Performance evaluation of eigensolvers in nanostructure computations

We are concerned with the computation of electronic and optical properties of quantum dots. Using the Energy SCAN (ESCAN) method with empirical pseudopotentials, we compute interior eigenstates around the band gap which determine their properties. Numerically, this interior Hermitian eigenvalue problem poses several challenges, both with respect to accuracy and efficiency. Using these criteria, we evaluate several state-of-the art preconditioned iterative eigensolvers on a range of CdSe quantum dots of various sizes. All the iterative eigensolvers are seeking for the minimal eigenvalues of the folded operator with reference shift in the band-gap. The tested methods include standard Conjugate-Gradient (CG)-based RayleighQuotient minimization, Locally Optimal Block-Preconditioned CG (LOBPCG) and two variants of the Jacobi Davidson method: JDQMR and GD+1. Our experimental results conclude that the Jacobi Davidson method is often faster than the CG based method.