Abstract
Sparse linear algebra is essential for a wide variety of scientific applications. The availability of highly parallel sparse solvers and preconditioners lies at the core of pretty much all multi-physics and multi-scale simulations. Technology is nowadays expanding to target exascale platforms. I am going to present some work on Algebraic Multigrid Preconditioners in which we try to face these challenges to make Exascale Computing possible. The talk will focus on one side on the theoretical aspects pertaining to the construction of the multigrid hierarchy for which the main novelty is the de- sign and implementation of new parallel smoothers and a coarsening algorithm based on aggregation of unknowns employing weighted graph matching tech- niques. On the other, the talk also focuses on the libraries developed to cover the needs of having parallel BLAS feature for sparse matrices that are capable of running on machines with thousands of high-performance cores; and to dis- cuss the advancements made by the new smoothers and coarsening algorithm as an improvement in terms of numerical scalability at low operator complexity over the algorithms available in previous releases of the package. I will present weak scalability results on two of the most powerful supercomputers in Europe, for linear systems with sizes up to O(10 10 ) unknowns for a benchmark Poisson problem, and strong scaling result for a wind-simulation benchmark problem. This is a joint work with P. D’Ambra, and S. Filippone. This work is sup- ported by the EU under the Horizon 2020 Project Energy oriented Centre of Excellence: toward exascale for energy (EoCoE-II), Project ID: 824158