Abstract: In this paper,the authors first analyze some possible problems with various traditional preconditioning techniques to solve the sparse linear systems derived from two-dimension three-temperatures energy equations.Consequently,several modifications are provided to accommodate these well-known techniques to the problem here.Second,by incorporating these preconditioners and the newly provided MRILUT preconditioner into the Krylov subspace methods,the authors develop a software package PreIT2D3T.It is a high-performance,well-readable,and well-scalable package.Finally,two experiments to the whole simulation of actual inertial confinement fusion problems show that MRILUT is better than ILUT,and the current package has higher performance over the SPARSKIT package.

Key words: two-dimension three-temperatures energy equations, inertial confinement fusion, preconditioning, ILUT, Krylov subspace method

摘要： 首先针对二维三温能量方程组,系统分析了求解所得到的稀疏线性方程组时,采用多种传统预条件技术时将遇到的问题,并提出了相应的适应性改进。其次,在集成这些预条件,以及新提出的MRILUT预条件的基础上,基于Fortran语言研制了一个性能高、可读性强、可扩展性好的预条件Krylov子空间迭代法软件包PreIT2D3T。最后,对2个实际惯性约束聚变问题的全程数值模拟进行了实验,实验结果表明MRILUT优于ILUT,同时PreIT2D3T的性能也优于SPARSKIT软件包。

关键词: 二维三温能量方程组, 惯性约束聚变, 预条件, ILUT, Krylov子空间迭代