多贝西小波密度泛函的高效并行计算及电荷体系应用

多贝西小波在实空间和傅立叶空间都是正交的，具有非常好的局域性。近年来，以多贝西小波作为完备基函数求解Kohn-Sham方程的密度泛函计算方法受到国际上的高度关注，但其高效并行应用仍然面临瓶颈。本项目针对多贝西密度泛函并行算法开展研究,探索GPU加速、Wannier局域化等新的并行计算技术，并在电荷体系开展快速求解应用。包括：1）探索运用尺度函数和小波进行高精度网格计算的预置条件和算法，研究求解Kohn-Sham方程中快速卷积运算的高效解法器；2）探索几类边界条件下的泊松解法器等高精度网格解法器的GPU加速；3）改进Block波函数投影方法，提高多贝西小波密度泛函的Wannier局域化并行计算技术，探索带电荷体系在空间的轨道分布和占据数。我们拟开展的研究在新材料设计、固体物理、量子化学等领域具有重要应用背景，将促进该领域高性能并行计算软件的研发。

Daubechies wavelets are orthogonal both in real space and in Fourier space, and has very good locality. In recent years, density functional calculations based on daubechies wavelets used as complete basis function for solving Kohn-Sham equation are used for the calculations of electronic structure, but its high-performance applications are still facing bottlenecks. This project will carry the research on parallel algorithm for daubechies wavelets density functional calculations, and using the new technologies including GPU acceleration, Wannier localization, etc., to abtain fast solving and application in charged systems. Including, 1) To explore the preset conditions and algorithms in multi-grid calculations using scaling function and wavelet, and study the high efficient solver for the calculating of convolution in Kohn-Sham equations. 2) To explore the GPU acceleration for high efficient multigrid solver including Poisson solver in surface boundary condition and three-dimensional periodic boundary condition. 3) To improve the method of projection in Block wave function, and the parallel computing technology of Wannier localization technologies in Daubechies basis density functional calculations. We will also perform the study on orbital distribution in space and the occupation of charged systems. Our research has important application background in the fields of new materials design, solid state physics, and quantum chemistry, etc. It will contribute to the development of high-performance parallel computing software.