量子化学计算的研究与发展同国防科技、材料科学、医药科学、环境科学和生物科学等均密切相关. 该领域面临的基本问题之一是如何有效地求解大规模偏微分方程特征值问题. 这类问题的难点在于计算量随体系大小呈指数增长，特征函数空间具有高频振荡等. 本项目将针对量子化学、材料科学等领域中的偏微分方程特征值问题，做以下研究工作：利用弱有限元方法，结合迭代法、多重网格方法、自适应网格方法等，发展快速稳定的求解特征值问题的数值计算方法，研究相关的数学理论，构造适应高性能计算机的可扩展并行算法，实现逾万处理器核上的高效数值模拟，以更好地刻画相关领域的微观结构及特性. 这些理论与数值计算方法的研究将有助于人们对量子化学与材料科学领域中相关现象的认识，有着重要的实用价值和现实意义.

The research and development of quantum chemical calculation is closely related with national defense、materials science、medical science、environmental science、biological sciences，etc. One of the basic problems of this field is how to solve large-scale eigenvalue problem of partial differential equations (PDEs) effectively. The main challenges of this kind of problems are involved of nonlinear、high computational cost, and high frequency oscillation with the eigenfunctions. In this project, the weak Galerkin finite element method, combining with the iteration method、multigrid method and adaptive method, is applied for solving the eigenvalue problem of PDEs. The proposed theoretical and computational research will significantly strengthen our ability in dealing with challenging issues within quantum chemistry and medical science, which is valuable and has long lasting impact in advancing science and technology.