非线性特征值计算的方法与应用

我们拟针对微观物质结构数值模拟，发展非线性偏微分算子特征值问题的适应E级计算机的高可扩展自适应计算方法和高效非线性迭代法，研究其可靠性与有效性的数学理论；为模拟微观物质结构软件提供新型高效算法，并通过典型问题的求解验证算法的有效性. 特别是，我们将从轨道更新与离散动力系统的角度来探索与分析非线性特征值问题的新型的自洽迭代加速算法与能量极小问题的优化算法，丰富与发展并行轨道更新算法和非线性迭代法，并将之应用到有关第一原理计算软件以及典型的电子结构模拟， 为进一步开展二维材料和钚表面氧化问题等国家需求计算打下基础.

We aim to develop highly scalable adaptive computational methods and highly efficient nonlinear iteration approaches that are friendly to exascale supercomputer, to study the corresponding mathematical theory of their reliability and efficiency, to provide new efficient algorithms for the software for simulating the microstructure of matter, and to justify the efficiency of the methods based on some typical problem calculations. In particular, we will probe and analyze the accelerated self-consistent field iteration methods and energy minimization based optimization algorithms from the orbital-updating and discretized dynimical system approaches, enrich and develop parallel orbital-updating algorithms and nonlinear iteration methods, and apply them to some relevant softwares for the first principles electronic structure calculations and typical electronic structure simluations to lay the foundation for the further computation of 2D materials and surface oxidation of Plutonium.