New Eigensolvers and Preconditioners for Large Scale Nanoscience Simulations Presenter: Andrew Canning, LBNL Authors: Christof Voemel, Andrew Canning, Osni Marques and Lin-Wang Wang CRD, LBNL Stanimire Tomov and Jack Dongarra ICL, University of Tennessee

We present results for new iterative eigensolvers based on conjugate gradients and variants of Davidson in the context of semi- empirical plane wave electronic structure calculations. These new methods give significant speedup over existing conjugate gradient methods used in electronic structure calculations. The new methods will be demonstrated for CdSe quantum dots as well as quantum wires (single electron devices) constructed from layers of InP and InAs.

These systems are studied in the context of a semi-empirical potential where we typically solve for a few states around the gap allowing us to study large scale nanosystems. The parallelization of this approach will also be discussed as well as scaling results to large processor counts. We will also present results for a new preconditioner based on bulk-band states. This new preconditioner is based on the observation that in the interior of large quantum dots the eigenstates are well approximated by the bulk eigenstates.

Therefore the bulk eigenstates which are cheap to calculate can be used as a preconditioner for the Quantum Dot as well as for the starting vector for the eigensolver.