Scalable AMG Preconditioners for Computational Science at Extreme Scale

The challenge of exascale requires rethinking numerical algorithms and mathematical software for efficient exploitation of heterogeneous massively parallel supercomputers. In this talk, we present some activities aimed at developing highly scalable and robust sparse linear solvers for solving scientific and engineering applications with a huge number of degrees of freedom (dof)[1]. We discuss algorithmic advances and implementation aspects in the design of Algebraic MultiGrid (AMG) preconditioners based on aggregation, to be used in conjunction with Krylov-subspace projection methods, suitable to exploit high levels of parallelism of current petascale supercomputers. These activities are carried on within two ongoing European Projects, the Energy-oriented Center of Excellence (EoCoE-II) and the EuroHPC TEXTAROSSA project, having the final aim to provide methods and tools for preparing scientific applications in facing and successfully grasping the near future exascale challenge. Beyond possible advances in base software technology to make available programming environments that tend to hide the details of the hardware, we still need to rethink and redesign numerical methods and applications, especially for irregular computations and memory-bound kernels, like sparse solvers.