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### Abstract

AMG4PSBLAS (Al g e b r a i c Mu l t iGr i d Pr e c o n d i t i o n e r s Pa c k a g e b a s e d o n 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 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. 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.

This guide provides a brief description of the functionalities and the user interface of AMG4PSBLAS.

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