref{sec:started}, where the Fortran codes of a +few sample programs are also shown. A reference guide for the user +interface routines is provided in +Section~\ref{sec:userinterface}. Information on the extension of the +package through the addition of new smoothers and solvers is reported +in Section~\ref{sec:adding}. The error handling mechanism used by the +package is briefly described in Section~\ref{sec:errors}. The +copyright terms concerning the distribution and modification of +AMG4PSBLAS are reported in Appendix~\ref{sec:license}. %%% Local Variables: %%% mode: latex diff --git a/docs/src/userguide.tex b/docs/src/userguide.tex index 88bffece..9ee2d4cc 100644 --- a/docs/src/userguide.tex +++ b/docs/src/userguide.tex @@ -154,7 +154,7 @@ Preconditioners Package based on PSBLAS} \flushright \large Software version: 1.2\\ %\todaym -\large December 31st, 2025 +\large December 23rd, 2025 \end{minipage}} %\addtolength{\textwidth}{\centeroffset} \vspace{\stretch{2}} diff --git a/docs/src/userhtml.tex b/docs/src/userhtml.tex index 37dcd98c..fed11d47 100644 --- a/docs/src/userhtml.tex +++ b/docs/src/userhtml.tex @@ -114,7 +114,7 @@ %\today Software version: 1.2\\ %\today - December 31st, 2025 + December 23rd, 2025 \clearpage \ \\ \thispagestyle{empty} diff --git a/docs/src/userinterface.tex b/docs/src/userinterface.tex index 3fbcb832..f313980c 100644 --- a/docs/src/userinterface.tex +++ b/docs/src/userinterface.tex @@ -160,7 +160,7 @@ the smoothers. However, for simplicity, shortcuts are provided to set all versions of point-Jacobi, hybrid (forward) Gauss-Seidel, and hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined just by setting \fortinline|'SMOOTHER_TYPE'| to certain specific -values (see Tables~\ref{tab:p_smoother}), without the need to set +values (see Table~\ref{tab:p_smoother}), without the need to set \fortinline|'SUB_SOLVE'| as well. The smoother and solver objects are arranged in a @@ -182,47 +182,50 @@ the polynomial used. Consequently, the \fortinline|'SMOOTHER_SWEEPS'| option is the \fortinline|'POLY_DEGREE'| option. This smoother is paired with a base smoother object, whose iterations are accelerated using the specified polynomial smoothing technique. By default, the $\ell_1$-Jacobi smoother serves as the base smoother, offering theoretical -guarantees on the resulting convergence factor~\cite{DDFMT2024,LOTTES}. Alternative combinations -are experimental and lack established guarantees.\\ +guarantees on the resulting convergence +factor~\cite{DDFMT2024,LOTTES}. Alternative combinations are +experimental.\\ +% and lack established guarantees.\\ \textbf{Remark 4.} Many of the coarsest-level solvers apply to a -specific coarsest-matrix layout; -therefore, setting the solver after the layout may change the layout -to either distributed or replicated. -Similarly, setting the layout after the solver may change the solver. - -More precisely, UMFPACK and SuperLU require the coarsest-level -matrix to be replicated, while SuperLU\_Dist and KRM require it to be distributed. -In these cases, setting the coarsest-level solver implies that -the layout is redefined according to the solver, ovverriding any +specific coarsest-matrix layout; therefore, setting the solver after +the layout may change the layout to either distributed or replicated, +and similarly, setting the layout after the solver may change the +solver. More specifically, UMFPACK and SuperLU require the coarsest-level +matrix to be replicated, while SuperLU\_Dist and KRM require it to be +distributed; therefore, setting the coarsest-level solver implies +that the layout is redefined according to the solver, ovverriding any previous settings. MUMPS, point-Jacobi, hybrid Gauss-Seidel and block-Jacobi can be applied to replicated and distributed matrices, thus their choice does not modify any previously specified layout. It is worth noting that, when the matrix is replicated, -the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers and their $\ell_1-$ versions -reduce to the corresponding local solver objects (see Remark~2). -For the point-Jacobi and Gauss-Seidel solvers, these objects -correspond to a \emph{single} point-Jacobi sweep and a \emph{single} -Gauss-Seidel sweep, respectively, which are very poor solvers. - -On the other hand, the distributed layout can be used with any solver -but UMFPACK and SuperLU; therefore, if any of these two solvers has already -been selected, the coarsest-level solver is changed to block-Jacobi, -with the previously chosen solver applied to the local blocks. -Likewise, the replicated layout can be used with any solver but SuperLu\_Dist and KRM; -therefore, if SuperLu\_Dist or KRM have been previously set, the coarsest-level -solver is changed to the default sequential solver. - -In a parallel setting with many cores, we suggest to the users to change the default -coarsest solver for using the KRM choice, i.e. a parallel distributed iterative solution of the -coarsest system based on Krylov methods. - -\textbf{Remark 4.} The argument \fortinline|idx| can be used to allow finer -control for those solvers; for instance, by specifying the keyword -\fortinline|'MUMPS_IPAR_ENTRY'| and an appropriate value for \fortinline|idx|, it is -possible to set any entry in the MUMPS integer control array. -See also Sec.~\ref{sec:adding}. +the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers and +their $\ell_1-$ versions reduce to the corresponding local solver +objects (see Remark~2). For the point-Jacobi and Gauss-Seidel solvers, +these objects correspond to a \emph{single} point-Jacobi sweep and a +\emph{single} Gauss-Seidel sweep, respectively, which are very poor +solvers. + +On the other hand, the distributed layout can be used with any solver +except and SuperLU; therefore, if any of these two solvers has +already been selected, the coarsest-level solver is changed to +block-Jacobi, with the previously chosen solver applied to the local +blocks. Likewise, the replicated layout can be used with any solver +but SuperLu\_Dist and KRM; therefore, if SuperLu\_Dist or KRM have +been previously set, the coarsest-level solver is changed to the +default sequential solver. + +In a parallel setting with many cores, we suggest to the users to +change the default coarsest solver for using the KRM choice, i.e. a +parallel distributed iterative solution of the coarsest system based +on Krylov methods. + +\textbf{Remark 4.} The argument \fortinline|idx| can be used to allow +finer control for those solvers; for instance, by specifying the +keyword \fortinline|'MUMPS_IPAR_ENTRY'| and an appropriate value for +\fortinline|idx|, it is possible to set any entry in the MUMPS integer +control array. See also Sec.~\ref{sec:adding}. %The \verb|what,val| pairs described here are those of the predefined %moother/solver objects; newly developed solvers may define new pairs %according to their needs.