Conjugate-gradient eigenvalue solvers in computing electronic properties of nanostructure architectures. (15th March 2007)

• Record Type: Journal Article
• Authors: Tomo, Stanimire; Langou, Julien; Dongarra, Jack; Canning, Andrew; , Lin-Wang Wang
• Is Part Of: International journal of computational science and engineering. Volume 2:Number 3/4(2006)
• Page Start: 205
• Page End: 212
• Publication Date: 2007-03-15
• Subjects: computational nanotechnology -- parallel eigenvalue solvers -- quantum dots -- conjugate gradient methods -- block methods -- nanoscale technology -- electronic properties -- nanostructure architectures; Computer science -- Mathematics -- Periodicals; Computer simulation -- Mathematical aspects -- Periodicals; Computational intelligence -- Periodicals; 004.015105
• Languages: English
• ISSNs: 1742-7185

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.