A General-Purpose AMG Linear Solver for High Performance Computing

Abstract

The numerical simulation of modern engineering problems via finite elements requires the solution of sparse linear systems of millions or even billions of unknowns. The algebraic multigrid (AMG) methods are the most common choice as linear solvers because of their fast convergence even for large-size problems. In this communication, we propose Chronos, a massively parallel implementation of a novel AMG framework, specifically designed to address complex problems by adapting its components, from the smoother, to the coarse grid correction and prolongation to the problem at hand. This work demonstrates not only the numerical performance of the proposed library, but also its robustness and adaptability to very challenging matrices, arising from different fields of application.