Chronos: A general purpose classical AMG solver for High Performance Computing

Abstract

The numerical simulation of the physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large scale simulations are concerned, one of the most computationally expensive task is the solution of linear systems arising from the discretization of the partial differential equations governing the physical processes. This work presents Chronos, a collection of linear algebra functions specifically designed for the solution of large, sparse linear systems on massively parallel computers (https://www.m3eweb.it/chronos/). Its emphasis is on modern, effective and scalable AMG preconditioners for High Performance Computing (HPC). This work describes the numerical algorithms and the main structures of this software suite, especially from the implementation standpoint. Several numerical results arising from practical mechanics and fluid dynamics applications with hundreds of millions of unknowns are addressed and compared with other state-of-the-art linear solvers, proving Chronos efficiency and robustness.

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“…On the other hand, in recent years, many new methods are developed on building high-efficient preconditioner for large linear systems derived from PDE. The algebraic multigrid (AMG) preconditioner [7] can significantly improve the convergence rate of the iterative solver, thus reduce the iteration number to several hundred to several dozens [12].…”