Abstract: How to compute the generalized eigenvalues of positive definite matrices with ideal computing efficientcy for large scale parallel is one of the key problems in calculating electronic structure and many high performance computing subjects. It also has significant meaning in the development of future E-scale computing. Max Planck Society proposed an eigenvalue solver for petaflop-applications (ELPA) recently. Based on ELPA, this paper develops an open source general eigenvalue solver GenELPA, which can transform the generalized eigenvalue problems to standard eigenvalue problems automatically, and then use ELPA to do the calculation. It has decent performance on both computing speed and parallel efficiency, and also easy to use because of its ScaLAPACK-like interface. This paper applies it on the first principle software ABACUS (atomic-orbital based ab-initio computation at USTC), which is an open-source computer code package aiming for large-scale electronic structure simulations from first principles, and obtains ideal speedup.

Key words: generalized eigenvalue, ELPA, electronic structure, ABACUS

摘要： 高效率的大规模并行求解广义本征值方程是在计算电子结构等高性能计算学科中的一个重要课题，在未来E级计算的发展上有重要的意义。根据马普研究所近几年开发的一种面向P级应用的本征值求解库（eigenvalue solver for petaflop-applications，ELPA），针对广义本征值问题，开发了一款开源并行广义本征值求解器GenELPA，实现了从广义本征值问题到一般本征值问题的转换方法，避免了潜在的问题；然后调用ELPA进行计算，具有良好的计算速度和并行效率；同时采用了类似ScaLAPACK的接口，更加易于使用。在第一性原理软件ABACUS（atomic-orbital based ab-initio computation at USTC）中的实际应用表明该求解器具有理想的计算速度提升。

关键词: 广义本征值, ELPA, 电子结构, ABACUS软件