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本文提出一个利用“黑匣子”思想并行求解高阶广义矩阵本征问题的分块消去迭代算法,并在国家智能计算机研究开发中心研制的大规模并行计算机曙光1000上成功地解算了非线性光学晶体电子结构计算中的1572阶复共轭对称矩阵偶的广义矩阵本征问题,应用于中国科学院福建物质结构研究所陈创天等人发现的LBO非线性光学晶体电子结构分析,使用能带方法完成了该晶体电子态的自治计算.我们对新算法进行了迭代过程收敛性、误差分析、并行设计、并行效率的分析研究与数值实验.
In this paper, we propose a block-elimination iterative algorithm that uses the “black box” idea to solve in parallel the intrinsic problems of high-order generalized matrices in parallel, and successfully solves the problem of nonlinear optical crystals on a large-scale parallel computer Shuguang 1000 developed by National Intelligent Computer Research and Development Center The generalized matrix eigenproblem of the 1572-order complex conjugate symmetric matrices even in the calculation of electronic structure is applied to the electronic structure analysis of LBO nonlinear optical crystals found by Chen Chongtian et al., Fujian Institute of Material Structure, Chinese Academy of Sciences. The energy band method is used to complete the Autocorrelation of Crystal Electronic States. We performed the convergence, error analysis, parallel design, parallel efficiency analysis and numerical experiments of the new algorithm.