Preconditioners for PSBLAS


Preconditioners for PSBLAS


Parallel AMG Preconditioners

Highly Parallel Smoothers

Tested on tens of thousands of cores

Excellent innovation in the EU Innovation Radar


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 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.

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.

The package employs object-oriented design techniques in 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 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.


Library releases for AGM4PSBLAS.

Release Date Sources Documentation Works with
Version 1.1.1 September 29, 2023 ZIP Archive PDF HTML PSBLAS 3.8.1, PSBLAS-EXT Version 1.3.2
Version 1.1.0 May 24, 2022 ZIP Archive PDF HTML PSBLAS 3.8.0, PSBLAS-EXT 1.3.0-rc1
Version 1.0 May 11, 2021 ZIP Archive PDF HTML PSBLAS, PSBLAS-EXT 1.3.0-rc1
Version 1.0-rc2 April 12, 2021 ZIP Archive PDF HTML PSBLAS 3.7.0, PSBLAS-EXT 1.3.0-rc1

Library releases for MLD2P4 can be downloaded from: mld2p4/releases

Release Date Sources
Version 2.2.2 6 May 2020 ZIP Archive


An HTML version of the library documentation can be found on the page AMG4PSBLAS documentation. In any case, the software releases contain a copy of the documentation and a pdf version of it.


  1. Unpack the tar file in a directory of your choice (preferrably outside the main PSBLAS directory).
  2. run configure --with-psblas=<ABSOLUTE path of the PSBLAS install directory> adding the options for MUMPS, SuperLU, SuperLU_Dist, UMFPACK as desired. See MLD2P4 User’s and Reference Guide (Section 3) for details.
  3. Tweak if you are not satisfied.
  4. make
  5. Go into the test subdirectory and build the examples of your choice.
  6. (if desired): make install


  • The single precision version is supported only by MUMPS and SuperLU; thus, even if you specify at configure time to use UMFPACK or SuperLU_Dist, the corresponding preconditioner options will be available only from the double precision version.
  • The preconditioners in AMG4PSBLAS extend those of PSBLAS and are meant to be used with the PSBLAS Krylov solvers; so in an existing program you need to modify the type of the preconditioner object and its settings, but the rest of the application needs not be changed.

EoCoE - Software as service portal

In the European project “Energy oriented Center of Excellence: toward exascale for energy” we made available a software as service portal: This permits to test several cutting-edge computational methods for accelerating the transition to the production, storage and management of clean, decarbonized energy. Among them you have the possibility of running PSBLAS+AMG4PSBLAS on some test problems to become familiar with using the software.

The AMG4PSBLAS team.

Contributors to MLD2P4:

  • Daniela di Serafino
  • Ambra Abdullahi Hassan
  • Alfredo Buttari