我们拟针对模拟物质微观结构的非线性偏微分算子特征值问题，发展高效实用的非线性迭代方法、网格自适应方法和离散问题的可扩展计算方法，研究相关的数学理论，探索如何实现逾万处理器核上的高效数值模拟. 特别是,研究Kohn-Sham方程多层耦合离散、拟Newton类自洽场迭代、代数特征值问题的实空间预处理以及分层并行程序实现与应用.

We aim to develop highly efficient and practical nonlinear iterative methods, mesh based adaptive methods as well as scalable computational methods of the discretized problems, study their corresponding mathematical theory and probe how to carry out highly efficient numerical simulation on computers with more than ten thousand CPU cores, for solving eigenvalue problems associated with nonlinear partial differential operators arising from simulating the microstructure of matter. In particular, we shall investigate multi-level coupled discretizations for Kohn-Sham equation, quasi-Newton-type self-consistent field iterations, real space preconditioners for algebraic eigenvalue problems, and the implementation and application of a multi-level parallel software package.