关键词: 广义本征值, ELPA, 电子结构, ABACUS软件

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