摘要
时间相关偏微分方程隐式离散后,通常需要求解一个稀疏线性代数方程组序列.利用序列中相邻方程组性质的差异性与相似性,自适应地选取预条件子,提升方程组序列的并行求解效率,从而缩短总体求解时间,是一个值得研究的问题.本文针对科学与工程计算中广泛使用的代数多重网格(AMG)预条件子,设计了方程组序列相关的自适应预条件策略.通过惯性约束聚变(ICF)的辐射流体力学数值模拟典型应用,验证了该策略的有效性.测试结果表明,在某高性能计算机的3125个CPU核上,自适应预条件策略可将并行效率从47%提升到61%,将模拟总时间从19.7 h降为14.5 h.
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.
出处
《中国科学：信息科学》
CSCD
北大核心
2016年第10期1411-1420,共10页
Scientia Sinica(Informationis)
基金
国家重点基础研究发展计划(973)(批准号:2011CB309702)
国家自然科学基金(批准号:61370067
91430218
91530324)资助项目
