Conjugate-gradient eigenvalue solvers in computing electronic properties of nanostructure architectures
by Stanimire Tomo, Julien Langou, Jack Dongarra, Andrew Canning, Lin-Wang Wang
International Journal of Computational Science and Engineering (IJCSE), Vol. 2, No. 3/4, 2006

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.

Online publication date: Wed, 14-Mar-2007

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