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

Authors: Stanimire Tomo, Julien Langou, Jack Dongarra, Andrew Canning, Lin-Wang Wang

Addresses: 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

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.

Keywords: computational nanotechnology; parallel eigenvalue solvers; quantum dots; conjugate gradient methods; block methods; nanoscale technology; electronic properties; nanostructure architectures.

DOI: 10.1504/IJCSE.2006.012774

International Journal of Computational Science and Engineering, 2006 Vol.2 No.3/4, pp.205 - 212

Available online: 14 Mar 2007 *

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