N阶电子结构理论及其在千万原子体系中的应用
An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system
摘要：
本文提出了一种线性代数理论-多重Arnoldi方法，并利用广义本征值方程实现了大规模（N阶）电子结构计算。一组线性方程组，在（zS-H）x = b的形式，同时解决多个Krylov子空间。该方法是在一个仿真软件包ELSES（http：www.elses.jp）与紧绑定形式的哈密顿实现。对金属材料和绝缘材料进行了有限温度分子动力学模拟。在工作站上实现了用$10^7$原子的计算。并行效率最高可达1，024个CPU核心。
英文摘要：
A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are solved simultaneously with multiple Krylov subspaces. The method is implemented in a simulation package ELSES (http://www.elses.jp) with tight-binding-form Hamiltonians. A finite-temperature molecular dynamics simulation is carried out for metallic and insulating materials. A calculation with $10^7$ atoms was realized by a workstation. The parallel efficiency is shown upto 1,024 CPU cores.
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