State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems

The band edge states determine optical and electronic properties of semiconductor nano-structures which can be computed from an interior eigenproblem. We study the reliability and performance of state-of-the-art iterative eigensolvers on large quantum dots and wires, focusing on variants of preconditioned CG, Lanczos, and Davidson methods. One Davidson variant, the GD + k (Olsen) method, is identified to be as reliable as the commonly used preconditioned CG while consistently being between two and three times faster.