Current applications in Computational and Data Science often require the solution of large and sparse linear systems. The notion of "large" is qualitative and there is a clear tendency to increase it; currently, it is not unusual the need to solve systems with millions or even billions of unknowns. The methods of choice to efficiently solve the above systems on high-end massively parallel computers are the Krylov methods, whose convergence and scalability properties are related to the choice of suitable preconditioning techniques.
In this tutorial, we will present AMG4PSBLAS (Algebraic MultiGrid Preconditioners for PSBLAS) which provides efficient and easy-to-use preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) computational framework.
The package, whose features are constantly updated within the EoCoE project, includes multilevel cycles and smoothers widely used in multigrid methods. A purely algebraic approach is applied to generate coarse-level corrections so that no geometric background is needed concerning the matrix to be preconditioned. We will present the main features of the package and example of usage of the main APIs needed to setup the preconditioner, together with its application within the Krylov solvers available from PSBLAS. Some results on test cases relative to the EoCoE application areas highlight how the PSBLAS/AMG4PSBLAS software framework can be used to obtain highly scalable linear solvers.