Conjugate-gradient eigenvalue solvers in computing electronic properties of nanostructure architectures

Authors:
Stanimire Tomo;Julien Langou;Jack Dongarra;Andrew Canning;Lin-Wang Wang
Affiliations:
Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN 37996-3450, USA.;Department of Mathematical Sciences, University of Colorado at Denver and Health Sciences Center, Denver, CO 80217-3364, USA.;Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN 37996-3450, USA.;Lawrence Berkeley National Laboratory, Computational Research Division, Berkeley, CA 94720, USA.;Lawrence Berkeley National Laboratory, Computational Research Division, Berkeley, CA 94720, USA
Venue:
International Journal of Computational Science and Engineering
Year:
2006

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Abstract

In this paper we report on our efforts to test and expand the current state-of-the-art in eigenvalue solvers applied to the field of nanotechnology. We singled out the non-linear Conjugate Gradients (CG) methods as the backbone of our efforts for their previous success in predicting the electronic properties of large nanostructures and made a library of three different solvers (two recent and one new) that we integrated into the Parallel Energy SCAN (PESCAN) code to perform a comparison. The methods and their implementation are tuned to the specifics of the physics problem. The main requirements are to be able to find (1) a few, approximately 4-10, of the (2) interior eigenstates, including (3) repeated eigenvalues, for (4) large Hermitian matrices.