Efficient and Scalable Calculation of Complex Band Structure using Sakurai-Sugiura Method
Efficient and Scalable Calculation of Complex Band Structure using Sakurai-Sugiura Method
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DOI：
10.1145/3126908.3126942
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发表时间：
2017-09
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影响因子：
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通讯作者：
S. Iwase;Y. Futamura;A. Imakura;T. Sakurai;T. Ono
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文献类型：
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作者：
S. Iwase;Y. Futamura;A. Imakura;T. Sakurai;T. Ono
复杂能带结构（CBSs）是表征材料静态和动态电子特性的有效方法。尽管取得了很大的进展，但对数百个原子的CBS的第一性原理计算仍然要求很高。本文提出了一种高效且可扩展的计算方法来计算CBSs。其基本思想是将实空间网格格式的Kohn-Sham方程表示为一个二次特征值问题，用Sakurai-Sugiura方法只计算构造CBS所需的解。该方法的串行性能与传统方法相比，在运行时和内存使用方面都有显著的优势。此外，由于Sakurai-Sugiura方法的分层并行性和实空间网格的区域分解技术，我们可以在使用Oakforest-PACS的2,048个节点（139,264个核）的10,000多个原子的硼氮掺杂碳纳米管的CBS计算中实现出色的可扩展性。CCS概念•计算数学$\右列$非线性方程；•应用计算$\右箭头$物理；
Complex band structures (CBSs) are useful to characterize the static and dynamical electronic properties of materials. Despite the intensive developments, the first-principles calculation of CBS for over several hundred atoms are still computationally demanding. We here propose an efficient and scalable computational method to calculate CBSs. The basic idea is to express the Kohn-Sham equation of the real-space grid scheme as a quadratic eigenvalue problem and compute only the solutions which are necessary to construct the CBS by Sakurai-Sugiura method. The serial performance of the proposed method shows a significant advantage in both runtime and memory usage compared to the conventional method. Furthermore, owing to the hierarchical parallelism in Sakurai-Sugiura method and the domain-decomposition technique for real-space grids, we can achieve an excellent scalability in the CBS calculation of a boron and nitrogen doped carbon nanotube consisting of more than 10,000 atoms using 2,048 nodes (139,264 cores) of Oakforest-PACS. CCS CONCEPTS • Mathematics of computing $\rightarrow$ Nonlinear equations; • Applied computing $\rightarrow$ Physics;