A bulk-based preconditioner and its efficiency in accelerating eigensolvers for electronic nano-structure calculations

A. Canning, J. Dongarra, O. Marques, S. Tomov, C. Vömel, and L-W. Wang

Email: tomov@cs.utk.edu
Postal address: University of Tennessee, 1122 Volunteer Blvd., Suite 203, Knoxville, TN 37996-3450

The focus of this work is to accelerate the parallel computation of interior eigenstates for large Hermitian matrices arising from plane-wave discretization of effective single-particle Schrödinger equations. Of interest is solving for a small number of interior eigenstates around the band gap of colloidal quantum dots (these eigenstates model electronic and optical properties of the system at hand).

We developed a bulk-based technique that uses the eigenstates from the bulk materials constituent for the quantum dot to design an improved preconditioner (compared to diagonal) and a better starting vector choice (compared to random). For large quantum dots this led to about a factor of 4 decrease in the number of iterations until convergence compared to previous calculations.

In this talk I will describe the mathematical problem at hand, explain the proposed acceleration techniques, and give results on their scalability, efficiency as compared to previous calculations (diagonal preconditioning with random starting vector), and as a comparison when used in combination with different eigensolvers.