An adaptive AMG preconditioning strategy for solving large-scale sparse linear systems

Abstract

A series of sparse linear systems must be solved in applications that are based on the implicit solution of time-dependent partial differential equations (PDEs). Preconditioned iterative methods are usually employed to solve such sparse linear systems. AMG is one of the most popular preconditioners in real applications. However, it results in poor parallel scalability, owing to its setup phase. In this paper, by utilizing the differences and similarities in property among the systems in series, an adaptive AMG preconditioning strategy is presented to improve the parallel scalability. The results obtained for a radiation hydrodynamics computation within an ICF simulation demonstrate the efficiency and improvement of the adaptive strategy. For a typical model, the new strategy improves the parallel efficiency from 47\% to 61\%, and reduces the CPU time from 19.7 h to 14.5 h.