量子本征值问题实空间方法研究

项目名称： 量子本征值问题实空间方法研究

项目编号： No.10871198

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 武器工业

项目作者： 周爱辉

作者单位： 中国科学院数学与系统科学研究院

项目金额： 23万元

中文摘要： 利用第一原理计算手段来探索微观多体系统的物理规律、研究和模拟微观世界的物理过程、预测材料的结构和物性、为新材料的开发和应用提供科学的依据，是未来科学发展的一项重要任务.而第一原理计算的关键在于求解量子本征值问题.我们围绕几类量子本征值问题的数值算法设计、分析及其在电子结构计算中的应用开展了有成效的研究：设计与分析了一类本征值问题的高效有限元/有限体组合离散方法与自适应算法，并将这些高效有限元/有限体组合离散方法与自适应算法新思路应用到了第一原理电子结构实空间并行计算程序的框架中；基于PHG平台,在并行计算机上有效地计算了上千个原子的体系的基态总能和电子结构, 并成功在天河一号超级计算机扩展超过了6000个CPU核.

中文关键词： 量子本征值；组合离散；自适应；并行计算

英文摘要： It is a very important task in the furtue science development that to apply the first-principles calculations to probe the physical law of microscopic many-body system, investigate and simulate the physical progress of microworld, predict the structure and property of materials, and then provide a scientific basis for the development and application of new materials. While it is solving quantum eigenvalue problems that takes a key role in the first-principles calculations. In this project, we have studied the numerical method for a class of quantum eigenvalue problems, including its construction, analysis, and application to electronic structure calculations, and made a very satisfying achievement: designed and analyzed high efficient localization and combination based finite element/finite volume discretizations and adaptive algoritms, of which the new ideas were applied to our first-principles real space electronic structure calculation code; based on PHG toolbox, effieiently simluated by parallel computers the electronic structure and ground state total energy of several typical atomic systems, including some system with over 1000 atoms; succesfully scaled our simulation to over 6000 CPU cores on Tianhe-1A supercomputer,too.

英文关键词： quantum eigenvalue; comnination based discretization;adaptive;parallel computing