新的线性代数理论和一亿原子量子材料的K计算机模拟
Novel linear algebraic theory and one-hundred-million-atom quantum material simulations on the K computer
摘要：
本文综述了我们在新型线性代数算法及其在大规模量子材料模拟或电子结构计算中的应用方面的最新进展和最新结果。该算法是（zS-H）x=b形式的广义移位线性方程组的Krylov子空间（迭代）求解器，而不是传统的广义特征值方程。该方法是在我们的顺序- $N$计算代码ELSES（http：//www.elses.jp/）的基础上从头计算模型化的系统。该代码在K计算机上以高并行效率实现了一亿个原子或100 nm尺度的量子材料模拟，最多可使用所有内置处理器内核。本文还解释了几个方法方面，如使用XML文件和“新手”模式，为一般用户。在我们的实际问题（http：//www.elses.jp/matrix/）的稀疏矩阵数据库的准备。内本征值问题是量子材料模拟的一个普遍需要。目前的研究是一个跨学科的，有时被称为“应用-算法-架构协同设计”。协同设计将在exa级科学计算中发挥关键作用。
英文摘要：
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are Krylov-subspace (iterative) solvers for generalized shifted linear equations, in the form of (zS-H)x=b,in stead of conventional generalized eigen-value equation. The method was implemented in our order-$N$ calculation code ELSES (http://www.elses.jp/) with modelled systems based on ab initio calculations. The code realized one-hundred-million-atom, or 100-nm-scale, quantum material simulations on the K computer in a high parallel efficiency with up to all the built-in processor cores. The present paper also explains several methodological aspects, such as use of XML files and 'novice' mode for general users. A sparse matrix data library in our real problems (http://www.elses.jp/matrix/) was prepared. Internal eigen-value problem is discussed as a general need from the quantum material simulation. The present study is a interdisciplinary one and is sometimes called 'Application-Algorithm-Architecture co-design'. The co-design will play a crucial role in exa-scale scientific computations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
